Competition between parallel sensorimotor learning systems

When our movements are perturbed, we become aware of our errors, and through our own strategy, or instructions from a coach, engage an explicit learning system to improve our outcome (Morehead et al., 2017; Mazzoni and Krakauer, 2006). This awareness, is not required to adapt; our brain also uses an implicit learning system that partially corrects behavior without our conscious awareness (Morehead et al., 2017; Mazzoni and Krakauer, 2006). How do these two systems interact during sensorimotor adaptation?

Suppose that both systems learn from the same error. In this case, when one system adapts, it will reduce the error that drives learning in the other system; thus, the two parallel systems will compete to ‘consume’ a common error. Alternatively, suppose the two systems learn from separate errors, and each produces an output to minimize its own error. In this case, when one system adapts to its error, it could change behavior in ways that paradoxically increase the other system’s error.

Current models suggest that adaptation is driven by two distinct error sources: a task error (Leow et al., 2020; Körding and Wolpert, 2004; Langsdorf et al., 2021), and a prediction error (Mazzoni and Krakauer, 2006; Tseng et al., 2007; Kawato, 1999). One leading theory suggests that the explicit system acts to decrease errors in task performance, while the implicit system acts to reduce errors in predicting sensory outcomes (Mazzoni and Krakauer, 2006; Taylor and Ivry, 2011; Wong and Shelhamer, 2012). In this model, strategies have no impact on implicit learning. A second theory suggests that task errors can drive learning in both systems (Leow et al., 2020; Kim et al., 2019; McDougle et al., 2015; Miyamoto et al., 2020). In this model, implicit and explicit systems will compete with one another.

Suppose implicit and explicit systems share at least one common error source. What will happen when experimental conditions enhance one’s explicit strategy? In this case, increases in explicit strategy will siphon away the error that the implicit system needs to adapt, thus reducing total implicit learning without directly changing implicit learning properties (e.g. its memory retention or sensitivity to error). This reduction in implicit learning creates the illusion that the implicit system was directly altered by the experimental manipulation, when in truth, it was only responding to changes in strategy.

Competitive interactions like this highlight the need to distinguish between an adaptive system’s learning properties such as its sensitivity to an error, and its learning timecourse, that is the contribution it makes to overall adaptation at any point in time. In a competitive system, an adaptive processes’ learning timecourse depends not only on its own learning properties, but also its competitors’ learning properties. In cases where implicit and explicit systems share an error source, one system’s behavior can be shaped not only by its past experience, but also by changes in the other system. Thus, competition may play an important role in savings (Haith et al., 2015; Coltman et al., 2019; Kojima et al., 2004; Medina et al., 2001; Mawase et al., 2014) and interference paradigms (Sing and Smith, 2010; Lerner et al., 2020; Caithness et al., 2004) where learning properties change over time. Measuring the interdependence between implicit and explicit learning may help to explain the disconnect between studies that have suggested acceleration in motor learning is subserved solely by explicit strategy (Haith et al., 2015; Huberdeau et al., 2019; Morehead et al., 2015; Avraham et al., 2020; Avraham et al., 2021), and studies that have pointed to concomitant changes in implicit learning systems (Leow et al., 2020; Yin and Wei, 2020; Albert et al., 2021).

Here, we begin by mathematically (McDougle et al., 2015; Miyamoto et al., 2020; Smith et al., 2006; Albert and Shadmehr, 2018; Thoroughman and Shadmehr, 2000) considering the extent to which implicit and explicit systems are engaged by task errors and prediction errors. The hypotheses make diverging predictions, which we test in various contexts. Our work suggests that in some contexts (Mazzoni and Krakauer, 2006; Taylor and Ivry, 2011), prediction errors and task errors both make important contributions to implicit learning (Results Part 3). In other contexts, the data suggest that the implicit system is primarily driven by task errors shared with the explicit system (Results Part 1). In this latter case, the competition theory explains why increases (Neville and Cressman, 2018; Benson et al., 2011) or decreases (Fernandez-Ruiz et al., 2011; Saijo and Gomi, 2010) in explicit strategy cause an opposite change in implicit learning. This model explains why in some cases implicit adaptation can saturate as perturbations grow (Neville and Cressman, 2018; Bond and Taylor, 2015; Tsay et al., 2021a), but not others (Tsay et al., 2021a; Salomonczyk et al., 2011). The model also explains why participants that utilize large explicit strategies can exhibit less implicit (Miyamoto et al., 2020) or procedural learning (Fernandez-Ruiz et al., 2011), than those who do not. Finally, the theory provides an alternate way to interpret implicit contributions to two learning hallmarks: savings (Haith et al., 2015) and interference (Lerner et al., 2020) (Results Part 2).

Altogether, our results illustrate that sensorimotor adaptation is shaped by competition between parallel learning systems, both engaged by task errors.

In visuomotor rotation paradigms, participants move a cursor that travels along a rotated path (Figure 1A). This perturbation causes adaptation, resulting in both implicit recalibration (Figure 1A, implicit) and explicit (intentional) re-aiming (Figure 1A, aim) (Mazzoni and Krakauer, 2006; Taylor and Ivry, 2011; Taylor et al., 2014; Shadmehr et al., 1998).

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Current models suggest that the rotation r creates two distinct error sources. One error source is the deviation between cursor and target: a target error (Leow et al., 2020; Körding and Wolpert, 2004; Langsdorf et al., 2021). Notably, this target error (Figure 1A, target error) is altered by both implicit (x_i) and explicit (x_e) adaptation:

In addition, a second error is created due to our expectation that the cursor should move toward where we aimed our movement: a sensory prediction error (SPE) (Mazzoni and Krakauer, 2006; Tseng et al., 2007; Kawato, 1999). SPE is the deviation between the aiming direction (the expected cursor motion) and where we observed the cursor’s actual motion (Figure 1A, sensory prediction error). Critically, because this error is anchored to our aim location, it changes over time in response to implicit adaptation alone:

How does the implicit learning system respond to these two error sources? State-space models describe implicit adaptation as a process of learning and forgetting (McDougle et al., 2015; Miyamoto et al., 2020; Smith et al., 2006; Albert and Shadmehr, 2018; Thoroughman and Shadmehr, 2000):

Forgetting is controlled by a retention factor (a_i) which determines how strongly we retain the adapted state. Learning is controlled by error sensitivity (b_i) which determines the amount we adapt in response to an error (e.g. an SPE or a target error).

Here, we will contrast two possibilities: (1) the implicit system responds primarily to target error, or (2) the implicit system responds primarily to SPE. In a target error learning system, explicit strategy will reduce the target error in Equation 1. This decrease in target error will lead to a competition between implicit and explicit systems, that is increasing explicit strategy reduces target error, which will then decrease implicit learning. Competition in a target error model will occur over the entire learning timecourse and can lead to unintuitive implicit learning phenotypes (Appendix 1.2). While these implicit behaviors can be observed at any point during adaptation, they are easiest to examine during steady-state adaptation (Appendix 1.1).

Consider how Equation 3 behaves in the steady-state condition. Like adapted behavior (Kim et al., 2019; Albert et al., 2021; Vaswani et al., 2015; Kim et al., 2018), Equation 3 approaches an asymptote with extended exposure to a rotation. This steady-state (Figure 1B, implicit) occurs when learning and forgetting counterbalance each other.

Consider a system where target errors alone drive implicit learning. In this system, total (steady-state) implicit learning is determined by Equations 1 and 3:

Equation 4 demonstrates a competition between implicit and explicit systems; the total amount of implicit adaptation (x_i^ss) is driven by the difference between the rotation r and total explicit adaptation (x_e^ss).

Now consider a system where SPEs drive implicit learning. SPEs (Equation 2) are unaltered by strategy. In this case, total implicit learning is determined by Equations 2 and 3:

Equation 5 demonstrates an independence between implicit and explicit systems; the total amount of implicit adaptation depends solely on the rotation’s magnitude, not one’s explicit strategy.

Here, we explore how implicit learning systems respond to explicit strategy, and whether behavior is more consistent with competition or independence. Competition and independence can be studied at any point during the adaptation timecourse (Appendix 1). We will primarily examine steady-state learning, where the competition equation (Equation 4) and independence equation (Equation 5) make simple predictions. The critical insight is that in an independent system (SPE learning), increasing the explicit strategy (Figure 1B, magenta solid and dashed) does not alter implicit adaptation (Figure 1B, independence, compare black and cyan). However, in a competitive system (Equation 4), the same increase in strategy will indirectly decrease implicit learning (Figure 1B, competition, compare black and cyan).

To analyze these possibilities, we begin by examining how changes in explicit strategy alter implicit learning in response to variations in rotation magnitude, experimental instructions, rotation type, and at the individual participant level (Part 1). Next, we describe how competition between implicit and explicit systems could in principle mask changes in implicit learning (Part 2). Finally, we will examine studies which suggest implicit error sources vary across experimental conditions due to the presence and/or absence of multiple visual stimuli in the experimental workspace (Part 3).

Part 1: Measuring how implicit learning responds to changes in explicit strategy

Here, we measure how implicit learning and explicit strategy vary across several factors: (1) rotation size, (2) instructions, (3) gradual versus abrupt rotations, and (4) individual subjects. We will ask whether the variations in implicit and explicit learning are consistent with the competition or independence theories.

Implicit responses to rotation size suggest a competition with explicit strategy

Over extended exposure to a rotation, adaptation appears to saturate (Morehead et al., 2017; Albert et al., 2021; Vaswani et al., 2015; Kim et al., 2018). How does implicit learning contribute to steady-state saturation, and what learning model best describes its behavior?

In Neville and Cressman, 2018, participants adapted to a 20°, 40°, or 60° rotation (Figure 1C). As is common, adaptation reached a steady-state prior to eliminating the target error (Albert et al., 2021; Figure 1C, solid vs. dashed lines). To measure implicit learning, participants were instructed to reach to the target without aiming (Figure 1C, no aiming). The independence model (Equation 5) predicts that the implicit response should scale as the rotation increases. On the contrary, total implicit learning was insensitive to rotation size; it reached only 10° and remained constant despite a threefold increase in rotation magnitude (Figure 1D). To estimate explicit strategy, we subtracted the implicit learning measure from the total adapted response. Opposite to implicit learning, explicit strategy increased proportionally with the rotation’s size (Bond and Taylor, 2015; Tsay et al., 2021a; Figure 1E).

In the competition model, implicit learning is driven by the difference between the rotation and explicit strategy (r – x_e^ss in Equation 4). As a result, when an increase in rotation magnitude is matched by an equal increase in explicit strategy (Figure 1—figure supplement 1A, same), the implicit learning system’s driving force will remain constant (Figure 1—figure supplement 1B, same). This constant driving input leads to a phenotype where implicit learning appears to ‘saturate’ with increases in rotation size (Figure 1—figure supplement 1C, same).

To investigate whether this mechanism is consistent with the implicit response, we examined how explicit strategy and the implicit driving force varied with rotation size. As rotation size increased, explicit strategies increased substantially (Figure 1E). Under the competition model, these rapid changes in explicit strategy produced an implicit driving force that responded little to rotation magnitude; while the rotation increased by 40°, the driving force changed by less than 2.5° (Figure 1F). Thus, the competition Equation (Figure 1G, competition) suggested that implicit learning would not vary with rotation size, as we observed in the measured data (Figure 1G, data).

In other words, the competition model suggests that the implicit system can exhibit an unintuitive saturation when its driving input remains constant. The key prediction is that by altering explicit strategy, this driving input will change, changing the implicit response to rotation size. One possibility is to weaken the explicit system’s response to the rotation (Figure 1—figure supplement 1A, slower) which should increase the steady-state of the implicit system (Figure 1—figure supplement 1C, slower).

To test this idea, we used a stepwise rotation (Yin and Wei, 2020). In Experiment 1, participants (n = 37) adapted to a stepwise perturbation which started at 15° but increased to 60° in 15° increments (Figure 1H). Twice toward the end of each rotation block, we assessed implicit adaptation by instructing participants to aim directly to the target (Figure 1H, gray regions). Supplemental analysis suggested that the implicit system reached its steady-state during each learning period (Appendix 2), although this is not required to test the competition theory (Appendix 1.2). Critically, the stepwise rotation onset decreased explicit responses relative to the abrupt rotations used by Neville and Cressman, 2018; explicit strategies increased with a 94.9% gain (change in strategy divided by change in rotation) across the abrupt groups in Figure 1E, but only a 55.5% gain in the stepwise condition shown in Figure 1J. In the competition model, this reduction in strategy increased the implicit system’s driving input (Figure 1K). The increased driving input produced a “scaling” phenotype in the competition model’s implicit response (Figure 1L, competition) which closely matched the measured implicit data (Figure 1I; 1 L, data; rm-ANOVA, F(3,108)=99.9, p < 0.001, η_p²=0.735).

Thus, the implicit system can exhibit both saturation (Figure 1G) and scaling (Figure 1L), consistent with the competition model. Recent work by Tsay et al., 2021a suggests a third steady-state implicit phenotype: non-monotonicity. In their study, the authors examined a wider range in rotation size, 15° to 90° (Figure 1M). A no-aiming period revealed total implicit adaptation each group (n = 25/group). Curiously, whereas implicit learning increased between the 15° and 30° rotations, it appeared similar in the 60° rotation group, and then decreased in the 90° rotation group (Figure 1N). This non-monotonic behavior was inconsistent with the independence model where implicit learning is proportional to rotation size (Figure 1Q, independence).

To determine whether this non-monotonicity could be captured by the competition theory, we considered again how explicit re-aiming increased with rotation size (Figure 1O). We observed an intriguing pattern. When the rotation increased from 15° to 30°, explicit strategy responded with a very low gain (4.5%, change in strategy divided by change in rotation). An increase in rotation size to 60° was associated with a medium-sized gain (80.1%). The last increase to 90° caused a marked change in the explicit system: a 53.3° increase in explicit strategy (177.7% gain). Thus, explicit strategy increased more than the rotation had. Critically, this condition produces a decrease in the implicit driving input in the competition theory (Figure 1—figure supplement 1, faster). Overall, we estimated that this large variation in explicit learning gain (4.5–80.1% to 177.7%) should yield non-monotonic behavior in the implicit driving input (Figure 1P): an increase between 15° and 30°, no change between 30° and 60°, and a decrease between 60° and 90°. As a result, the competition theory (Figure 1Q, competition) exhibited a non-monotonic envelope, which closely tracked the measured data (Figure 1Q, data).

Unfortunately, there is a potential problem in our analysis: implicit and explicit learning measures were not independent, because explicit strategy was estimated using implicit reach angles (i.e. explicit learning equals total learning minus implicit learning). Did this bias our analysis towards the competition model? To answer this question, Equation 4 can be stated as x_i^ss = p_i(r – x_e^ss) where p_i is the learning gain determined by the implicit system’s retention and error sensitivity (i.e. a_i and b_i). We can replace the explicit strategy (x_e^ss) appearing in this equation noting that x_e^ss = x_T^ss – x_i^ss, where x_T^ss equals total steady-state adaptation. With this, the model relates implicit learning to total learning: x_i^ss = p_i(1 – p_i)^–1(r – x_T^ss), as opposed to explicit learning, and can be used to test the competition model without correlated learning measures (see Appendix 3). We reexamined all three experiments in Figure 1, using total adaptation to predict implicit learning with the competition model (Figure 1—figure supplement 2). This alternate method yielded nearly identical predictions (Figure 1—figure supplement 2, ‘model-2’) as Equation 4 (Figure 1—figure supplement 2, ‘model-1’). Thus, the qualitative and quantitative correspondence between the competition model and the measured data was not due to how we operationalized implicit and explicit learning (see Appendix 3).

Collectively, these studies demonstrate that the implicit system can exhibit at least three distinct behavioral phenomena: saturation, scaling, or non-monotonicity. The competition model matched all three phenotypes, due to the implicit system’s response to explicit strategy. The SPE learning model described by the independence equation, however, could only produce a scaling phenotype (Figure 1I). Could the SPE learning model be altered to produce implicit learning phenotypes other than scaling? One possibility is that a saturation phenotype (Figure 1D) could be built into the SPE model by adding a restriction, that is an upper bound, on total implicit adaptation, as observed in studies where participants experience invariant error perturbations (Morehead et al., 2017; Kim et al., 2018). With that said, the 10° implicit responses observed across the three rotations in Neville and Cressman, 2018, are much lower than the 20°–25° ceiling suggested by recent error-clamp studies (Kim et al., 2018), and the 35–45° implicit responses observed in some standard rotation studies (Salomonczyk et al., 2011; Maresch et al., 2021). More importantly, a learning model with a rotation-insensitive upper bound on implicit learning would be inconsistent with the scaling (Figure 1I) and nonmonotonic (Figure 1N; see Appendix 6.6) phenotypes we observed. We will explore other extensions to this SPE model in several analyses in the Control analyses section below.

Increase in explicit strategy suppresses implicit learning

The competition model predicts that increasing explicit strategy will decrease implicit learning, even when the rotation size is the same. In contrast, the independence theory predicts that implicit learning will be insensitive to differences in explicit strategy (extensions to this model are considered in Control analyses).

To test these ideas, we considered another condition tested by Neville and Cressman, 2018 where participants were exposed to the same 20°, 40°, or 60° rotation, but received coaching instructions. The coaching sharply improved adaptation over the non-instructed group (Figure 2A, compare purple with black). To understand how implicit and explicit learning contributed to these changes, we analyzed the mean implicit and explicit reach angles measured across all three rotation sizes (each individual response is shown in Figure 2—figure supplement 1).

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Unsurprisingly, explicit adaptation was enhanced in the participants that received coaching instructions. Explicit re-aiming increased by approximately 10° (Figure 2B, t(61)=2.29, p = 0.026, d = 0.56). However, while instruction enhanced explicit strategy, it suppressed implicit learning, decreasing total implicit learning by approximately 32% (Figure 2C, data, t(61)=2.62, p = 0.011, d = 0.66). To interpret this implicit response, we fit the competition (Equation 4) and independence equations (Equation 5) to the behavior across all experimental conditions (six groups: 3 rotation magnitudes, 2 instruction conditions), while holding the implicit learning parameters in the model constant (i.e. holding a_i and b_i constant across all conditions).

As in Figure 1, implicit learning in the independence model does not respond to explicit strategy, and is not altered by instruction (Figure 2C, implicit learning, indep.). On the other hand, the competition model accurately suggested that total implicit learning would decrease by approximately 3° (data showed 2.98° decrease, model produced a 2.92° decrease) in response to increases in explicit strategy (Figure 2C, implicit learning, competition, t(61)=2.05, p = 0.045, d = 0.52). Altogether, the competition theory parsimoniously captured how the implicit system responded to explicit instruction (Figure 2C) as well as changes in rotation size (Figure 1G) with the same model parameter set (same a_i and b_i in the competition equation).

Decrease in explicit strategy enhances implicit learning

Next, we examined how implicit learning responds to decreases in explicit strategy. Yin and Wei, 2020 recently demonstrated that explicit strategies can be suppressed using gradual rotations. The competition theory predicts that decreasing explicit strategy will lead to greater implicit adaptation. We tested this prediction in Exp. 1. Participants were exposed to a 60° rotation, either abruptly (n = 36), or in a stepwise manner (n = 37) where perturbation magnitude increased by 15° across four distinct learning blocks (Figure 2D). We measured implicit and explicit learning during each block, as in Figure 1. To compare gradual and abrupt learning, we analyzed reach angles during the 4th learning block, where both groups experienced the 60° rotation size (Figure 2E).

As in Yin and Wei, 2020, participants in the stepwise condition exhibited a 10° reduction in explicit re-aiming (Figure 2F, two-sample t-test, t(71)=4.97, p < 0.001, d = 1.16). Reductions in strategy led to a decrease in total adaptation in the stepwise group by approximately 4°, relative to the abrupt group (Figure 2E, right-most gray region (last 20 trials); two-sample t-test, t(71)=3.33, p = 0.001, d = 0.78), but an increase in implicit learning by approximately 80% (Figure 2G, data, two-sample t-test, t(71)=6.4, p < 0.001, d = 1.5). Thus, the data presented a curious pattern; greater total adaptation in the abrupt condition was paradoxically associated with reduced implicit adaptation. As expected, these surprising patterns did not match the independence model (Figure 2G, indep.), in which implicit learning does not respond to changes in explicit strategy.

To test whether implicit learning patterns matched the competition model we fit Equation 4 to implicit and explicit reach angles measured in Blocks 1–4, across the stepwise and abrupt conditions, while holding the model’s implicit learning parameters (a_i and b_i) constant. The competition model correctly predicted that the decrease in strategy in the gradual condition should produce an increase in implicit learning (Figure 2G, comp., two-sample t-test, t(71)=4.97, p < 0.001, d = 1.16). In addition, the competition model predicted a decrease in total learning, consistent again with the data (the model yielded 53.47° total adaptation in abrupt, and 50.42° in gradual: values not provided in Figure 2). The model’s negative correlation between implicit learning and total adaptation occurred in two steps: (1) greater abrupt strategies increased overall adaptation, but (2) siphoned away target errors, reducing implicit adaptation.

We analyzed another hypothesis: changes in implicit adaptation were caused by variation in error sensitivity (e.g. greater implicit error sensitivity in the stepwise condition), rather than competition. Note, however, that the implicit learning gain, p_i, is given by p_i = b_i(1 – a_i+ b_i)^–1. Because the b_i term appears in both numerator and denominator, total implicit learning varies slowly with changes in b_i (Appendix 4). Accordingly, supplemental analyses (Appendix 4, Figure 2—figure supplement 2) showed that no change in b_i could yield the 80% increase in stepwise implicit learning in Figure 2G, let alone the 46% increase in implicit learning in the no-instruction group in Figure 2C. Thus, while variation in implicit error sensitivity might contribute to changes in steady-learning learning, its role is minor compared to error competition.

In summary, we observed that explicit strategies could be suppressed by increasing the rotation gradually. Reductions in explicit strategy were associated with increased implicit adaptation (Figure 2G) as predicted by the competition theory. Furthermore, the same competition theory parameter set (i.e. same a_i and b_i, see Materials and methods) accurately matched the extent to which implicit learning responded to decreases in explicit strategy (Figure 2G) as well as increases in rotation size (Figure 1L). It is interesting to note that these implicit patterns are broadly consistent with the observation that gradual rotations improve procedural learning (Saijo and Gomi, 2010; Kagerer et al., 1997), although these earlier studies did not properly tease apart implicit and explicit adaptation (see the Saijo and Gomi analysis described in Appendix 5).

Implicit adaptation responds to between-subject differences in explicit adaptation

Use of explicit strategy is highly variable between individuals (Miyamoto et al., 2020; Fernandez-Ruiz et al., 2011; Bromberg et al., 2019). According to the competition theory (Equation 4), implicit and explicit learning will negatively co-vary according to a line whose slope and bias are determined by the properties of the implicit learning system (a_i and b_i). In Experiment 2, we tested this prediction. In one group, we limited preparation time to inhibit time-consuming explicit strategies (Fernandez-Ruiz et al., 2011; McDougle and Taylor, 2019; Figure 3D–F, Limit PT). In the other group, we imposed no preparation time constraints (Figure 3A–C, No PT Limit). We measured a_i and b_i in the Limit PT group and used these values to predict the implicit-explicit relationship across No PT Limit participants.

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As expected, Limit PT participants dramatically reduced their reach latencies throughout the adaptation period (Figure 3F), whereas the No PT Limit participants exhibited a sharp increase in movement preparation time after perturbation onset (Figure 3C), indicating explicit re-aiming (Langsdorf et al., 2021; Haith et al., 2015; Albert et al., 2021; Fernandez-Ruiz et al., 2011; McDougle and Taylor, 2019). Consistent with explicit strategy suppression, learning proceeded more slowly and was less complete under the preparation time limit (compare Figure 3B&E; two-sample t-test on last 10 adaptation epochs: t(20)=3.27, p = 0.004, d = 1.42).

Next, we measured the retention factor a_i during a terminal no feedback period (Figure 3E, dark gray, no feedback) and error sensitivity b_i during the steady-state adaptation period. Steady-state implicit error sensitivity (note errors are small at steady-state creating high b_i) was consistent with recent literature (Figure 3—figure supplement 1A-C). Together, this retention factor (a_i = 0.943) and error sensitivity (b_i = 0.35), produced a specific form of Equation 4, x_i = 0.86 (30 – x_e). We used this result to predict how implicit and explicit learning should vary across participants in the No PT Limit group (Figure 3G, blue line).

To measure implicit and explicit learning in the No PT Limit group, we instructed participants to move their hand through the target without any re-aiming at the end of the rotation period (Figure 3B, no aiming). The precipitous change in reaching angle revealed implicit and explicit components of adaptation (post-instruction reveals implicit; voluntary decrease in reach angle reveals explicit). We observed a striking correspondence between the No PT Limit implicit-explicit relationship (Figure 3G, black dot for each participant; ρ = −0.95) and that predicted by the competition equation (Figure 3G, blue). The slope and bias predicted by Equation 4 (–0.86 and 25.74°, respectively) differed from the measured linear regression by less than 5% (Figure 3G, black line, R² = 0.91; slope is –0.9 with 95% CI [-1.16,–0.65] and intercept is 25.46° with 95% CI [22.54°, 28.38°]).

In addition, we also asked participants to verbally report their aiming angles prior to concluding the experiment. These responses were variable, with 25% reported in the incorrect direction. Because strategies are susceptible to sign-flipped errors (McDougle and Taylor, 2019), we assumed these misreported strategies represented the correct magnitude, but the incorrect sign, and thus took their absolute value. While reported explicit strategies were on average greater than our probe-based measure, and report-based implicit learning was on average smaller than our probe-based measure (Figure 3—figure supplement 2A&B; paired t-test, t(8)=2.59, p = 0.032, d = 0.7), the two report-based measures exhibited a strong correlation which aligned with the competition theory’s prediction (Figure 3—figure supplement 2C; R² = 0.95; slope is –0.93 with 95% CI [-1.11,–0.75] and intercept is 25.51° with 95% CI [22.69°, 28.34°]).

In summary, individual participants exhibited an inverse relationship between implicit and explicit learning; participants who used large explicit strategies inadvertently suppressed their implicit learning, a pattern consistent with error-based competition.

Limiting reaction time strongly suppresses explicit strategy and increases implicit learning

Our analysis in Experiment 2 had two important limitations. First, the competition theory used implicit learning parameters measured under limited preparation time conditions (Leow et al., 2020; Fernandez-Ruiz et al., 2011; Leow et al., 2017): how effectively does this condition suppress explicit learning? Second, our individual-level implicit and explicit learning measures were intrinsically correlated because they both depended on probe-based reach angles (i.e. implicit is no aiming probe, and explicit is total learning minus no aiming probe).

To address these limitations, we conducted a laptop-based control experiment (Experiment 3). Participants (n = 35) adapted to a 30° rotation (Figure 3I), but this time, we measured implicit adaptation using the no-aiming instruction over an extended 20-cycle period (Figure 3I, no aiming). We calculated early (the first no-aiming cycle; Figure 3Q) and late (last 15 no-aiming cycles; Figure 3P) implicit learning measures. Explicit strategy was estimated by subtracting the first no-aiming cycle from total adaptation. Thus, our explicit strategy measure was not calculated using late implicit learning trials; these two measures were no longer spuriously correlated. Regardless, we still observed a strong relationship between explicit strategy and late implicit learning; greater strategy use was associated with reduced late implicit adaptation (Figure 3P, ρ = −0.78, p< 0.001).

Next, we repeated this experiment, but under limited preparation time conditions in a separate participant cohort (Figure 3L, Experiment 3, Limit PT, n = 21). As for the Limit PT group in Exp. 2, we imposed a strict bound on reaction time to suppress movement preparation time (compare Figure 3J&M). Once the rotation period ended, participants were told to stop re-aiming. The decrease in reach angle revealed each participant’s explicit strategy (Figure 3N). When no reaction time limit was imposed (No PT Limit), re-aiming totaled 11.86° (Figure 3N, black). In addition, we did not detect a statistically significant difference in re-aiming across Exps. 2 and 3 (t(42)=0.50, p = 0.621). As in earlier reports (Leow et al., 2020; Albert et al., 2021; Fernandez-Ruiz et al., 2011; Leow et al., 2017), limiting reaction time dramatically suppressed explicit strategy, yielding only 2.09° of re-aiming (Figure 3N, red). Thus, these data showed that our limited reaction time technique was highly effective at suppressing explicit strategy.

Consistent with the competition theory, suppressing explicit strategy increased implicit learning by approximately 40% (Figure 3O, No PT Limit vs. Limit PT, two-sample t-test, t(54)=3.56, p < 0.001, d = 0.98). We again used the Limit PT group’s behavior to estimate implicit learning parameters (a_i and b_i) as we did in Exp. 2 (Figure 3G). Using these parameters, the competition theory (Equation 4) predicted that implicit and explicit adaptation should be related by the line: x_i = 0.658(30 – x_e). As in Exp. 2, we observed a striking correspondence between this model (Figure 3Q, bottom, model) and the actual implicit-explicit relationship measured in participants in the No PT Limit group (Figure 3Q, bottom, points). The slope and bias predicted by Equation 4 (–0.665 and 19.95°, respectively) differed from the measured linear regression by less than 5% (Figure 3Q, bottom brown line, R² = 0.78; slope is –0.63 with 95% CI [-0.74,–0.51] and intercept is 19.7° with 95% CI [18.2°, 21.3°]).

In summary, Exp. 3 provided additional evidence that implicit and explicit systems compete with one another at the individual-participant level. Participants who relied more on strategy exhibited reductions in implicit learning, as predicted by the competition theory. Moreover, by limiting preparation time on each trial, explicit strategies were strongly suppressed, allowing us to estimate the time course of the implicit system’s adaptation.

Control analyses

Implicit learning exhibits generalization: a decay in adaptation measured when subjects move to positions across the workspace (Hwang and Shadmehr, 2005; Krakauer et al., 2000; Fernandes et al., 2012). Implicit generalization is centered where participants aim (Day et al., 2016; McDougle et al., 2017). For this reason, implicit learning measured when aiming towards the target, can underapproximate total implicit learning. Subjects that aim more (larger strategy) can exhibit a larger reduction in measured implicit learning. Might this contribute to the negative implicit-explicit correlations in Exps. 1–3?

To test this idea, we compared our data to generalization curves measured in past studies (Krakauer et al., 2000; Day et al., 2016; McDougle et al., 2017; Figure 4). Absolute implicit responses are shown in Figure 4B, and normalized measures are shown in Figure 4A (see Appendix 6.1). Implicit learning in Exps. 2&3 declined 300% more rapidly than predicted by past generalization studies (Figure 4A&B). Moreover, this comparison in Figure 4A–C is not appropriate under the generalization hypothesis. In Exps. 2&3, explicit strategies are estimated as total learning minus implicit learning. If implicit learning measured at the target underapproximates total implicit learning measured at the aim location, then the explicit strategies we calculate will overapproximate the actual strategy used by each participant. We need to correct these strategies prior to comparing to past generalization curves (Appendix 6.2). The corrected generalization curves (Figure 4C, E2 and E3 lines) that produce the patterns in Figure 4A&B exhibited an unphysiological narrowing: their standard deviation (width) was 85% smaller than that reported in recent studies (Krakauer et al., 2000; Day et al., 2016; McDougle et al., 2017) (σ is about 5.5° versus 37.76° in McDougle et al., see Appendix 6.1). These same issues occurred in the group-level phenomena that we analyzed in Figures 1 and 2: no plausible generalization curve could explain the implicit response to instruction, rotation onset (abrupt/gradual), and rotation size (Appendices 6.4 and 6.5). As an example, the variations in implicit learning across abrupt and stepwise groups in Exp. 1 would require a generalization curve that is 90% narrower than recent estimates (McDougle et al., 2017) (see Appendix 6.4 and Figure 4—figure supplement 1; σ = 3.87° versus 37.76° in McDougle et al., 2017).

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We extended the independence model with implicit generalization and compared its behavior to the competition theory. The competition model is given by x_i^ss = p_i(r – x_e^ss), where p_i is an implicit learning gain. The SPE generalization model is x_i^measured = p_irg(x_e^ss), where g(x_e^ss) encodes generalization (derivation in Appendix 6.2). We specified g(x_e^ss) with McDougle et al., 2017. We considered models where g(x_e^ss) was linear (Figure 4D–F, SPE gen. linear) and g(x_e^ss) was normal (SPE gen. normal). Then we fit each model’s p_i to match implicit learning during the 60° stepwise rotation in Exp. 1. We used this gain to predict the implicit-explicit relationship across the three earlier learning periods (B1-B3 in Figure 4D). The generalization models yielded poor matches to the held-out data (model RMSE in Figure 4E, rm-ANOVA, F(2,72)=13.7, p < 0.001, η_p² = 0.276). Further, a model comparison showed that competition best described individual subject data, minimizing AIC in 84% of stepwise participants (Figure 4G, Appendix 6.3). Poor SPE generalization model performance was not due to misestimating generalization curve properties; we conducted a sensitivity analysis in which we varied the generalization curve’s width. The competition model was superior across the entire range (Figure 4H, Appendix 6.3).

To understand why the competition theory alone generalized across rotation sizes, we fit linear regressions to the data in each rotation period. The regression slopes and 95% CIs are shown in Figure 4F (data). Remarkably, the measured implicit-explicit slope appeared to be constant across all rotation sizes. This invariance was directly consistent with the competition theory (Figure 4F, competition) which possesses an implicit gain p_i that remains constant across rotations (like the data). But in generalization models (Figure 4F, generalization), the gain relating implicit and explicit learning is not constant; it changes as the rotation gets larger (see Appendix 6.3). In sum, data in Exps. 1–3 were poorly explained by an SPE model extended with generalization.

We considered one last control analysis. The competition equation predicts that implicit-explicit correlations are caused by the implicit system’s response to variations in strategy. An SPE learning model could create correlations the opposite way: individuals who possess less implicit learning compensate by increasing their explicit strategy. This scenario can be described by x_e^ss = p_e(r – x_i^ss) where p_e is the explicit response gain. This model has three properties (Appendix 7.2). First, implicit and explicit learning will show a negative relationship (Figure 5A). Second, increases in implicit learning will tend to increase total adaptation (Figure 5C). Finally, increasing implicit learning leaves smaller errors to drive explicit strategy, resulting in a negative correlation between strategy and total adaptation (Figure 5B). While the competition model also predicts negative implicit-explicit correlations (Figure 5D), the other pairwise correlations differ (Appendix 7.1). Increases in explicit strategy lead to greater total learning (Figure 5E), but reduce the error which drives implicit learning, leading to a negative correlation between implicit learning and total adaptation (Figure 5F).

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We analyzed these predictions in the No PT Limit group in Exp. 3 (Appendix 7.4). Our observations matched the competition theory; greater explicit strategy was associated with greater total adaptation (Figure 5G, ρ = 0.84, p < 0.001), whereas greater implicit learning was associated with lower total adaptation (Figure 5H, ρ = −0.70, p < 0.001). We repeated these analyses in other datasets (Appendix 7.4) that measured implicit learning with no-aiming probe trials: (1) 60° rotation groups (combined across gradual and abrupt groups) in Experiment 1, (2) 60° groups reported by Maresch et al., 2021 (combined across the CR, IR-E, and IR-EI groups), and (3) 60° rotation group in Tsay et al., 2021a These data matched the competition theory: negative implicit-explicit correlations (Figure 5—figure supplement 1G-I), positive explicit-total correlations (Figure 5—figure supplement 1D-F), and negative implicit-total correlations (Figure 5—figure supplement 1A-C).

In summary, while an SPE learning model could exhibit negative correlations between implicit and explicit adaptation, it does not predict a negative correlation between steady-state implicit learning and total adaptation (nor a positive relationship between steady-state explicit strategy and total adaptation), as we observed in the data. The data were consistent with the competition theory, where the implicit system responds to variations in explicit strategy. However, there is a critical caveat. The predictions outlined above assumed that implicit learning properties (contained within p_i) are the same across every participant. This is unlikely to be true, and variation in p_i across subjects (e.g. changes in error sensitivity) will undermine some correlations in Figure 5, particularly the relationship between implicit learning and total adaptation. This phenomenon and past studies where it appears to occur are treated in Appendix 8.

Part 2: Competition with explicit learning can mask changes in the implicit learning system

Here, we show that in the competition model, implicit learning may undergo savings, without changing its learning timecourse. Next, we limit preparation time to detect increases and decreases in implicit learning.

Two ways to interpret the implicit response in a savings paradigm

When participants are exposed to the same perturbation twice, they adapt more quickly the second time. This phenomenon is known as savings and is a hallmark of sensorimotor adaptation (Smith et al., 2006; Herzfeld et al., 2014; Zarahn et al., 2008). Multiple studies have attributed this process solely to changes in explicit strategy (Haith et al., 2015; Huberdeau et al., 2019; Morehead et al., 2015; Avraham et al., 2021; Huberdeau et al., 2015).

For example, in an earlier work (Haith et al., 2015), we trained participants (n = 14) to reach to one of two targets, coincident with an audio tone (Figure 6A). By shifting the displayed target approximately 300ms prior to tone onset on a minority of trials (20%), we forced participants to execute movements with limited preparation time (Low preparation time; Figure 6A, middle). On all other trials (80%) the target did not switch resulting in high preparation time movements (Figure 6A, left). We measured adaptation to a 30° rotation during high preparation time (Figure 6B, left) and low preparation time trials (Figure 6B, middle) across two separate exposures (Day 1 and Day 2).

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To detect savings, we calculated the learning rate on low and high preparation time trials. Savings appeared to require high preparation time; learning rate increased during the second exposure on high preparation time trials, but not low preparation time trials (Figure 6B, right; two-way rm-ANOVA, preparation time by exposure number interaction, F(1,13)=5.29, p = 0.039; significant interaction followed by one-way rm-ANOVA across Days 1 and 2: high prep. time with F(1,13)=6.53, p = 0.024, η_p²=0.335; low preparation time with F(1,13)=1.11, p = 0.312, η_p²=0.079). To corroborate this rate analysis, we also measured savings via early changes in reach angle (first 5 rotation cycles) across Days 1 and 2 (Figure 6C, left and middle). Only high preparation time trials exhibited a statistically significant increase in reach angle, consistent with savings (Figure 6C, right; two-way rm-ANOVA, prep. time by exposure interaction, F(1,13)=13.79, p = 0.003; significant interaction followed by one-way rm-ANOVA across days: high prep. time with F(1,13)=11.84, p = 0.004, η_p²=0.477; low prep. time with F(1,13)=0.029, p = 0.867, η_p²=0.002).

Because explicit strategies can be suppressed by limiting movement preparation time under some conditions (Huberdeau et al., 2019; Fernandez-Ruiz et al., 2011; McDougle and Taylor, 2019), in our initial study we interpreted these data to mean that savings relied solely on time-consuming explicit strategies. Multiple studies have reached similar conclusions (Haith et al., 2015; Huberdeau et al., 2019; Morehead et al., 2015; Avraham et al., 2021; Huberdeau et al., 2015), suggesting that the implicit learning system is not improved by multiple exposures to a rotation.

However, the competition theory provides an alternate possibility: changes in the implicit learning system may occur but are hidden because of competition with explicit learning. To show this unintuitive phenomenon, we fit the competition model to individual participant behavior under the assumption that low preparation time trials relied solely on implicit adaptation, but high preparation time trials relied on both implicit and explicit adaptation. The model generated implicit (Figure 6D, blue) and explicit (Figure 6D, magenta) states that tracked the behavior well on high preparation time trials (Figure 6D, solid black line) and also low preparation time trials (Figure 6D, dashed black line).

Next, we considered the implicit and explicit error sensitivities estimated by the model, which are commonly linked to changes in learning rate (Coltman et al., 2019; Mawase et al., 2014; Lerner et al., 2020; Albert et al., 2021; Herzfeld et al., 2014). The model unmasked a surprising possibility: even though savings was observed only on high preparation time trials, but not low preparation time trials (Figure 6B&C), the model suggested that both the implicit and explicit systems exhibited a statistically significant increase in error sensitivity (Figure 6D, right; two-way rm-ANOVA, within-subject effect of exposure number, F(1,13)=10.14, p = 0.007, η_p²=0.438; within-subject effect of learning process, F(1,13)=0.051, p = 0.824, η_p²=0.004; exposure by learning process interaction, F(1,13)=1.24, p = 0.285).

In contrast, a model where the implicit system adapted to SPEs as opposed to target errors (the independence model) suggested that only the explicit system exhibited a statistically significant increase in error sensitivity (Figure 6E; two-way rm-ANOVA, learning process (i.e. implicit vs explicit) by exposure interaction, F(1,13)=7.016, p = 0.02; significant interaction followed by one-way rm-ANOVA across exposures: explicit system, F(1,13)=9.518, p = 0.009, η_p²=0.423; implicit system, F(1,13)=2.328, p = 0.151, η_p²=0.152).

In summary, when we reanalyzed our earlier data, the competition and independence theories suggested that our data could be explained by two contrasting hypothetical outcomes. If we assumed that implicit and explicit systems were independent, then only explicit learning contributed to savings, as we concluded in our original report. However, if we assumed that the implicit and explicit systems learned from the same error (competition model), then both implicit and explicit systems contributed to savings. Which interpretation is more parsimonious with measured behavior?

Competition with explicit strategy can alter measurement of implicit learning

The idea that implicit error sensitivity can increase without any change in implicit learning rate (Figure 6) is not intuitive. What the competition model suggests is that when the explicit system increases its learning rate as in Figure 6D, it leaves a smaller target error to drive implicit learning. However, despite this decrease in target error, low preparation time learning was similar on Days 1 and 2 (Figure 6B). Because we assumed that low preparation time learning relied on the implicit system, the competition theory required that the implicit system must have experienced an increase in error sensitivity to counterbalance the reduction in target error magnitude. In other words, though increase in implicit error sensitivity did not increase total implicit learning, it still contributed to savings. That is, had implicit error sensitivity remained the same, low preparation time learning would decrease on Day 2, and less overall savings would occur.

To understand how our ability to detect changes in implicit adaptation can be altered by explicit strategy we constructed a competition map (Figure 7A). Imagine that we want to compare behavior across two timepoints or conditions. Figure 7A shows how changes in implicit error sensitivity (x-axis) and explicit error sensitivity (y-axis) both contribute to measured implicit aftereffects (denoted by map colors), based on the competition equation (note that the origin denotes a 0% change in error sensitivity relative to Day 1 adaptation in Haith et al., 2015). The left region of the map (cooler colors) denotes combinations of implicit and explicit changes that decrease implicit adaptation. The right region of the map (hotter colors) denotes combinations that increase implicit adaptation. The middle black region represents combinations that manifest as a perceived invariance in implicit adaptation ( < 5% absolute change in implicit adaptation).

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This map defines several distinct areas (Figure 7B). Region A denotes a ‘matching’ decrease between implicit adaptation and error sensitivity; total implicit learning will decline across two separate learning periods due to a reduction in implicit error sensitivity. Region D is similar. Here, total implicit learning will increase across two separate learning periods due to an increase in implicit error sensitivity.

The other regions show less intuitive cases. In Region B, there is a ‘mismatching’ change in total implicit learning and implicit error sensitivity; here total implicit learning decreases even though implicit error sensitivity has increased or stayed the same. Likewise, in Region E, total implicit learning will increase across two separate learning periods, though implicit error sensitivity has decreased or stayed the same.

Indeed, we have already described these cases in Figure 2. For example, by enhancing the explicit system via coaching (Figure 2A–C), implicit learning decreased. This scenario is equivalent to moving up the y-axis of the map (Figure 7C, top). The same implicit system will decrease its output (Figure 7C, bottom) when normal levels of explicit strategy are increased (Figure 7C, middle). On the other hand, suppressing explicit strategy by gradually increasing the rotation (Figure 2D–G), or limiting reaction time (Figure 3N&O), increased implicit learning without changing any implicit learning properties. This scenario is equivalent to moving down the y-axis of the competition map (Figure 7D, top). The same implicit system will increase its output (Figure 7D, bottom) when normal levels of explicit strategy are then suppressed (Figure 7D, middle).

Now, let us consider the savings experiment in Figure 6. The competition theory predicted (Figure 6D) that explicit error sensitivity increased by approximately 70.6% during the second exposure, whereas the implicit system’s error sensitivity increased by approximately 41.5% (Figure 7E, middle). These changes in implicit and explicit adaptation describe a single point in the competition map, denoted by the gray circle in Figure 7E (top). This experiment occupies Region C, which indicates that despite the 41.5% increase in implicit error sensitivity, the total implicit learning will increase by less than 5% (Figure 7E, bottom). In other words, the competition model suggests the possibility that implicit learning improved between Exposures 1 and 2, but this change was hidden by a dramatic increase in explicit strategy (which suppressed implicit learning during Exposure 2).

To test this prediction, we can suppress explicit adaptation, thus eliminating competition (Figure 7F, middle). Such an intervention would move our experiment from Region C to Region D (Figure 7F, top) where we will observe greater change in the implicit process (Figure 7D, bottom). We examined this possibility in a new experiment.

Savings in implicit learning is unmasked by suppression of explicit strategy

In Exp. 4 (Figure 8), participants experienced two 30° rotations, separated by washout trials with veridical feedback (mean reach angle over last three washout cycles was 0.55 ± 0.47°, one-sample t-test against zero, t(9)=1.16, p = 0.28; not shown in Figure 8). To suppress explicit strategy, we restricted reaction time on every trial, which in Exp. 3, greatly reduced explicit learning (Figure 3N; re-aiming decreases from 12° to about 2°). Under these reaction time constraints, participants exhibited reach latencies around 200ms (Figure 8B, top).

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While occasionally limiting preparation time prevented savings in Haith et al., 2015 (Figure 8A, low preparation time on 20% of trials), inhibiting strategy use on every trial in Experiment 4 yielded the opposite outcome (Figure 8B). Low preparation time learning rates increased by more than 80% in Experiment 4 (Figure 8C top; mixed-ANOVA exposure number by experiment type interaction, F(1,22)=5.993, p = 0.023; significant interaction followed by one-way rm-ANOVA across exposures: Haith et al. with F(1,13)=1.109, p = 0.312, η_p²=0.079; Experiment 4 with F(1,9)=5.442, p = 0.045, η_p²=0.377). Statistically significant increases in reach angle were detected immediately following rotation onset in Experiment 4 (Figure 8B, bottom), but not our earlier data (Figure 8C, bottom; mixed-ANOVA exposure number by experiment interaction, F(1,22)=4.411, p = 0.047; significant interaction followed by one-way rm-ANOVA across exposures: Haith et al. with F(1,13)=0.029, p = 0.867, η_p²=0.002; Experiment 4 with F(1,9)=11.275, p = 0.008, η_p²=0.556).

In sum, when explicit learning was inhibited on every trial, low preparation time behavior showed savings (Figure 8B). But when explicit learning was inhibited less frequently, low preparation time behavior did not exhibit a statistically significant increase in learning rate (Figure 8A). The competition theory provided a possible explanation; that an implicit system expressible at low preparation time exhibits savings, but these changes in implicit error sensitivity can be masked by competition with explicit strategy.

However, the savings we measured at limited preparation time may not be solely due to changes in implicit learning, but also cached explicit strategies (Huberdeau et al., 2019; McDougle and Taylor, 2019). Indeed, when we limited preparation time in Exp. 3, participants still exhibited a small decrease (2.09°) in reach angle when we instructed them to stop aiming (Figure 3L, no aiming; Figure 3N and E, red). These small residual strategies could have contributed to the 8° reach angle measured early during the second rotation in Exp. 4 (Figure 8C, implicit difference, no comp.).

What that said, the ‘aiming angle’ we measured in the Limit PT group in Exp. 3, may overestimate the extent to which participants can use explicit strategy in our limited preparation time paradigm. That is, the decrease in reach angle we observed when participants were told to stop aiming (Figure 3L, no aiming) may be due to time-based decay in implicit learning (Neville and Cressman, 2018; Maresch et al., 2021) over the 30 s instruction period, as opposed to a voluntary reduction in strategy.

To test this alternate interpretation, we collected another limited preparation group (n = 12, Figure 8—figure supplement 1A, decay-only, black). But this time, participants were instructed that the experiment’s disturbance was still on, and that they should continue to move the ‘imagined’ cursor through the target during the terminal no feedback period. Despite this instruction, reach angles decreased by approximately 2.1° (Figure 8—figure supplement 1B, black). Indeed, we detected no statistically significant difference between the change in reach angle in this decay-only group, and the Limit PT group in Experiment 3 (Figure 8—figure supplement 1B; two-sample t-test, t(31)=0.016, p = 0.987).

This control experiment suggested that ‘explicit strategies’ we measured in the Limit PT condition were more likely caused by time-dependent decay in implicit learning. Indeed, our Limit PT protocol may eliminate explicit strategy. This additional analysis lends further credence to the hypothesis that savings in Experiment 4 was primarily due to changes in the implicit system rather than cached explicit strategies.

Impairments in implicit learning contribute to anterograde interference

Exp. 4 suggested that the implicit system can exhibit savings. We next wondered whether these changes are bidirectional: can the implicit learning rate decrease? When subjects learn two opposing perturbations in sequence, their adaptation slows due to another hallmark of adaptation, anterograde interference.

In Experiment 5, we exposed two groups of participants to opposing visuomotor rotations of 30° and –30° in sequence (Experiment 5). In one group, the perturbations were separated by a 5-min break (Figure 9A). In a second group, the break was 24 hr in duration (Figure 9B). We inhibited explicit strategies by strictly limiting reaction time. Under these constraints, participants executed movements at latencies near 200ms (Figure 9A&B, middle, blue). These reaction times were approximately 50% lower than those observed when no reaction time constraints were imposed on participants, as in our earlier work (Lerner et al., 2020; Figure 9A&B, middle, green).

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To assess changes in low preparation time learning, we measured the adaptation rate during each rotation period. In addition, we re-analyzed the adaptation rates obtained in our earlier work (Lerner et al., 2020) where participants were tested in a similar paradigm but without any reaction time constraints. While both low preparation time and high preparation time trials exhibited decreases in learning rate which improved with the passage of time (Figure 9C; two-way ANOVA, main effect of time delay, F(1,50)=5.643, p = 0.021, η_p²=0.101), these impairments were greatly exacerbated by limiting preparation time (Figure 9C; two-way ANOVA, main effect of preparation time, F(1,50)=11.747, p = 0.001, η_p²=0.19). This result was unrelated to initial differences in error across rotation exposures; we obtained analogous results (see Materials and methods) when learning rate was calculated after the ‘zero-crossing’ in reach angle (two-way ANOVA, main effect of time delay, F(1,50)=4.23, p = 0.045, η_p²=0.067; main effect of prep. time, F(1,50)=8.303, p = 0.006, η_p²=0.132).

Thus, inhibiting explicit strategy via preparation time constraints revealed a strong and sustained anterograde deficit in implicit learning. Under normal reaction time conditions, adaptation rates were less impaired, suggesting that explicit strategies may have partially compensated and masked lingering deficits in the implicit system’s sensitivity to error.

Part 3: Limitations of the competition theory

The competition theory assumes that learning in the implicit system is driven by only one error. Here we show that this single error hypothesis is unlikely to be true in every condition. To demonstrate the theory’s limitations, we examine two earlier studies and speculate how the theory might be extended to account for these more sophisticated behaviors.

The implicit system may adapt to multiple target errors at the same time

In Mazzoni and Krakauer, 2006, we tested two sets of participants. In a no-strategy group, participants adapted to a standard 45° rotation (Figure 10A, blue, no-strategy, adaptation) followed by washout (Figure 10A, blue, no-strategy, washout). In a second group, participants made two initial movements with the rotation (Figure 10A, red, strategy, 2 movements no instruction). Then we coached subjects to aim toward a neighboring target (45° away) which entirely compensated for the rotation. Participants adopted the aiming strategy, bringing the primary target error to zero (Figure 10A, red, strategy, instruction). Curiously, even though the primary target error had now been eliminated, reaching movements gradually drifted beyond the primary target, overcompensating for the rotation. These involuntary changes implicated an implicit process.

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When we compared the rate of learning with and without strategy in Mazzoni and Krakauer, 2006, we found that it was not different during the initial exposure to the perturbation (Figure 10B, gray, mean adaptation over rotation trials 1–24, Wilcoxon rank sum, p = 0.223). This statistical test led us to conclude in Mazzoni and Krakauer, that implicit adaptation was driven by a sensory prediction error that did not depend on the primary target and was not altered by explicit strategy.

However, there remained an unsolved puzzle. While the initial rates of adaptation were the same irrespective of strategy, adaptation diverged later in learning (Figure 10B, compare strategy and no-strategy curves after initial gray region; two-sample t-test, p < 0.005), with the no-strategy group exhibiting a larger aftereffect (see aftereffect in Figure 10C; two-sample t-test, p < 0.005). Might these late differences have been caused by participants in the strategy group abandoning their explicit strategy as it led to larger and larger errors? This possibility seemed unlikely. When we asked participants to stop using their aiming strategy and to move instead toward the primary target (Figure 10A, do not aim rotation on) their movement angle changed by 47.8° (difference between three movements before and three movements after instruction), indicating that they had continued to maintain the instructed explicit re-aiming strategy near 45°.

We wondered if interactions between implicit and explicit learning could help solve this puzzle. First, we considered the competition model that best described the experiments in Figures 1—7. In this model, the implicit system is driven exclusively by error with respect to the primary target (Equation 1) (Figure 10D, top, e₁). While this model predicted learning in the standard no-strategy condition, it failed to account for the drift observed when participants were given an explicit strategy (Figure 10D, no learning in strategy group). This was not surprising. If implicit learning is driven by the primary target’s error, it will not adapt in the strategy group because participants explicitly reduce target error to zero at the start of adaptation (note that 45° in Figure 10D means a 0° primary target error).

We next considered the possibility that implicit learning was driven exclusively by an error with respect to the aimed target (target 2, Figure 10E, top, e₂), as we concluded in our original study (Mazzoni and Krakauer, 2006). While this model correctly predicted non-zero implicit learning in the no-strategy and strategy groups, it could not account for any differences in learning that emerged later during the adaptation period (Figure 10E, bottom).

Finally, we noted that participants in the strategy group were given two contrasting goals. One goal was to aim for the neighboring target, whereas the other goal was to move the cursor through the primary target (both targets were always visible). Therefore, we wondered if participants in the strategy group learned from two distinct target errors: cursor with respect to target 1, and cursor with respect to target 2 (Figure 10F, top). In contrast, participants in the no-strategy group attended solely to the primary target, and thus learned only from the error between the cursor and target 1. Thus, we imagined that implicit learning in the strategy group was driven by two target errors: e₁ was cursor with respect to target 1, and e₂ was cursor with respect to target 2:

(6) $\begin{array}{c}{x}_{i,1}^{\left(n+1\right)}=a_i{x}_{i,1}^{\left(n\right)}+b_i{e}_1^{\left(n\right)}\\ x_{i,2}^{\left(n+1\right)}=a_i{x}_{i,2}^{\left(n\right)}+b_i{e}_2^{\left(n\right)}\end{array}$

These two modules then combined to determine the total amount of implicit learning (i.e. x_i = x_i,1+ x_i,2).

Interestingly, when we applied the dual target error model (Equation 6) to the strategy group, and the single target error model (Equations (1) and (3)) to the no-strategy group, the same implicit learning parameters (a_i and b_i) closely tracked the observed group behaviors (black model in Figure 10B). These models correctly predicted that initial learning would be similar across the strategy and no-strategy conditions but would diverge later during adaptation (Figure 10F). How was this possible?

In Figure 10G, we show how the primary target error and aiming target error evolved over time in the instructed strategy group. Initially, strategy reduces primary target error to zero (Figure 10G, primary target error). Thus, early in learning, the implicit system is driven predominantly by aiming target error. For this reason, initial learning will appear similar to the no-strategy group which also adapts to only one error. However, as the error with respect to the aimed target decreases, error with respect to the primary target increases but in the opposite direction (Figure 10G; see schematic in Figure 10F). Therefore, the primary target error opposes adaptation to the aiming target error. This counteracting force causes implicit adaptation to saturate prematurely. Hence, participants in the no-strategy group, who do not experience this error conflict, adapt more.

It is important, however, to note a limitation in these analyses. Our earlier study did not employ the standard conditions used to measure implicit aftereffects: that is instructing participants to aim directly at the target, and also removing any visual feedback. Thus, the proposed model relies on the assumption that differences in washout were primarily related to the implicit system. These assumptions need to be tested more completely in future experiments.

In summary, the conditions tested by Mazzoni and Krakauer show that the simplistic idea that adaptation is driven by only one target error, or only one SPE, cannot be true in general (Tsay et al., 2021b). We propose a new hypothesis that when people move a cursor to one visual target, while aiming at another visual target, cursor error with respect to each target contributes to implicit learning. When one target error conflicts with the other target error, the implicit learning system may exhibit an attenuation in total adaptation.

This experiment alone does not reveal the nature of aiming target error. That is, in the strategy group, the error between the aim direction and the cursor is both an SPE, but also a target error (because participants are aiming at a neighboring target). We explore this distinction in the next section.

The persistence of sensory prediction error, in the absence of target error

Our analysis in Figure 10A–G suggested that when participants see two targets, one to aim toward with their hand and one to move the cursor to, the landmarks can act as two different target errors. To what extent do these errors depend on the target’s physical presence in the workspace? Taylor and Ivry, 2011 tested this idea, repeating the instruction paradigm used by Mazzoni and Krakauer, though with nearly four times the number of adaptation trials (Figure 10I, instruction with target, black). Interestingly, while the reach angle exhibited the same implicit drift described by Mazzoni and Krakauer, with many more trials participants eventually counteracted this drift by modifying their explicit strategies, bringing their target error back to zero (Figure 10I, black). At the end of adaptation, participants exhibited large implicit aftereffects when instructed to stop aiming (Figure 10I, right, aftereffect; t(9)=5.16, p < 0.001, Cohen’s d = 1.63).

In a second experiment, participants were taught how to re-aim their reach angles during an initial baseline period, but during adaptation itself, they were not provided with physical aiming targets (Figure 10I, instruction without target). In this case, only SPEs (not a target error) could drive implicit learning towards the aimed location. Even without physical aiming landmarks, participants immediately eliminated error at the primary target after being instructed to re-aim (Figure 10I, middle, yellow). Curiously, without the physical aiming target, these participants did not exhibit an implicit drift in reach angle at any point during the adaptation period and exhibited only a small implicit aftereffect during the washout period (Figure 10I, right, t(9)=3.11, p = 0.012, Cohen’s d = 0.985). In fact, the aftereffect was approximately three times larger when participants aimed towards a physical target during adaptation than when this target was absent (Figure 10I, right, aftereffect; two-sample t-test, t(18)=2.85, p = 0.012, Cohen’s d = 0.935).

A target error (competition) model is consistent with some of these results, but not all. The model correctly predicts that when only a single target is present, performance during adaptation will not exhibit a drift, even though people are aiming. However, it does not explain why this condition still leads to the small aftereffect. Further, with two targets, it correctly predicts that adaptation will drift, as in Mazzoni and Krakauer, but it does not explain how this is eliminated late during adaptation; this reversal in drift would seem to indicate a compensatory and gradual reduction in explicit strategy (Taylor and Ivry, 2011; McDougle et al., 2015; Taylor et al., 2014).

Together, the data suggested a remarkable depth to the implicit system’s response to error. While implicit learning was greatest in response to target error, removing the physical target still permitted SPE-driven learning, albeit to a smaller degree. Whether this aiming-related error is both a target error and an SPE occurring together, or solely an SPE enhanced by a salient visual stimulus, remains unknown.

Sensorimotor adaptation relies on an explicit process shaped by intention (Taylor et al., 2014; Hwang et al., 2006), and an implicit process driven by unconscious correction (Morehead et al., 2017; Mazzoni and Krakauer, 2006; Kim et al., 2018). Here, we examined the possibility that these two parallel systems can become entangled when they respond to a common error source: target (i.e. task) error (Leow et al., 2020; Kim et al., 2019). The data suggested that this coupling resembles a competition by which enhancing the explicit system’s response rapidly depletes error, decreasing the driving force for implicit adaptation. Thus, providing instructions on how to reduce errors enhances the explicit system, but comes at the cost of robbing the implicit system of what it needs to adapt.

This simple rule explained why the implicit system can operate in three modes, one that appears insensitive to perturbation magnitude, another that scales with the perturbation’s size, and a third that exhibits non-monotonic behavior (Figure 1). It also predicted that priming or suppressing explicit awareness can inversely change implicit adaptation (Figure 2). As a result, subjects that utilize strategies inadvertently suppress their implicit learning (Figures 3—5). This inhibition can continue to the extent that improvements in implicit learning (e.g. savings) are masked by dramatic upregulation in strategic learning (Figures 6—8).

The task-error driven implicit system likely exists in parallel with other implicit processes (Leow et al., 2020; Kim et al., 2019; Morehead and Orban de Xivry, 2021). For example, in cases where primary target errors are eliminated, small amounts of implicit adaptation persist (Figure 10). These residual changes are likely due to sensory prediction errors (Mazzoni and Krakauer, 2006; Leow et al., 2020; Taylor and Ivry, 2011; Kim et al., 2019) as well as other target errors that remain in the workspace (Figure 10I). When these error sources oppose one another, competition between parallel implicit learning modules may inhibit the overall implicit response (Figure 10A–C).

In a broader sense, these competitive interactions extend beyond implicit and explicit processes, to other parallel neural circuits that respond to a common error. Changes in one neural circuit’s response to error may be indirectly driven, or hidden, by a parallel circuit. Thus, competition may lead to long-range interactions between neuroanatomical regions that subserve separate neural processes. For example, strategic learning systems housed within the cortex (Shadmehr et al., 1998; Milner, 1962; Gabrieli et al., 1993), may exert indirect changes on a subcortical structure like the cerebellum, which is widely implicated in subconscious adaptation (Tseng et al., 2007; Donchin et al., 2012; Smith and Shadmehr, 2005; Izawa et al., 2012; Wong et al., 2019; Becker and Person, 2019; Morton and Bastian, 2006).

Our work involves reevaluation of earlier literature; this includes data from Haith et al., 2015 in Figures 6 and 8, data from Lerner et al., 2020 in Figure 9, data from Neville and Cressman, 2018 in Figures 1 and 2, data from Saijo and Gomi, 2010 in Figure 2—figure supplement 3, data from Mazzoni and Krakauer, 2006 in Figure 10, data from Taylor and Ivry, 2011 in Figure 10, data from McDougle et al., 2017 in Figure 4, data from Day et al., 2016 in Figure 4, data from Tsay et al., 2021a in Figure 1, data from Maresch et al., 2021 in Figure 5—figure supplement 1, and data from Krakauer et al., 2000 in Figure 4. Relevant details for all studies are summarized in the sections below alongside the new data collected for this work (Exps. 1–5). Note that some methods are described in Appendices 1–8.

In the main text, the competition and independence models predict steady-state implicit learning, x_i^ss. But each theory applies to the entire timecourse, not solely asymptotic learning. Here, we will derive general expressions that apply on each trial k. We will then show that the scaling, saturation, and non-monotonic phenotypes in Figure 1, occur throughout the entire implicit learning timecourse (in the competition model).

In Figure 1H–L, we applied the competition and independence theories to the stepwise group in Exp. 1. While these models do not solely apply to asymptotic learning (see Appendix 1), here we analyze whether the exposures during B1 (15°), B2 (30°), B3 (45°), and B4 (60°), lasted long enough to achieve implicit steady-state adaptation. That is, the scaling phenotype we noted in the implicit response could be influenced by two factors: (1) rotation size, and (2) exposure time.

In the stepwise condition in Exp. 1 we observed that implicit adaptation increased across the 15°, 30°, 45°, and 60° rotation blocks (Figure 1—figure supplement 4A; rm-ANOVA, F(3,38)=99.9, p < 0.001, η_p²=0.735). Were these increase due to changing the rotation’s magnitude, or additional accumulation in the implicit response over time which had not yet saturated? Comparison with other comparable data sets, suggests that implicit learning likely saturated during each block in the Exp. 1 stepwise group. Here, we will describe each data set in turn.

Most importantly, the abrupt rotation group provides a way to verify the timecourse of implicit learning in Exp. 1. Total implicit learning was assayed four times in the abrupt group. Each probe overlapped with a stepwise rotation period. For example, the initial probe in the abrupt condition occurred during B1, when implicit learning was measured in the 15° stepwise rotation. Similarly, the B2, B3, and B4 implicit measurements in the abrupt group overlapped with the 30°, 45°, and 60° rotation periods in the stepwise group. Implicit learning measures across all four abrupt periods are shown in Figure 1—figure supplement 4B. We tested whether total implicit learning varied across the four blocks in the abrupt condition. We did not detect a statistically significant effect of block number on implicit learning (rm-ANOVA, F(3,105)=2.21, p = 0.091, η_p²=0.059). The same was true when we compared solely the first and last blocks (paired t-test, t(35)=1.53, p = 0.134). This indicated that in the 60° rotation condition there was little to no change in implicit learning following B1. This suggests that a single rotation block was sufficient to achieve steady-state adaptation even in the largest rotation condition tested: 60°.

Does this generalize to smaller rotation sizes? While we did not measure implicit learning across multiple blocks in the 15°, 30°, and 45° stepwise conditions, we used a very similar experimental protocol in Salomonczyk et al., 2011: here three learning targets were also used, separated by 45° between targets, in an upper triangular wedge (the exact same conditions as Exp. 1). Note that these data provided another example where the implicit response scales with rotation size during a stepwise rotation sequence (Figure 1—figure supplement 4C). That is, when we increased the rotation in a stepwise manner across three blocks: 30° then 50° and lastly 70°, we observed strong increases in asymptotic implicit learning (p < 0.001). In this study we exposed another participant group to a 30° rotation and measured implicit learning across three consecutive blocks (Figure 1—figure supplement 4D). Critically, we did not detect any change in implicit learning across the three learning periods (all contrasts, p > 0.05). This matched our 60° rotation analysis in the abrupt group in Exp. 1. Thus, for both 30° and 60° rotations, a single block provides enough time to reach steady-state learning.

Lastly, we did not measure extended exposures to a 15° or 45° rotation, but Neville and Cressman, 2018 tested prolonged exposure to a 20° and 40° rotation in a similar paradigm (three targets, separated by 45° in an upper triangular wedge). No-instruction group implicit learning is shown in Figure 1—figure supplement 4E and F. We do not have access to the raw data, and so cannot run a repeated-measures ANOVA to test whether these groups exhibited a block-by-block change in implicit learning. However, comparing the first and third rotation blocks, we can calculate a maximum 0.7°–1.4° c hange in implicit learning. This represents a change between 7.6–16.5%, which are daunted by the 313% increase in implicit learning exhibited from the 15° to the 60° blocks in the Exp. 1 stepwise group.

In sum, the 60° implicit learning timecourse we measured in the abrupt group, the 30° implicit learning timecourse measures in Salomonczyk et al., 2011, and the 20° and 40° groups in Neville and Cressman, 2018., suggest that the implicit learning system exhibits little to no increase beyond the initial learning block. Each study was extremely comparable, testing participants with three learning targets, located in an upper triangular wedge spanning 45–135° in the workspace. We estimate that any changes in implicit learning due to exposure time alone were limited to about 1.4°, which is an order magnitude smaller than that observed across the stepwise blocks in Exp. 1 (14.5°). Therefore, our Exp. 1 analyses in Figures 1, 2 and 4, likely reflects steady-state implicit learning, or very nearly so.

In Section 1.1, we note a potential concern in our Figure 1 analysis, where our implicit and explicit learning measures were not independent; explicit strategy was estimated as total adaptation minus implicit learning: x_e^ss = x_T^ss - x_i^ss. Thus, when total adaptation is constant, implicit and explicit learning will exhibit a negative correlation simply due to the dependencies in our implicit and explicit learning measures. At a glance, this negative correlation may appear similar to the negative correlation between implicit and explicit learning embedded within the competition equation: x_i^ss = p_i(r - x_e^ss). Thus, it is reasonable to question whether the correspondence between our empirical data and the competition model in Figure 1, is unfairly biased by the intrinsic implicit-explicit dependencies in our empirical measures.

In short, suppose that two conditions, A and B, exhibit an increase in implicit learning. Using our explicit learning measures, we would expect a decrease in explicit strategy. This negative correspondence between implicit learning and explicit strategy may appear trivially predicted by the competition model. This, however, is not the case. For this trivial relationship to occur, total adaptation must be the same in A and B. In Figure 1, we calculate implicit and explicit learning measures across changes in rotation size, over which total adaptation varies in proportion to rotation magnitude. Thus, our empirical implicit and explicit learning measures will not necessarily match the competition model.

To explain this, let us consider a hypothetical scenario similar to the data recorded by Neville and Cressman. Suppose total adaptation and implicit learning are measured over three rotations sizes (20°, 40°, and 60°): total learning (19°, 36°, 53°), implicit learning (10°, 10°, 10°). As expected, total adaptation increases with rotation size. Implicit learning remained constant, as in the Neville and Cressman data set. Next, suppose we estimate explicit strategy, by subtracting total adaptation and implicit learning. This will yield the explicit strategy estimates: (9°, 26°, 43°). Thus, in this example, our implicit and explicit learning measures are dependent. How well does the competition model match these data?

To answer this question, we can calculate the implicit learning gain, p_i, for each rotation size. This can be calculated as p_i = x_i^ss/(r – x_e^ss). For the example above, the implicit learning gain would be equal to the set: (0.909, 0.714, 0.588). What this means, is that as the rotation increases, the implicit learning gain decreases by approximately 35.3%. These variations in p_i will not produce a good match between the data and model. To show this, we can estimate the optimal p_i that would minimize the squared error between the measured implicit learning, and model-predicted implicit learning. In this example, the optimal p_i value is 0.693. Using this gain, we can now use the model to predict how much implicit learning should occur in each rotation size condition. This would yield: (7.62°, 9.70°, 11.78°) in predicted learning. We can see even though implicit learning remained constant in the ‘real’ data, the competition equation predicts a 54.5% increase in implicit learning across the three rotation sizes.

What does this mean? This hypothetical example demonstrates that calculating explicit learning via a subtraction between total adaptation and implicit learning, will not automatically yield a good match between the empirical data and the competition model. Rather, the only way that the competition model will match data, is in the case where the conditions tested in an experiment abide by the principle that p_i is constant (or at least very similar) across various experimental conditions (e.g. rotation sizes). The three data sets we analyze in Figure 1, must obey this property, and thus, are intrinsically compatible with Equation 4.

Nevertheless, there is another way to corroborate the relationship between the model and data in Figure 1 that does not involve using implicit and explicit learning measures at the same time. By noting that x_e^ss = x_T^ss – x_i^ss, we can substitute this expression into Equation 4 to obtain a relationship between implicit learning and total adaptation: x_i^ss = p_i(1 – p_i)^–1(r – x_T^ss). This equation represents an alternate way to express the competition model which can be compared with the empirical data. Fortunately, here we compare x_i^ss and x_T^ss which were directly measured on separate trials (they are not dependent, in a statistical sense).

A simple thought experiment shows that when data do not agree with the competition model, x_i^ss and x_e^ss can show a correlation, but x_i^ss and x_T^ss will not (in general). Suppose 3 participants have 10°, 15°, and 5° implicit learning, respectively, and all have 20° total learning. Subtracting total learning and implicit learning will yield an estimated 10°, 5°, and 15° explicit strategy, respectively. The competition model will predict that implicit-explicit and implicit-total will show negative correlations. For these participants, the implicit-explicit correlation is –1, but the implicit-total correlation is 0, inconsistent with competition. That is, implicit-explicit show a correlation spuriously, but implicit-total were sampled independently, yielding a robust way to test the competition theory.

Thus, in the main text we repeated our competition model analysis in Figure 1 using the alternate equation. We used total adaptation measured in Exp. 1, Neville and Cressman, and Tsay et al., 2021a to predict implicit learning. To do this, we identified a p_i value in each data set that minimized the squared error between measured implicit learning and model-predicted implicit learning (in Neville and Cressman, the p_i value was calculated across six conditions (three rotations, 2 instruction types), in Exp. 1, the p_i value was calculated across five conditions (all four rotation sizes in the stepwise group, as well as the 60° abrupt condition), in Tsay et al., the p_i value was calculated across all four rotation sizes).

Our results are shown in Figure 1—figure supplement 2. The competition model predicted nearly identical implicit learning patterns when total adaptation was used as the independent variable (‘model-2’) and when explicit adaptation was used as the independent variable (‘model-1’). This control analyses shows that the close correspondence between measured behavior and model-predicted behavior in Figure 1, is not due to the way we empirically operationalized our learning measures. Rather, the properties embedded in the competition model (with a constant implicit learning gain) were intrinsically present within the data.

At various points in our work, we analyze how well the competition model, or independence model, can predict changes in implicit learning across various conditions. These models have one free parameter, the implicit learning gain: p_i = b_i(1 – a_i+ b_i)^–1. In each case, we assumed that the implicit learning gain is the same across experimental groups, that is only one gain is selected and applied to all experimental conditions. We made this choice to minimize the number of free variables; allowing p_i to vary across groups, would allow arbitrarily precise matches to the data. However, holding p_i constant across conditions, shows that the same equation applies across conditions, limiting overfitting and increasing model confidence.

This assumption, however, may seem inappropriate given that the implicit learning gain depends on error sensitivity, which varies with conditions such as error size (Albert et al., 2021; Kim et al., 2018; Marko et al., 2012). However, it is important to note that the implicit learning gain responds weakly to changes in error sensitivity. This insensitivity is due to the appearance of error sensitivity (b_i) in both the gain’s numerator and denominator: p_i = b_i(1-a_i+ b_i)^–1. For example, let us suppose that participants in Condition 1 have b_i = 0.2, but in Condition 2 b_i = 0.3, a 50% increase. For an implicit retention factor of 0.9565 (see in Materials and methods: Measuring properties of implicit learning), the implicit learning gain in Condition 1 would be p_i = 0.821 versus p_i = 0.873 in Condition 2. Thus, even though implicit error sensitivity was 50% larger in Condition 2, the implicit learning gain would change only 6.3%. For a more extreme case where implicit error sensitivity was double (0.4) in Condition 2, there would still only be a 9.8% change in implicit learning gain.

For these reasons, there are no physiologic changes in b_i that could create the 46.2% increase in implicit learning in Figure 2C (ratio of no instruction to instruction groups), and 82.3% increase in learning in Figure 2G (ratio of stepwise to abrupt). To show this, we conducted sensitivity analyses. Imagine that across two conditions, a reference condition, and a test condition, implicit sensitivity varies. We set the reference implicit error sensitivity to 0.1, 0.1625, 0.225, 0.2875, 0.35. We chose these values, because steady-state implicit error sensitivity determines steady-state implicit learning, which varied between 0.19 and 0.35 in Exps. 2 and 3; see Figure 3—figure supplement 1. Then we calculated how much p_i (total learning) will change, when this reference error sensitivity increases to a test error sensitivity: test error sensitivity was capped at the physiologic, yet exceedingly unlikely, upper bound of 1. Because p_i also depends on implicit retention, we also tested several possible values between 0.95–0.99. The results are depicted in Figure 2—figure supplement 2. Each column denotes the same analysis, but with a different retention factor. Each line denotes a different reference error sensitivity. The x-axis continuously varies the test error sensitivity.

For example, for the point highlighted by the black arrow in the second column: this point shows that total implicit learning will increase by about 20% (y-axis) in a scenario where implicit retention = 0.96, and implicit error sensitivity increases from 0.1625 (i.e., it is on the red line) in the reference condition to 0.8 (i.e., the x-axis value) in the test condition. This example is illustrative. Here b_i increase from 0.1625 to 0.8, a 392% increase, but total implicit learning only increases 20%. In sum, extreme variations in implicit error sensitivity, still produce small changes in total implicit learning.

In Figure 2—figure supplement 2, we indicated the 46.2% and 82.3% changes in Figure 2C&G with dashed horizontal lines. Note how no curve crosses either level, even though these represent several hundred % changes in implicit error sensitivity. Thus, it is not possible that variations in implicit error sensitivity could generate the changes in total implicit learning we examined in Figure 2.

On the other hand, consider the competition model, x_i^ss = p_i(r – x_e^ss). Distributing the p_i term yields: x_i^ss = p_ir – p_ix_e^ss. Note that p_i varied between about 0.6–0.8 in our studies, meaning that implicit learning is very sensitive to competition. The implicit system will decrease by approximately 60–80% each unit increase in explicit strategy. For these reasons, the competition model more readily produces large fluctuations in implicit learning, such as those observed in Figure 2.

In Experiment 1 in the main text, we analyze how abrupt and gradual perturbation onset alters the steady-state distribution for implicit and explicit learning. In this appendix, we conduct a similar investigation for data collected by Saijo and Gomi, 2010. In the first section, we describe the results of our analysis. In the second section, we describe the experimental paradigm and detail the methods used in our analysis.

Adapted movement patterns exhibit generalization: a decay in adaptation measured when participants reach towards new areas in the workspace (Hwang and Shadmehr, 2005; Krakauer et al., 2000; Fernandes et al., 2012). Recent studies have observed that this generalization is centered where participants aim their movement, as opposed to the visual target (Day et al., 2016; McDougle et al., 2017). In Exps. 1–3, we measured implicit adaptation by instructing participants to aim directly to the target without an explicit strategy. Had implicit learning truly been ‘centered’ at the aiming location and not the target, these no aiming trials may underapproximate total implicit learning. This discrepancy will increase with re-aiming. Thus, it may appear that individuals who aim more, possess less implicit learning. These generalization properties could contribute to the negative subject-to-subject relationships we observed in Figure 3. In other words, could an SPE model with plan-based generalization produce the implicit-explicit correlations that we observed in Figure 3? Our main text explores this possibility in Figure 4. Here, we expand on these analyses to provide additional intuition, derivations, and technical background.

In our Results, we considered how an SPE model might also predict negative correlations between implicit learning and explicit strategy. Suppose that implicit learning is driven by SPEs and is not altered by explicit strategy. However, a subject with a better implicit learning system (e.g. a higher implicit error sensitivity) will require less explicit re-aiming to reach a desired adaptation level. In other words, individuals with large SPE implicit learning may use less explicit strategy relative to those with less SPE implicit learning. Like the competition theory, this scenario would also yield a negative relationship between implicit and explicit learning, due to the way explicit strategies respond to variation in the implicit system. We will now show the diverging predictions this model makes, relative to the competition theory.

In Appendix 7, we detail how an SPE independence model, and a target error competition theory predict implicit and explicit learning should vary across participants. To review, the SPE model predicts (1) positive correlations between implicit learning and total adaptation, and (2) negative correlations between explicit strategy and total adaptation. On the other hand, the competition theory predicts (1) negative correlations between implicit learning and total adaptation, and (2) positive correlations between explicit strategy and total adaptation. We noted several datasets that supported the competition theory: our data in Experiment 3 (Figure 5G&H), experiments conducted by Maresch et al., 2021 (Figure 5—figure supplement 1A,D&G), our data in Experiment 1 (Figure 5—figure supplement 1B,E&H), and data collected by Tsay et al., 2021a (Figure 5—figure supplement 1C,F&I). Here, we detail a critical nuance in the competition theory’s predictions that may result in little to no correlation between implicit learning and total adaptation.

Source data files generated or analyzed during this study, as well as the associated analysis code, are included as supplements to Figures 1-10, as well as their associated Figure Supplements, and have also been deposited in OSF under accession code MZS6A.

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[Editors’ note: after the initial submission, the editors requested that the authors prepare an action plan. This action plan was to detail how the reviewer concerns could be addressed in a revised submission. What follows is the initial editorial request for an action plan.]

Thank you for sending your article entitled "Competition between parallel sensorimotor learning systems" for peer review at eLife. Your article is being evaluated by 3 peer reviewers, and the evaluation is being overseen by a Reviewing Editor and Michael Frank as the Senior Editor. The reviewers have opted to remain anonymous.

Given the list of essential revisions, including new experiments, the editors and reviewers invite you to respond as soon as you can with an action plan for the completion of the additional work. We expect a revision plan that under normal circumstances can be accomplished within two months, although we understand that in reality revisions will take longer at the moment. We plan to share your responses with the reviewers and then advise further with a formal decision. After full discussion, all reviewers agree that this work if accepted would have a significant impact on the field. However, the reviewers raised a list of major concerns over the proposed model and its data handling. In particular, a lack of strong alternative models, a possible lack of explanatory power for outstanding findings in the field, and a strong reliance on modeling assumptions make it hard to accept the paper/model as it currently stands. We hope the authors can adequately address the following major concerns. [Editors’ note, the major concerns referenced here are detailed later in this decision narrative].

[Editors’ note: the authors provided an initial action plan in response to reviewer comments. Following the initial action plan, the authors were provided additional reviewer comments. These concerns were addressed in a second action plan. Additional reviewer comments were provided after the second action plan. During the composition of a third action plan, a decision was made to reject the manuscript.]

[Editors’ note: the authors submitted for reconsideration following the decision after peer review. What follows is the decision letter after the first round of review.]

Thank you for resubmitting your work entitled "Competition between parallel sensorimotor learning systems" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by Michael J Frank as the Senior Editor. The reviewers have opted to remain anonymous.

All the reviewers concluded that the study is not ready for publishing in eLife. The primary concern is that the direct evidence for supporting the competition model is weak or simply lacking. In the previous manuscript, the only solid, quantitative evidence is the negative correlation between explicit and implicit learning (Figure 3H). But as we mentioned in the last letter decision, this negative correlation can also be obtained by the alternative (and mainstream) model based on both target error and sensory prediction error. You provided a piece of new but essential evidence to differentiate these two models in the revision plan. Still, this new result (i.e., the negative correlation between total learning and implicit learning) is at odds with multiple datasets that have been published. We find this will continue to be a problem even we provide you more time to revise the paper or continue to collect more data as listed in the revision plan. The submission has been on discussion for a prolonged period as the reviewers hope to see solid evidence for the conceptual step-up that you presented in the manuscript. However, we are regretful that the study is not ready for publishing as it currently stands.

[Editors’ note: the authors appealed the editorial decision. The appeal was granted and the authors were invited to submit a revised manuscript and response to reviewer comments. What follows are the reviewer comments provided after the initial submission of the manuscript.]

Concerns:

1. There is no clear testing of alternative models. After Figure 1 and 2, the paper goes on with the competition model only. The independent model will never be able to explain differences in implicit learning for a given visuomotor rotation (VMR) size, so it is not a credible alternative to the competition model in its current form. It seems possible that extensions of that model based on the generalization of implicit learning (Day et al. 2016, McDougle et al. 2017) or task-dependent differences in error sensitivity could explain most of the prominent findings reported here. We hope the authors can show more model comparison results to support their model.

2. The measurement of implicit learning is compromised by not asking participants to stop aiming upon entering the washout period. This happened at three places in the study, once in Experiment 2, once in the re-used data by Fernandez-Ruiz et al., 2011, and once in the re-used data by Mazzoni and Krakauer 2006 (no-instruction group). We would like to know how the conclusion is impacted by the ill-estimated implicit learning.

3. All the new experiments limit preparation time (PT) to eliminate explicit learning. In fact, the results are based on the assumption that shortened PT leads to implicit-only learning (e.g., Figure 4). Is the manipulation effective, as claimed? This paradigm needs to be validated using independent measures, e.g., by direct measurement of implicit and/or explicit strategy.

4. Related to point 3, it is noted that the aiming report produced a different implicit learning estimate than a direct probe in Exp1 (Figure S5E). However, Figure 3 only reported Exp1 data with the probe estimate. What would the data look like with report-estimated implicit learning? Will it show the same negative correlation results with good model matches (Figure 3H)?

5. Figure 3H is one of the rare pieces of direct evidence to support the model, but we find the estimated slope parameter is based on a B value of 0.35, which is unusually high. How is it obtained? Why is it larger than most previous studies have suggested? In fact, this value is even larger than the learning rate estimated in Exp 3 (Figure 6C). Is it related to the small sample size (see below)?

6. The direct evidence supporting a competition of implicit and explicit learning is still weak. Most data presented here are about the steady-state learning amplitude; the authors suggest that steady-state implicit learning is proportional to the size of the rotation (Equation 5). But this is directly contradictory to the experimental finding that implicit learning saturates quickly with rotation size (Morehead et al., 2017; Kim et al., 2018). This prominent finding has been dismissed by the proposed model. On the other hand, one classical finding for conventional VMR is that explicit learning would gradually decrease after its initial spike, while implicit learning would gradually increase. The competition model appears unable to account for this stereotypical interaction. How can we account for this simple pattern with the new model or its possible extensions?

7. General comments about the data:

Experiments 3 and 4 (Figures 6 and 7) do not contribute to the theorization of competition between implicit and explicit learning. The authors appear to use them to show that implicit learning properties (error sensitivity) can be modified, but then this conclusion critically depends on the assumption that the limit-PT paradigm produces implicit-only learning, which is yet to be validated.

Figure 4 is not a piece of supporting evidence for the competition model since those obtained parameters are based on assumptions that the competition model holds and that the limit-PT condition "only" has implicit learning.

8. Concerns about data handling:

All the experiments have a limited number of participants. This is problematic for Exp 1 and 2, which have correlation analysis. Note Fig 3H contains a critical, quantitative prediction of the model, but it is based on a correlation analysis of n=9. This is an unacceptably small sample. Experiment 3 only had 10 participants, but its savings result (argued as purely implicit learning-driven) is novel and the first of its kind.

Experiment 2: This experiment tried to decouple implicit and explicit learning, but it is still problematic. If the authors believe that the amount of implicit adaptation follows a state-space model, then the measure of early implicit is correlated to the amount of late implicit because Implicit_late = (ai)^N * Implicit_early where N is the number of trials between early and late. Therefore the two measures are not properly decoupled. To decouple them, the authors should use two separate ways of measuring implicit and explicit. To measure explicit, they could use aim report (Taylor, Krakauer and Ivry 2011), and to measure implicit independently, they could use the after-effect by asking the participants to stop aiming as done here. They actually have done so in experiment 1 but did not use these values.

Figure 6: To evaluate the saving effect across conditions and experiments, using the interaction effect of ANOVA shall be desired.

Figure 8: The hypothesis that they did use an explicit strategy could explain why the difference between the two groups rapidly vanishes. Also, it is unclear whether the data from Taylor and Ivry (2011) are in favor of one of the models as the separate and shared error models are not compared.

Reviewer #1:

The present study by Albert and colleagues investigates how implicit learning and explicit learning interact during motor adaptation. This topic is under heated debate in the sensorimotor adaptation area in recent years, spurring diverse behavioral findings that warrant a unified computational model. The study is to fulfill this goal. It proposes that both implicit and explicit adaptation processes are based on a common error source (i.e., target error). This competition leads to different behavioral patterns in diverse task paradigms.

I find this study a timely and essential work for the field. It makes two novel contributions. First, when dissecting the contribution of explicit and implicit learning, the current study highlights the importance of distinguishing apparent learning size and covert changes in learning parameters. For example, the overt size of implicit learning could decrease while the related learning parameters (e.g., implicit error sensitivity) remain the same or even increase. Many researchers for long have overlooked this dissociation. Second, the current study also emphasizes the role of target error in typical perturbation paradigms. This is an excellent waking call since the predominant view now is that sensory prediction error is for implicit learning and target error for explicit learning.

Given that the paper aims to use a unified model to explain different phenomena, it mixes results from previous work and four new experiments. The paper's presentation can be improved by reducing the use of jargon and making straightforward claims about what the new experiments produce and what the previous studies produce. I will give a list of things to work on later (minor concerns).

Furthermore, my major concern is whether the property of the implicit learning process (e.g., error sensitivity) can be shown subjective to changes without making model assumptions.

My major concern is whether we can provide concrete evidence that the implicit learning properties (error sensitivity and retention) can be modified. Even though the authors claim that the error sensitivity of implicit learning can be changed, and the change subsequently leads to savings and interference (e.g., Figures 6 and 7), I find that the evidence is still indirect, contingent on model assumptions. Here is a list of results that concern error sensitivity changes.

1. Figures 1 and 2: Instruction is assumed to leave implicit learning parameters unchanged.

2. Figure 4: It appears that the implicit error sensitivity increases during relearning. However, Fig4D cannot be taken as supporting evidence. How the model is constructed (both implicit and explicit learning are based on target error) and what assumptions are made (Low RT = implicit learning, High RT = explicit + implicit) determine that implicit learning's error sensitivity must increase. In other words, the change in error sensitivity resulted from model assumptions; whether implicit error sensitivity by itself changes cannot be independently verified by the data.

3. Figure 6: With limited PT, savings still exists with an increased implicit error sensitivity. Again, this result also relies on the assumption that limited PT leads to implicit-only learning. Only with this assumption, the error sensitivity can be calculated as such.

4. Figure 7: with limited PT anterograde interference persists, appearing to show a reduced implicit error sensitivity. Again, this is based on the assumption that the limited PT condition leads to implicit-only learning.

Across all the manipulations, I still cannot find an independent piece of evidence that task manipulations can modify learning parameters of implicit learning without resorting to model assumptions. I would like to know what the authors take on this critical issue. Is it related to how error sensitivity is defined?

Reviewer #2:

The paper provides a thorough computational test of the idea that implicit adaptation to rotation of visual feedback of movement is driven by the same errors that lead to explicit adaptation (or strategic re-aiming movement direction), and that these implicit and explicit adaptive processes are therefore in competition with one another. The results are incompatible with previous suggestions that explicit adaptation is driven by task errors (i.e. discrepancy between cursor direction and target direction), and implicit adaptation is driven by sensory prediction errors (i.e. discrepancy between cursor direction and intended movement direction). The paper begins by describing these alternative ideas via state-space models of trial by trial adaptation, and then tests the models by fitting them both to published data and to new data collected to test model predictions.

The competitive model accounts for the balance of implicit-explicit adaptations observed previously when participants were instructed how to counter the visual rotation to augment explicit learning across multiple visual rotation sizes (20, 40 and 60 degrees; Neville and Cressman, 2018). It also fits previous data in which the rotation was introduced gradually to augment implicit learning (Saijo and Gomi, 2010). Conversely, a model based on independent adaptation to target errors and sensory prediction errors could not reproduce the previous results. The competitive model also accounts for individual participant differences in implicit-explicit adaptation. Previous work showed that people who increased their movement preparation time when faced with rotated feedback had smaller implicit reach aftereffects, suggesting that greater explicit adaptation led to smaller implicit learning (Fernandes-Ruis et al., 2011). Here the authors replicated this general effect, but also measured both implicit and explicit learning under experimental manipulation of preparation time. Their model predicted the observed inverse relationship between implicit and explicit adaptation across participants.

The authors then turned their attention to the issue of persistent sensorimotor memory – both in terms of savings (or benefit from previous exposure to a given visual rotation) and interference (or impaired performance due to exposure to an opposite visual rotation). This is a topic that has a long history of controversy, and there are conflicting reports about whether or not savings and interference rely predominantly on implicit or explicit learning. The competition model was able to account for some of these unresolved issues, by revealing the potential for a paradoxical situation in which the error sensitivity of an implicit learning process could increase without observable increase in implicit learning rate (or even a reduction in implicit learning rate). The authors showed that this paradox was likely at play in a previous paper that concluded that saving is entirely explicit (Haith et al., 2015), and then ran a new experiment with reduced preparation time to confirm some recent reports that implicit learning can result in savings. They used a similar approach to show that long-lasting interference can be induced for implicit learning.

Finally, the authors considered data that has long been cited to provide evidence that implicit adaptation is obligatory and driven by sensory prediction error (Mazzoni and Krakauer, 2006). In this previous paper, participants were instructed to aim to a secondary target when the visual feedback was rotated so that the cursor error towards the primary target would immediately be cancelled. Surprisingly, the participants' reach directions drifted even further away from the primary target over time – presumably in an attempt to correct the discrepancy between their intended movement direction and the observed movement direction. However, a competition model involving simultaneous adaptation to target errors from the primary target and opposing target errors from the secondary target offers an alternative explanation. The current authors show that such a model can capture the implicit "drift" in reach direction, suggesting that two competing target errors rather than a sensory prediction error can account for the data. This conclusion is consistent with more recent work by Taylor and Ivry (2011), which showed that reach directions did not drift in the absence of a second target, when participants were coached to immediately cancel rotation errors in advance. The reason for small implicit aftereffect reported by Taylor and Ivry (2011) is open for interpretation. The authors of the current paper suggest that adaptation to sensory prediction errors could underlie the effect, but an alternative possibility is that there is an adaptive mechanism based on reinforcement of successful action.

Overall, this paper provides important new insights into sensorimotor learning. Although there are some conceptual issues that require further tightening – including around the issue of error sensitivity versus observed adaptation, and the issue of whether or not there is evidence that sensory prediction errors drive visuomotor rotation – I think that the paper will be highly influential in the field of motor control.

Line 19: I think it is possible that more than 2 adaptive processes contribute to sensorimotor adaptation – perhaps add "at least".

Lines 24-27: This section does not refer to specific context or evidence and is consequently obtuse to me.

Line 52: Again – perhaps add "at least".

Line 68: I am not really sure what you are getting at by "implicit learning properties" here. Can you clarify?

Line 203: I think the model assumption that there was zero explicit aiming during washout is highly questionable here. The Morehead study showed early washout errors of less than 10 degrees, whereas errors were ~ 20 degrees in the abrupt and ~35 degrees in the gradual group for Saijo and Gomi. I think it highly likely that participants re-aimed in the opposite direction during washout in this study – what effect would this have on the model conclusions?

Line 382: It would be helpful to explicitly define what you mean by learning, adaptation, error sensitivity, true increases and true decreases in this discussion – the terminology and usage are currently imprecise. For example, it seems to me that according to the zones defined "truth" refers to error sensitivity, and "perception" refers to observed behaviour (or modelled adaptation state), but this is not explicitly explained in the text. This raises an interesting philosophical question – is it the error sensitivity or the final adaptation state associated with any given process that "truly" reflects the learning, savings or interference experienced by that process? Some consideration of this issue would enhance the paper in my opinion.

Figure 5 label: Descriptions for C and D appear inadvertently reversed – C shows effect of enhancing explicit learning and D shows effect of suppressing explicit learning.

Line 438: The method of comparing learning rate needs justification (i.e. comparing from 0 error in both cases so that there is no confound due to the retention factor).

Line 539: I am not sure if I agree that the implicit aftereffect in the no target group need reflect error-based adaptation to sensory prediction error. It could result from a form of associative learning – where a particular reach direction is associated with successful target acquisition for each target. The presence of an adaptive response to SPE does not fit with any of the other simulations in the paper, so it seems odd to insist that it remains here. Can you fit a dual error model to the Taylor and Ivry (single-target) data? I suspect it would not work, as the SPE should cause non-zero drift (i.e. shift the reach direction away from the primary target).

Line 556: Be precise here – do you really mean SPE? It seems as though you only provided quantitative evidence of a competition between errors when there were 2 physical targets.

Line 606: Is it necessarily the explicit response that is cached? I think of this more as the development of an association between action and reward – irrespective of what adaptive process resulted in task success. It would be nice to know what happened to aftereffects after blocks 1 and 2 in study 3. An associative effect might be switched on and off more easily – so if a mechanism of that kind were at play, I would predict a reduced aftereffect as in Huberdeau et al.

Line 720: Ref 12 IS the Mazzoni and Krakauer study, ref 11 involves multiple physical targets, and ref 21 is the Taylor and Ivry paper considered above and in the next point. None of these papers therefore require an explanation based on SPE. However, ref #17 appears to provide a more compelling contradiction to the notion that target errors drive all forms of adaptation – as people adapt to correct a rotation even when there is never a target error (because the cursor jumps to match the cursor direction). A possible explanation that does not involve SPE might be that people retain a memory of the initial target location and detect a "target error" with respect to that location.

Line 737: I don't agree with this – the observation of an after-effect with only 1 physical target but instructed re-aiming so that there was 0 target error, certainly implies some other process besides a visual target error as a driver of implicit learning. However, as argued above, such a process need not be driven by SPE. Model-free processes could be at play…

Line 791: Some more detail on how timing accuracy was assured in the remote experiments is needed. The mouse sample rate can be approximately 250 Hz, but my experience with it is that there can be occasional long delays between samples on some systems. The delay between commands to print to the screen and the physical appearance on the screen can also be long and variable – depending on the software and hardware involved.

Line 861: How did you specify or vary the retention parameters to create these error sensitivity maps?

Line 865: Should not the subscripts here be "e" and "I" rather than "f" and "s"?

Line 1009: Why were data sometimes extracted using a drawing package (presumably by eye? – please provide further details), and sometimes using GRABIT in Matlab?

Line 1073: More detail about the timing accuracy and kinematics of movement are required.

Line 1148: Again – should not the subscripts here be e and I rather than f and s?

Reviewer #3:

In this paper, Albert and colleagues explore the role of target error and sensory prediction error on motor adaptation. They suggest that both implicit and explicit adaptation would be driven by target error. In addition, implicit adaptation is also influenced by sensory prediction error.

While I appreciate the effort that the authors have done to come up with at theory that could account for many studies, there is not a single figure/result that does not suffer from main limitations as I highlight in the major comments below. Overall, the main limitations are:

I believe that the authors neglect some very relevant papers that contradict their theory and model.

– They did not take into account some results on the topic such as Day et al. 2016 and McDougle et al. 2017. It is true that they acknowledge it and discuss it but I am not convinced by their arguments (more on this topic in a major comment about the discussion below).

– They did not take into account the fact that there is no proof that limiting RT is a good way to suppress the explicit component of adaptation. When the number of targets is limited, these explicit responses can then be cached without any RT cost. McDougle and Taylor, Nat Com (2019) demonstrated this for 2 targets (here the authors used only 4 targets). There exist no other papers that proof that limiting RT would suppress the explicit strategy as claimed by the authors. To do so, one needs to limit PT and to measure the explicit or the implicit component. The authors should prove that this assumption holds because it is instrumental to the whole paper. The authors acknowledge this limitation in their discussion but dismiss it quite rapidly. This manipulation is so instrumental to the paper that it needs to be proven, not argued (more on this topic in a major comment about the discussion below).

– They did not take into account the fact that the after-effect is a measure of implicit adaptation if and only if the participants are told to abandon any explicit strategy before entering the washout period (as done in Taylor, Krakauer and Ivry, 2011). This has important consequences for their interpretation of older studies because it was then never asked to participants to stop aiming before entering the washout period as the authors did in experiment 2.

There are also major problems with statistics/design:

– I disagree with the authors that 10-20 people per group (in their justification of the sample size in the second document) is standard for motor adaptation experiments. It is standard for their own laboratories but not for the field anymore. They even did not reach N=10 for some of the reported experiments (one group in experiment 1). Furthermore, this sample size is excessively low to obtain reliable estimation of correlations. Small N correlation cannot be trusted: https://garstats.wordpress.com/2018/06/01/smallncorr/

– Justification of sample size is missing. What was the criteria to stop data collection? Why is the number of participants per group so variable (N=9 and N=13 for experiment 1, N=17 for experiment 2, N=10 for experiment 3, N=10 ? per group for experiment 4). Optional stopping is problematic when linked to data peeking (Armitage, McPherson and Rowe, Journal of the Royal Statistical Society. Series A (General), 1969). It is unclear how optional stopping influences the outcome of the statistical tests of this paper.

– The authors should follow the best practices and add the individual data to all their bar graphs (Rousselet et al. EJN 2016).

– Missing interactions (Nieuwenhuis et al., Nature Neuro 2011), misinterpretation of non-significant p-values (Altman 1995 https://www.bmj.com/content/311/7003/485)

Given these main limitations, I don't think that the authors have a convincing case in favor of their model and I don't think that any of these results actually support the error competition model.

Detailed major comments per equation/figure/section:

Equation 2: the authors note that the sensory prediction error is "anchored to the aim location " (line 104-105) which is exactly what Day et al. 2016 and McDougle et al. 2017 demonstrated. Yet, they did not fully take into account the implication of this statement. If it is so, it means that the optimal location to determine the extent of implicit motor adaptation is the aim location and not the target. Indeed, if the SPE is measured with respect to the aim location and is linked to the implicit system, it means that implicit adaptation will be maximum at the aim location and, because of local generalization, the amount of implicit adaptation will decay gradually when one wants to measure this system away of that optimal location (Figure 7 of Day et al). This means that, the further the aiming direction is from the target, the smaller the amount of implicit adaptation measured at the target location will be. This will result in an artificial negative correlation between the explicit and implicit system without having to relate to a common error source.

Equation 3: the authors do not take into account results from their lab (Marko et al., Herzfeld) and from others (Wei and Kording) that show that the sensitivity to error depends on the size of the rotation.

Equation 5: In this equation, the authors suggest that the steady-state amount of implicit adaptation is directly proportional to the size of the rotation. Thanks to a paradigm similar to Mazzoni and Krakauer 2006, the team of Rich Ivry has demonstrated that the implicit response saturates very quickly with perturbation size (Kim et al., communications Biology, 2018, see their Figure 1).

Data from Cressman, Figure 1: Following Day et al., one should expect that, when the explicit strategy is larger (instruction group in Cressman et al. compared to the no-instruction group), the authors are measuring the amount of implicit adaptation further from aiming direction where it is maximum. As a result, the amount of implicit adaptation appears smaller in the instruction group simply because they were aiming more than the no-instruction group (Figure 1G).

– Figure 1H: the absence of increase in implicit adaptation is not due to competition as claimed by the authors but is due to the saturation of the implicit response with increasing rotation size (Kim et al. 2018). It saturates at around 20{degree sign} for all rotations larger than 6{degree sign}.

Data from Saijo and Gomi: Here the authors interpret the after-effect as a measure of implicit adaptation but it is not as the participants were not told that the perturbation would be switched off.

– Even if these after-effects did represent implicit adaptation, these results could be explained by Kim et al. 2018 and Day et al. 2016. For a 60{degree sign} rotation, the implicit component of adaptation will saturate around 15-20{degree sign} (like for any large perturbation). The explicit component has to compensate for that but it does a better job in the abrupt condition than in the gradual condition where some target error remains. Given that the aiming direction is larger in the abrupt case than in the gradual case, the amount of implicit adaptation is again measured further away from its optimal location in the abrupt case than in the gradual case (Day et al. 2016 and McDougle et al. 2017).

– There is no proof that introducing a perturbation gradually suppresses explicit learning (line 191). The authors did not provide a citation for that and I don't think there is one. People confound awareness and explicit (also valid for line 212). Rather, given that the implicit system saturates at around 20{degree sign} for large rotation, I would expect that the re-aiming accounts for 20{degree sign} of the ~40{degree sign} of adaptation in the gradual condition.

Line 205-215: The chosen parameters appear very subjective. The authors should perform a sensitivity analyses to demonstrate that their conclusions do not depend on these specific parameters.

Figure 3: The after-effect in the study of Fernandez-Ruiz et al. does not solely represent the implicit adaptation component as these researchers did not tell their participants that they should stop aiming during the washout.

– Correlations based on N=9 should not be considered as meaningful. Such correlation is subject to the statistical significance fallacy: it can only be true if it is significant with N=9 while this represents a fallacy (Button et al. 2013).

Experiment 1 of the authors suffer from several limitations:

– small sample size (N=9 for one group). Why is the sample size different between the two groups?

– Limiting RT does not abolish the explicit component of adaptation (Line 1027: where is the evidence that limit PT is effective in abolishing explicit re-aiming?). Haith and colleagues limited reaction time on a small subset of trials. If the authors want to use this manipulation to limit re-aiming, they should first demonstrate that this manipulation is effective in doing so (other authors that have used this manipulation but have failed to do validate it first). I wonder why the authors did not measure the implicit component for their limit PT group like they did in the No PT limit group. That is required to validate their manipulation.

– The negative correlation from Figure 3H can be explained by the fact that the SPE is anchored at the aiming direction and that, the larger the aiming direction is, the further the authors are measuring implicit adaptation away from its optimal location.

– The difference between the PT limit and NO PT limit is not very convincing. First, the difference is barely significant (line 268). Why did the authors use the last 10 epochs for experiment 1 and the last 15 for experiment 2? This looks like a post-hoc decision to me and the authors should motivate their choice and should demonstrate that their results hold for different choice of epochs (last 5, 10, 15 and 20) to demonstrate the robustness of their results. Second, the degrees of freedom of the t-test (line 268) does not match the number of participants (9 vs. 13 but t(30)?)

– Why did the authors measure the explicit strategy via report (Figure S5E) while they don't use those values for the correlations? This looks like a post-hoc decision to me.

Experiment 2:

– This experiment is based on a small sample size to test for correlations (N=17). What was the objective criterion used to stop data collection at N=17 and not at another sample size? This should be reported.

– This experiment does not decouple implicit and explicit in contrast to what the authors pretend. If the authors believe that the amount of implicit adaptation follows a state-space model, then the measure of early implicit is correlated to the amount of late implicit because Implicit_late = (ai)^N * Implicit_early where N is the number of trials between early and late. Therefore the two measures are not properly decoupled. To decouple them, the authors should use two separate ways of measuring implicit and explicit. To measure explicit, they could use aim report (Taylor, Krakauer and Ivry 2011) and to measure implicit independently, they could use the after-effect by asking the participants to stop aiming as done here. They actually have done so in experiment 1 but did not use these values.

Figure 4:

– Data from the last panel of Figure 4B (line 321-333) should be analyzed with a 2x2 ANOVA and not by a t-test if the authors want to make the point that the learning differences were higher in high PT than low PT trials (Nieuwenhuis et al., Nature Neuroscience, 2011).

– Lines 329-330: the authors should demonstrate that the explicit strategy is actually suppressed by measuring it via report. It is possible that limiting PT reduces the explicit strategy but it might not suppress it. Therefore, any remaining amount of explicit strategy could be subject to savings.

– Coltman and Gribble (2019) demonstrated that fitting state-space models to individual subject's data was highly unreliable and that a bootstrap procedure should be preferred. Lines 344-353: the authors should replace their t-tests with permutation tests in order to avoid fitting the model to individual subject's data.

– It is unclear how the error sensitivity parameters analysed in Figure 4D were obtained. I can follow in the Results section but there is basically nothing on this in the methods. This needs to be expanded.

– The authors make the assumption that the amount of implicit adaptation is the same for the high PT target and for the low PT target. What is the evidence that this assumption is reasonable? Those two targets are far apart while implicit adaptation only generalizes locally. Furthermore, low PT target is visited 4 times less frequently than the high PT target. The authors should redo the experiment and should measure the implicit component for the high PT trials to make sure that it is related to the implicit component for the low PT trials.

– I don't understand why the authors illustrated the results from line 344-349 on Figure 4D and not the results of the following lines, which are also plausible. By doing so, the authors biased the results in favor of their preferred hypothesis. This figure is by no means a proof that the competition hypothesis is true. It shows that "if" the competition hypothesis is true, then there are surprising results ahead. The authors should do a better job at explaining that both models provide different interpretation of the data.

Figure 5: This figure also represent a biased view of the results (like Figure 4D). The competition hypothesis is presented in details while the alternative hypothesis is missing. How would the competition map look like with separate errors, especially when taking into account that the SPE (and implicit adaptation) is anchored at the aiming direction (generalization)?

Figure 6:

This figure is compatible with the fact that limiting PT on all trials is not efficient to suppress explicit adaptation, at least less so than doing it on 20% of the trials (see McDougle et al. 2019 for why this is the case) and that the remaining explicit adaptation leads to savings.

– I don't understand why the authors did not measure implicit (and therefore explicit adaptation) directly in these experiment like they did in experiment 2. This would have given the authors a direct readout of the implicit component of adaptation and would have validated the fact that limiting PT might be a good way to suppress explicit adaptation. Again, this proof is missing in the paper.

– Experiment 3 is based on a very limited number of participants (N=10!). No individual data are presented.

– Data from Figure 6C should be analyzed with an ANOVA and an interaction between the factor experiment (Haith vs. experiment 3) and block (1 vs. 2) should be demonstrated to support such conclusion (Nieuwenhuis et al. 2011).

Figure 7:

The data contained in this figure suffer from the same limitations as in the previous graphs: limiting PT does not exclude explicit strategy, sample size is small (N=10 per group), no direct measure of implicit or explicit is provided.

– In addition, no statistical tests are provided beyond the two stars on the graph. The data should be analyzed with an ANOVA (Nieuwenhuis et al. 2011).

– The number of participants per group is never provided (N=20 for both groups together).

– It is unclear to me how this result contributes to the dissociation between the separate and shared error models.

Figure 8:

The whole explanation here seems post-hoc because none of the two models actually account for this data. The authors had to adapt the model to account for this data. Note that despite that, the model would fail to explain the data from Kim et al. 2018 that represents a very similar task manipulation.

– Line 463-467: the authors claim equivalence based on a non-significant p-value (Altman 1995). Given the small effect size, they don’t have any power to detect effects of small or medium size. They cannot conclude that there is no difference. They can only conclude that they don’t have enough power to detect a difference. As a result, it does NOT suggest that implicit adaptation was unaltered by the changes in explicit strategy.

– In Mazzoni and Krakauer, the aiming direction was neither controlled nor measured. As a result, given the appearance of a target error with training, it is possible that the participants aimed in the direction opposite to the target error in order to reduce it. This would have reduced the apparent increase in implicit adaptation. The authors argue against this possibility based on the 47.8{degree sign} change in hand angle due to the instruction to stop aiming. I remained unconvinced by this argument as I would like to get more info about this change (Mean, SD, individual data). Furthermore, it is unclear what the actual instructions were. Asking to stop aiming or asking to bring one’s invisible hand on the primary target will have different effects on the change in hand angle.

– The data during the washout period suffers from the fact that the participants from the no-strategy group were not told to stop aiming. The hypothesis that they did use an explicit strategy could explain why the difference between the two groups rapidly vanishes. In other words, if the authors want to use this experiment to demonstrate support any of their hypotheses, they should redo it properly by telling the participants to stop using any explicit strategy at the start of the washout period to make sure that the after-effect is devoid of any explicit strategy.

– It is unclear whether the data from Taylor and Ivry (2011) are in favor of one of the models as the separate and shared error models are not compared.

Discussion: it is important and positive that the authors discuss the limitation of their approach but I feel that they dismiss potential limitations rather quickly even though these are critical for their conclusions. They need to provide new data to prove those points rather than arguments.

On limiting PT (lines 605-615):

The authors used three different arguments to support the fact that limiting PT suppresses explicit strategy.

– Their first argument is that Haith did not observe savings in low PT trials. This is true but Haith only used low PT trials (with a change in target) on 20% of the trials. Restricting RT together with a switch in target location is probably instrumental in making the caching of the response harder. This is very different in the experiments done by the authors. In addition, one could argue that Haith et al. did not find evidence for savings but that these authors had limited power to detect a small or medium effect size (their N=12 per group). I agree that savings in low PT trials is smaller than in high PT trials but is savings completely absent in low PT trials? Figure 6H shows that learning is slightly better on block 2 compared to block 1. N=12 is clearly insufficient to detect such a small difference.

– Their second argument is that they used four different targets. McDougle et al. demonstrated caching of explicit strategy without RT costs for two targets and impossibility to do so for 12 targets. The authors could use the experimental design of McDougle if they wanted to prove that caching explicit strategies is impossible for four targets. I don't see why you could cache strategies without RT cost for 2 targets but not for 4 targets. This argument in not convincing.

– The last argument of the authors is that they imposed even shorter latencies (200ms) than Haith (300ms). Yet, if one can cache explicit strategies without reaction time cost, it does not matter whether a limit of 200 or 300ms is imposed as there is no RT cost.

On Generalization (line 678-702).

How much does the amount of implicit adaptation decays with increasing aiming direction? Above, I argued that the data from Day et al. would predict a negative correlation between the explicit and the implicit components of adaptation and a decrease in implicit adaptation with increasing rotation size. The authors clearly disagree on the basis of four arguments. None of them convinced me.

– First, they estimate this decrease to be only 5{degree sign} based on these two papers (FigS5A and B but 5C shows ~10{degree sign}). This seems to be a very conservative estimate as Day et al. reported a 10{degree sign} reduction in after-effects for 40{degree sign} of aiming direction (see their Figure 7). An explicit component of 40{degree sign} was measured by Neville and Cressman for a 60{degree sign} rotation. The 10{degree sign} reduction based on a 40{degree sign} explicit strategy fits perfectly with data from Figure 1G (black bars) and Figure 2F. Off course, the experimental conditions will influence this generalization effect but this should push the authors to investigate this possibility rather than to dismiss it because the values do not precisely match. How close should it match to be accepted?

– Second, it is unclear how this generalization changes with the number of targets (argument on lines 687-689). This has never been studied and cannot be used as an argument based on further assumptions. Furthermore, I am not sure that the generalization would be so different for 2 or 4 targets.

– Third, the authors measured the explicit strategy in experiment 1 via report in a very different way than what is usually used by the authors as the participants do not have to make use of them. It seems to be suboptimal as the authors did not use them for their correlation on Figure 3H and the difference reported in Figure S5E is tiny (no stats are provided) but is based on a very limited number of participants with no individual data to be seen. If it is suboptimal for Figure 3H why is it sufficient as an argument?

– Fourth, when interpreting the data of Neville and Cressman (line 690-692), the authors mention that there were no differences between the three targets even though two of them corresponded to aim directions for other targets. As far as I can tell, the absence of difference in implicit adaptation across the three targets is not mentioned in the paper by Neville and Cressman as they collapsed the data across the three targets for their statistical analyses throughout the paper. In addition, I don't understand why we should expect a difference between the three targets. If the SPE and the implicit process are anchored to the aiming direction and given that the aiming direction is different for the three targets, I would not expect that the aiming direction of a visible target would be influenced by the fact that, for some participants, this aiming direction corresponds to the location of an invisible target.

– Finally, the authors argue here about the size of the influence of the generalization effect on the amount of implicit adaptation. They never challenge the fact that the anchoring of implicit adaptation on the aiming direction and the presence of a generalization effect (independently of its size) leads to a negative correlation between the implicit and explicit component of adaptations (their Figure 3) without any need for the competition model.

Final recommendations

– The authors should perform an unbiased analysis of a model that include separate error sources, the generalization effect and a saturation of implicit adaptation with increasing rotation size. In my opinion, such model would account for almost all of the presented results.

– They should redo all the experiments based on limited preparation time and should include direct measures of implicit or/and explicit strategies (for validation purposes). This would require larger group size.

– They should replicate the experiments where they need a measure of after-effect devoid of any explicit strategies as this has only become standard recently (experiment for Figure 2 and Figure 8). Not that for Figure 8, they might want to measure the explicit aim during the adaptation period as well.

[Editors’ note: further revisions were suggested prior to acceptance, as described below.]

Thank you for resubmitting your work entitled "Competition between parallel sensorimotor learning systems" for further consideration by eLife. Your revised article has been evaluated by Michael Frank (Senior Editor) and a Reviewing Editor.

The manuscript has been improved but there are some remaining issues that need to be addressed, as outlined below:

One review raised the concern about Experiment 1, which presented perturbations with increasing rotation size and elicited larger implicit learning than the abrupt perturbation condition. However, this design confounded the condition/trial order and the perturbation size. The other concern is the newly added non-monotonicity data set from Tsay's study. On the one hand, the current paper states that the proposed model might not apply to error clamp learning; on the other hand, this part of the results was "predicted" by the model squarely. Thus, can it count as evidence that the proposed model is parsimonious for all visuomotor rotation paradigms? This message must be clearly stated with a special reference to error-clamp learning.

Please find the two reviewers' comments and recommendations below, and I hope this will be helpful for revising the paper.

Reviewer #1:

The present study investigates how implicit and explicit learning interacts during sensorimotor adaptation, especially the role of performance or target error during this interaction. It is timely for the area that needs a more mechanistic model to explain diverse findings accumulated in recent years. The revision has addressed previous major concerns and provided extra data that supports the idea that implicit and explicit processes compete for a common target error for a large proportion of studies in the area. The paper is thoughtfully organized and convincingly presented (though a bit too long), including a variety of data sets.

As a repeal submission, the current work has successfully addressed previous major concerns:

1) Direct evidence for supporting the competition model is lacking.

The revision added new evidence that total learning is negatively correlated with implicit learning but positively correlated with explicit learning (Figure 4G and H). This part of the data argues against the alternative SPE model and provides direct support to the competition model. The added appendix 3 also includes other studies' data sets to strengthen the supports.

Furthermore, Experiment1 is new with an incremental perturbation to decrease rotation awareness and thus provides new support for the model. This also helps to address the previous concern that the data from Saijo and Gomi is not clean enough due to a lack of stop-aiming instruction during the measurement of implicit learning. The other not-so-clean data set from Fernadez-Ruiz is removed from the main text in the revision. Putting together, these new data sets and analysis results constitute a rich set of direct supports that address the biggest concern in the previous submission.

2) Lack of testing alternative models.

The revision tested an alternative idea that explicit learning compensates for the variation in implicit learning instead of the other way around as in their competition model (Figure 4). It also tested an alternative model based on the generalization of implicit learning anchored on the aiming direction (Figure 5). The evidence is clear: both alternative models failed to capture the data.

3) The limited preparation time appears not to exclude explicit learning.

This concern was raised by all previous reviewers. The reviewers also pointed out a possible indicator of explicit learning, i.e., a small spurious drop in reaching angle at the beginning of the no-aiming washout phase. The revision provided a new experiment to show that the small drop is most likely due to a time-dependent decay of implicit learning during the 30s instruction period. This new data set (Exp 3) is indeed convincing and important. I am impressed with the authors' thoughtful effort to explain this subtle and tricky issue.

In sum, I believe the revision did an excellent job of addressing all previous major concerns with more data, more thorough analysis, and more model comparisons. Here I suggest a few minor changes for this revision:

Line 59: the cited papers (17-21) did not all suggest savings resulted from changes of the implicit learning rate, as implied by the context here.

Some references are not in the right format: ref1 states "Journal of Neuroscience," while refs2 and 4 state "The Journal of neuroscience : the official journal of the Society for Neuroscience." Possibly caused by downloads from google scholar. Please keep it consistent.

Line66: replace the semicolon with a comma. Also, is citation 9 about showing a dominant role of SPE?

Figure 1H: it appears the no-aiming trials were at the end of each stepwise period, but in the Methods, it is stated that these trials appeared twice (at the middle and the end). Which version is true?

L1331: why use bootstrapping here? Why not simply fit the model to individual subjects (given n = 37 here)? Interestingly, when comparing 60-degree stepwise vs. 60-degree abrupt, a direct fit to individuals was used… In the Results, it is stated that a single parameter can parsimoniously "predict" the data. But in the Methods, it is clear that all data were used to "fit" the parameter p_i. Can we call this a prediction, strictly? Is it possible to fit a partial data set to show the same results? Not through bootstrapping but through using, say, two stepwise phases? This type of prediction has been done for Exp2, but not here.

Line 195: the authors ruled out the potential bias caused by the interdependence between implicit and explicit learning as one was obtained from subtracting the other from the total learning. By rearranging the model (Equation4) to have the implicit learning as a function of total learning (as opposed to explicit learning), and by showing the model prediction would not change after this re-arrangement, the authors tried to argue that the modeling results are not free from the inter-dependence of two types of learning. I think that this argument aims for the wrong target. The real concern is that implicit and explicit learning are not independently measured, which is true no matter how the model equation is arranged. The prediction of the rearranged model, of course, would provide the same model prediction since this does not change the model at all, given the inter-dependence of variables. All the data in Figure 1 have this problem. It is a data problem, not a model problem. And, the data refute the alternative, independent model, that is. There is no need to re-arrange the model without solving the problem in data.

The authors added the data set from Tsay et al. to Part 1, which shows a non-monotonic change of implicit learning with increasing rotation. However, this is only one version of their data set obtained by the online platform; the other version of the same experiment conducted in person shows a different picture with constant implicit learning over different rotations. Any particular reason to report one version instead of the other? Here owes an explanation to the readers.

Line 203: dual model -> competition model

Line463: "that the x-axis in Figures 5A-C slightly overestimates explicit strategy", the axis overestimates…

Line 496: this paragraph starts with a why question (why the competition model works better), but it does not address the question but shows it works better.

Figure 6C: not clear what the right panel is without axis labeling and a detailed description in the caption.

Line 563: the family dinner story is interesting and naughty, but our readers might not need it, especially when the paper is already long. I suggest removing it and starting this section with the burning question of why the implicit error sensitivity changes without the changes of implicit learning size.

Line 589: what is Timepoint 1 and 2, never mentioned before or in the figure. It is also confusing with a capital T.

Figure 7C: it would make much better sense to plot total learning in C along with the implicit and explicit learning.

L595: the data presented before in Figures2 are explained in this map illustration. Enhancing or suppressing explicit learning has been conceptualized as moving along the y-axis without changing the implicit error sensitivity. Retrospectively, this is also the case when the model is fitted to these data by assuming a constant implicit learning rate in previous figures. Is there any evidence to support this assumption for model fitting, or can we safely claim varying implicit learning rates could not account for the data better than otherwise?

L685: we observe implicit learning is suppressed as a result of anterograde interference. Without preparation time constraints, the impairment in implicit learning is less. Is there any way to compare their respectively implicit error sensitivity? This would give us some information about how explicit learning compensates.

Figure 10G: the conceptual framework is speculative. It is fine to discuss the possible neurophysiological underpinnings in the Discussion as it currently stands. But we are better off removing it from the Results.

Reviewer #4:

In this paper, Albert et al. test a novel model where explicit and implicit motor adaptation processes share an error signal. Under this error sharing scheme, the two systems compete – that is, the more that explicit learning contributes to behavior, the less that implicit adaptation does. The authors attempt to demonstrate this effect over a variety of new experiments and a comprehensive re-analysis of older experiments. They contend that the popular model of SPEs exclusively driving implicit adaptation (and implicit/explicit independence) does not account for these results. Once target error sensitivity is included into the model, the resulting competition process allows the model to fit a variety of seemingly disparate results. Overall, the competition model is argued to be the correct model of explicit/implicit interactions during visuomotor learning.

I'm of two minds on this paper. On the positive side, this paper has compelling ideas, a laudable breadth and amount of data/analyses, and several strong results (mainly the reduced-PT results). It is important for the motor learning field to start developing a synthesis of the 'Library of Babel' of the adaptation literature, as is attempted here and elsewhere (e.g., D. Wolpert lab's 'COIN' model). On the negative side, the empirical support feels a bit like a patch-work – some experiments have clear flaws (e.g., Exp 1, see below), others are considered in a vacuum that dismisses previous work (e.g., nonmonotonicity effect), and many leftover mysteries are treated in the Discussion section rather than dealt with in targeted experiments. While some of the responses to the previous reviewers are effective (e.g., showing that reduced PT can block strategies), others are not (e.g., all of Exp 1, squaring certain key findings with other published conflicting results, the treatment of generalization). The overall effect is somewhat muddy – a genuinely interesting idea worth pursuing, but unclear if the burden of proof is met.

(1) The stepwise condition in Exp 1 is critically flawed. Rotation size is confounded with time. It is unclear – and unlikely – that implicit learning has reached an asymptote so quickly. Thus, the scaling effect is at best significantly confounded, and at worst nearly completely confounded. I think that this flaw also injects uncertainty into further analyses that use this experiment (e.g., Figure 5).

(2) It could be argued that the direct between-condition comparison of the 60° blocks in Exp 1 rescues the flaw mentioned above, in that the number of completed trials is matched. However, plan- or movement-based generalization (Gonzalez Castro et al., 2011) artifacts, which would boost adaptation at the target for the stepwise condition relative to the abrupt one, are one way (perhaps among others) to close some of that gap. With reasonable assumptions about the range of implicit learning rates that the authors themselves make, and an implicit generalization function similar to previous papers that isolate implicit adaptation (e.g., σ around ~30°), a similar gap could probably be produced by a movement- or plan-based generalization model. [I note here that Day et al., 2016 is not, in my view, a usable data set for extracting a generalization function, see point 4 below.]

(3) The nonmonotonicity result requires disregarding the results of Morehead at al., 2017, and essentially, according to the rebuttal, an entire method (invariant clamp). The authors do mention and discuss that paper and that method, which is welcome. However, the authors claim that "We are not sure that the implicit properties observed in an invariant error context apply to the conditions we consider in our manuscript." This is curious and raises several crucial parsimony issues, for instance: the results from the Tsay study are fully consistent with Morehead 2017. First, attenuated implicit adaptation to small rotations (not clamps; Morehead Figure 5) could be attributed to error cancellation (assuming aiming has become negligible to nonexistent, or never happened in the first place). This (and/or something like the independence model) thus may explain the attenuated 15° result in Figure 1N. Second, and more importantly, the drop-off of several degrees of adaptation from 30°/60° to 90° in Figure 1N is eerily similar to that seen in Morehead '17. Here's what we're left with: An odd coincidence whereby another method predicts essentially these exact results but is simultaneously (vaguely) not applicable. If the authors agree that invariant clamps do limit explicit learning contributions (see Tsay et al. 2020), it would seem that similar nonmonotonicity being present in both rotations and invariant error-clamps works directly against the competition model. Moreover, it could be argued that the weakened 90˚ adaptation in clamps (Morehead) explains why people aim more during 90° rotations. A clear reason, preferably with empirical support, for why various inconvenient results from the invariant clamp literature (see point 6 for another example) are either erroneous, or different enough in kind to essentially be dismissed, is needed.

(4) The treatment given to non-target based generalization (i.e., plan/aim) is useful and a nice revision w/r/t previous reviewer comments. However, there are remaining issues that muddy the waters. First, it should be noted that Day et al. did not counterbalance the rotation sign. This might seem like a nitpick, but it is well known that intrinsic biases will significantly contaminate VMR data, especially in e.g. single target studies. I would thus not rely on the Day generalization function as a reasonable point of comparison, especially using linear regression on what is a Gaussian/cosine-like function. It appears that the generalization explanation is somewhat less handicapped if more reasonable generalization parameterizations are considered. Admittedly, they would still likely produce, quantitatively, too slow of a drop-off relative to the competition model for explaining Exps 2 and 3. This is a quantitative difference, not a qualitative one. W/r/t point 1 above, the use of Exp 1 is an additional problematic aspect of the generalization comparison (Figure 5, lower panels). All in all, I think the authors do make a solid case that the generalization explanation is not a clear winner; but, if it is acknowledged that it can contribute to the negative correlation, and is parameterized without using Day et al. and linear assumptions, I'd expect the amount of effect left over to be smaller than depicted in the current paper. If the answer comes down to a few degrees of difference when it is known that different methods of measuring implicit learning produce differences well beyond that range (Maresch), this key result becomes less convincing. Indeed, the authors acknowledge in the Discussion a range of 22°-45° of implicit learning seen across studies.

(5) I may be missing something here, but is the error sensitivity finding reported in Figure 6 not circular? No savings is seen in the raw data itself, but if the proposed model is used, a sensitivity effect is recovered. This wasn't clear to me as presented.

(6) The attenuation (anti-savings) findings of Avraham et al. 2021 are not sufficiently explained by this model.

(7) Have the authors considered context and inference effects (Heald et al. 2020) as possible drivers of several of the presented results?

[Editors’ note: The authors appealed the original decision. What follows is the authors’ response to the first round of review.]

Concerns:

1. There is no clear testing of alternative models. After Figure 1 and 2, the paper goes on with the competition model only. The independent model will never be able to explain differences in implicit learning for a given visuomotor rotation (VMR) size, so it is not a credible alternative to the competition model in its current form. It seems possible that extensions of that model based on the generalization of implicit learning (Day et al. 2106, McDougle et al. 2017) or task-dependent differences in error sensitivity could explain most of the prominent findings reported here. We hope the authors can show more model comparison results to support their model.

Two studies have measured generalization in rotation tasks with instructions to aim directly at the target (Day et al., 2016; McDougle et al., 2017) and have demonstrated that learning generalizes around one’s aiming direction, as opposed to the target direction. As the reviewers note, this generalization rule can contribute to the negative correlation we observed between explicit learning and exclusion-based implicit learning. To address this, in our revised manuscript we directly compare the competition model to an alternative SPE generalization model. Our new analysis is documented in Figure 4 in the revised manuscript. First, we empirically compare the relationship between implicit and explicit learning in our data to generalization curves measured in past studies. In Figures 4A-B we overlay data that we collected in Experiments 2 and 3 with generalization curves measured by Krakauer et al. (2000) and Day et al. (2016). In this way, we test whether generalization is consistent with the correlations between implicit and explicit learning that we measured in our experiments.

In Figures 4B,C, we show dimensioned (i.e., in degrees) relationships between implicit and explicit learning. In Figure 4A, we show a dimensionless implicit measure in which implicit learning is normalized to its “zero strategy” level. To estimate this value, we used the y-intercepts in the linear regressions labeled “data” in Figures 3G and Q. Most notably, the magenta line (Day 1T) shows the aim-based generalization curve measured by Day et al. (2016), where assays were used to tease apart implicit and explicit learning.

These new results demonstrate that implicit learning in Experiments. 2 and 3 (black and brown points) declined about 300% more rapidly with increases in explicit strategy, than predicted by generalization measured by Day et al. (2016). Two empirical considerations would also suggest that the discrepancy between our data and the Day et al. (2006) generalization curve is even larger than that observed in Figures 4A-B.

1. Day et al. (2006) use 1 adaptation target, whereas our tasks used 4 targets. Krakauer et al. (2000) demonstrated that the generalization curve widens with increases in target number (see Figure 4AC). Thus, the Day et al. (2006) study data likely overestimate the extent of generalization-based decay in implicit learning expected in our experimental conditions.

Our “explicit angle” in Figures 4A-B is calculated by subtracting total adaptation and exclusion-based implicit learning. Thus, under the plan-based generalization hypothesis, this measure would overestimate explicit strategy. A generalization-based correction would “contract” our data along the x-axis in Figures 4C-E, increasing the disconnect between our results and the generalization curves. To demonstrate this, we conducted a control analysis where we corrected our explicit measures according to the Day et al. generalization curve (see Appendix 4 in revised manuscript). Our results are shown in Figure . As predicted, correcting explicit measures yielded a poorer match between the data and generalization hypothesis (see discrepancy below each inset).

These analyses show that the alternative hypothesis of plan-based generalization is inconsistent with our measured data, though it could make minor contributions to the relationships we report between implicit and explicit learning (analysis shown on Section 2.2., Lines 442-468 in revised manuscript).

These analyses have relied on an empirical comparison between our data and past generalization studies. But we can also demonstrate mathematically that the implicit and explicit learning patterns we measured are inconsistent with the generalization hypothesis. First, recall that the competition equation states that steady-state implicit learning varies inversely with explicit strategy according to (Equation 4):

We can condense this equation by defining an implicit proportionality constant, p:${\displaystyle x_i^{\text{ss}}=pr-{\text{px}}_e^{\text{ss}},wherep=\frac{b_i}{1-a_i+b_i}}$

These new data provide a way to directly compare the competition model to an SPE generalization model. The key prediction, again, is to test how the relationship between implicit and explicit learning varies with the rotation’s magnitude. To do this, we calculated the implicit proportionality constant (p above) in the competition model and the SPE generalization model, that best matched the measured implicit-explicit relationship. We calculated this value in the 60° learning block alone, holding out all other rotation sizes. We then used this gain to predict the implicit-explicit relationship across the held-out rotation sizes. The competition model is shown in the solid black line in Figure 5D. The Day et al. (2016) generalization model is shown in the gray line. The total prediction error across the held-out 15°, 30°, and 45° rotation periods was two times larger in the SPE generalization model (Figure 4E, repeated-measures ANOVA, F(2,35)=38.7, p<0.001, η_p²=0.689; post-hoc comparisons all p<0.001). Issues with the SPE generalization model were not caused by misestimating the generalization gain, m. We fit the SPE generalization model again this time allowing both π and m to vary to best capture behavior in the 60° period (Figure 4D, SPE gen. best B4). This optimized model generalized very poorly to the held-out data, yielding a prediction error three times larger than the competition model (Figure45D, SPE gen best B4).

To understand why the competition model yielded superior predictions, we fit separate linear regressions to the implicit-explicit relationship measured during each rotation period. The regression slopes and 95% CIs are shown in Figure 4F (data). Remarkably, the measured implicit-explicit slope appeared to be constant across all rotation magnitudes in agreement with the competition theory (Figure 4H, competition). These measurements sharply contrasted with the SPE generalization model, which predicted that the regression slope would decline as the rotation magnitude decreased.

In summary, data in Experiment 1 were poorly described by an SPE learning model with aim-based generalization. While generalization may add to the correlations between implicit and explicit learning, its contribution is small relative to the competition theory. New analyses are described in Section 2.2 in the revised paper.

These analyses all considered how a negative relationship between implicit and explicit learning could emerge due to generalization (as opposed to competition). In our revised work, we consider an additional mechanism by which this inverse relationship could occur. Suppose that implicit learning is driven solely by SPEs as in earlier models. In this case, implicit learning should be immune to changes in explicit strategy. However, a participant that has a better implicit learning system will require less explicit re-aiming to reach a desired adaptation level. In other words, individuals with large SPE-driven learning may use less explicit strategy relative to those with less SPE-driven implicit learning. Like the competition model, this scenario would also yield a negative relationship between implicit and explicit learning, due to the way explicit strategies respond to variation in the implicit system. In other words, the competition equation supposes that the implicit-explicit relationship arises because the implicit system responds to variability in explicit strategy. An SPE learning model supposes that the implicit-explicit relationship arises because the explicit system responds to variability in implicit learning.

To model the latter possibility, suppose that the implicit system responds solely to an SPE. Total implicit learning is given by (Equation 5), and can be re-written as x_i^ss = p_ir, where π is a gain that depends on implicit learning properties (a_i and b_i). Thus, implicit learning is centered on p_ir, but varies according to a normal distribution: x_i^ss = N(p_ir,σ_i²) where σ_i represents the standard deviation in implicit learning. The target error that remains to drive explicit strategy is equal to the rotation minus implicit adaptation: r – x_i^ss. A negative relationship between implicit and explicit strategy will occur when explicit strategy responds in proportion to this error, x_e^ss = p_e(r – x_i^ss) where p_e is the explicit system’s response gain.

Overall, this model predicts important pairwise relationships between implicit learning, explicit strategy, and total adaptation (equations provided on Lines 1577-1620 in paper, and also in Figure 4). First, as noted implicit learning and explicit adaptation will show a negative relationship. Second, increases in implicit learning will tend to increase total adaptation. These increases in implicit learning will leave smaller errors to drive explicit learning, resulting in a negative relationship between explicit strategy and total learning. Figures 5A-C illustrate these pairwise relationships in our revised manuscript.

How do these relationships compare to the competition equation, in which implicit learning is driven by target errors? Suppose that participants choose a strategy that scales with the rotation’s size according to p_er (p_e is the explicit gain) but varies across participants (standard deviation, σ_e). Thus, x_e^ss is given by a normal distribution N(p_er,σ_e²). The target error which drives implicit learning is equal to the rotation minus explicit strategy. The competition theory proposes that the implicit system is driven in proportion to this error according to: x_i^ss = p_i(r – x_e^ss), where π is an implicit learning gain that depends on implicit learning parameters a_i and b_i (see Equation 4). This model will produce a negative correlation between implicit learning and explicit strategy. People that use a larger strategy will exhibit greater total learning. Simultaneously, increases in strategy will leave smaller errors to drive implicit learning, resulting in a negative relationship between implicit learning and total learning. These 3 predictions are illustrated in Figures 5D-F in our revised manuscript; these relationships correspond to linear equations which are provided on Lines 1577-1620 in paper, and also in Figure 5.

In sum, both an SPE learning model and a target error learning model could exhibit negative participant level correlations between implicit learning and explicit learning (Figures 5A and 5D). However, they make opposing predictions concerning the relationships between total adaptation and each individual learning system. To test these predictions, we considered how total learning was related to implicit and explicit adaptation measured in the No PT Limit group in Experiment 3. These data are now show in Figures 5GandH in our revised work.

Our observations closely agreed with the competition theory; increases in explicit strategy led to increases in total adaptation (Figure 5G, ρ=0.84, p<0.001), whereas increases in implicit learning were associated with decreases in total adaptation (Figure 5H, ρ=-0.70, p<0.001). We repeated similar analyses across additional data sets which also measured implicit learning via exclusion (i.e., no aiming) trials: (1) the 60° rotation condition (combined across gradual and abrupt groups) in Experiment 1, (2) the 60° rotation groups reported by Maresch et al. (2021), and (3) the 60° rotation group described by Tsay et al. (2021). We obtained the same result as in Experiment 3. Participants exhibited negative correlations between implicit learning and explicit strategy, positive correlations between explicit strategy and total adaptation, and negative correlation between implicit learning and total adaptation. These additional results are reported in Figure 5-Supplement 1 in the revised manuscript.

Thus, these additional studies also matched the competition model’s predictions, but rejected the SPE learning model on two accounts: (1) the relationship between implicit learning and total adaptation was negative, not positive as predicted by the SPE model, and (2) the relationship between explicit learning and total adaptation was positive, not negative as predicted by the SPE model.

Our revised manuscript notes an important caveat with this last analysis. Indeed, the competition model predicts on average that implicit learning will exhibit a negative correlation with total adaptation (across individual participants). However, this prediction assumes that implicit learning properties (retention and error sensitivity, the gain p_i above) are identical across participants, an unlikely possibility. Variation in the implicit learning gain (e.g., Participant A has an implicit system that is more sensitive to error) will promote a positive trend between implicit learning and total adaptation, that will weaken the negative correlations generated by implicit-explicit competition. Thus, pairwise correlations between implicit learning, explicit strategy, and total adaptation will vary probabilistically across experiments. While it is critical the reader keep this in mind, a complete investigation of these second-order phenomena is complex and beyond the scope of our work. For this reason, we treat these issues in Appendix 3 in the revised manuscript. Appendix 3 describes several experimental conditions (e.g., variation in explicit strategy across participants, average explicit learning) that will alter the participant-level relationship between implicit and explicit learning.

Summary

In our revised manuscript we compare the competition theory to two alternate models that also yield a negative participant-level relationship between implicit learning and explicit strategy. The first alternate model supposes that implicit learning is driven by SPEs, but is altered by plan-based generalization. The second alternate model supposes that implicit learning is driven by SPEs, but explicit strategies respond to variability in implicit learning across participants.

The generalization model, however, did not match our data:

1. Implicit learning declined 300% more rapidly than predicted by generalization (Figures 4A-C).

2. The implicit-explicit learning relationship did not accurately generalize across rotation sizes in the SPE generalization model (Figures 4DandE).

3. The gain relating implicit and explicit learning remained the same across rotation sizes, rejecting the SPE generalization model, but supporting the competition theory (Figure 4F).

The alternate model where explicit systems respond to subject-to-subject variability in SPE-driven implicit learning did not match our data:

1. We observed a negative relationship between implicit learning and total adaptation in Experiment 3 (Figure 4H) and 3 additional datasets (Figure 4-Supplement 1) as predicted by the competition theory, but in contrast to the SPE learning model.

2. We observed a positive relationship between implicit learning and total adaptation in Experiment 3 (Figure 4G) and 3 additional datasets (Figure 4-Supplement 1) as predicted by the competition theory, but in contrast to the SPE learning model.

Given the importance of these analyses, we devote an entire section (Part 2) of our revised manuscript to comparisons with alternate SPE learning models (Lines 374-504 in revised manuscript). We also describe second-order phenomena in Appendix 3 of our revised manuscript (Lines 2167-2414).

2. The measurement of implicit learning is compromised by not asking participants to stop aiming upon entering the washout period. This happened at three places in the study, once in Experiment 2, once in the re-used data by Fernadez-Ruiz et al., 2011, and once in the re-used data by Mazzoni and Krakauer 2006 (no-instruction group). We would like to know how the conclusion is impacted by the ill-estimated implicit learning.

We agree with the reviewers’ concerns, with one clarification: in Experiment 2 we did instruct participants to stop aiming prior to the no feedback washout period, so this criticism is not relevant to Experiment 2 (note Experiment 2 is now Experiment 3 in the revised work). With that said, this criticism would apply to the Saijo and Gomi (2010) analysis in our original manuscript, which was not noted in the reviewers’ concern. Here, we will address each limitation noted by the reviewers in turn.

Saijo and Gomi (2010)

Let us begin with the Saijo and Gomi (2010) analysis. In our original manuscript, we used conditions tested by Saijo and Gomi to investigate one of the competition theory’s predictions: decreasing explicit strategy for a given rotation size will increase implicit learning. Specifically, we analyzed whether gradual learning suppressed explicit strategy in this study, thus facilitating greater implicit adaptation. While our analysis was consistent with this hypothesis, as noted by the reviewers, there is a limitation; washout trials were used to estimate implicit learning, though participants were not directly instructed to stop aiming. This represents a potential error source. For this reason, in our revised manuscript, we have collected new data to test the competition model’s prediction.

These new data also examine gradual and abrupt rotations. In Experiment 1 (new data in the paper), participants were exposed to a 60° rotation, either abruptly (n=36), or in a stepwise manner (n=37) where the rotation magnitude increased by 15° across 4 distinct learning blocks (Figure 2D). Unlike Saijo and Gomi, implicit learning was measured via exclusion during each learning period by instructing participants to aim directly towards the target. As we hypothesized, in Figure 2F, we now demonstrate that stepwise rotation onset (which yields smaller target errors) muted the explicit response to the rotation (compared to abrupt learning). The competition model predicts that decreases in explicit strategy should facilitate greater implicit adaptation. To test this prediction, we compared implicit learning across the gradual and abrupt groups during the fourth learning block, where both groups experienced the 60° rotation size (Figures 2E and G).

Consistent with our hypothesis, participants in the stepwise condition exhibited a 10° reduction in explicit re-aiming (Figure 2F, two-sample t-test, t(71)=4.97, p<0.001, d=1.16), but a concomitant 80% increase in their implicit recalibration (Figure 2G, data, two-sample t-test, t(71)=6.4, p<0.001, d=1.5). To test whether these changes in implicit learning matched the competition model, we fit the independence Equation (Equation 5) and the competition Equation (Equation 4) to the implicit and explicit reach angles measured in Blocks 14, across the stepwise and abrupt conditions, while holding implicit learning parameters constant. In other words, we asked whether the same parameters (a_i and b_i) could parsimoniously explain the implicit learning patterns measured across all 5 conditions (all 4 stepwise rotation sizes plus the abrupt condition). As expected, the competition model predicted that implicit learning would increase in the stepwise group (Figure 2G, comp., 2-sample t-test, t(71)=4.97, p<0.001), unlike the SPE-only learning model (Figure 2G, indep.).

Thus, in our revised manuscript we present new data that confirm the hypothesis we initially explored in the Saijo and Gomi (2010) dataset: decreasing explicit strategy enhances implicit learning. These new data do not present the same limitation noted by the reviewers. Lastly, it is critical to note that while stepwise participants showed greater implicit learning, their total adaptation was approximately 4° lower than the abrupt group (Figure 2E, right-most gray area (last 20 trials); two-sample t-test, t(71)=3.33, p=0.001, d=0.78). This surprising phenomenon is predicted by the competition equation. When strategies increase in the abrupt rotation group, this will tend to increase total adaptation. However, larger strategies leave smaller errors to drive implicit learning. Hence, greater adaptation will be associated with larger strategies, but less implicit learning. Indeed, the competition model predicted 53.47° total learning in the abrupt group but only 50.42° in the stepwise group. Recall that, we described this paradoxical phenomenon at the individual-participant level in Point 1 above. Note that this pattern was also observed by Saijo and Gomi. Surprisingly, when participants were exposed to a 60° rotation in a stepwise manner, total adaptation dropped over 10°, whereas the aftereffect exhibited during the washout period nearly doubled.

Summary

In our revised paper we have removed this Saijo and Gomi analysis from the main figures, and instead use this as supportive data in Figure 2-Supplement 2, and also in Appendix 2. We now state, “It is interesting to note that these implicit learning patterns are broadly consistent with the observation that gradual rotations improve procedural learning^34,43, although these earlier studies did not properly tease apart implicit and explicit adaptation (see the Saijo and Gomi analysis described in Appendix 2).”

We have replaced this analysis with our new data in Experiment 1. In these new data, abrupt and gradual learning was compared using the appropriate implicit learning measures. These new data are included in both Figures 1 and 2 in the revised manuscript. Importantly, these new data point to the same conclusions we reached in our initial Saijo and Gomi analysis.

Mazzoni and Krakauer (2006)

The reviewers note that the uninstructed group in Mazzoni and Krakauer was not told to stop aiming during the washout period. We agree with the potential error source. However, it is important to note that these data were not included to directly support the competition model, but as a way to demonstrate its limitations. For example, in Mazzoni and Krakauer (2006) our simple target error model cannot reproduce the measured data. That is, in the instructed group implicit learning continued despite eliminating the primary target error. Thus, in more complicated scenarios where multiple visual landmarks are used during adaptation, the learning rules must be more sophisticated than the simple competition theory. Here we showed that one possibility is that both the primary target and the aiming target drive implicit adaptation via two simultaneous target errors. Our goal by presenting these data (and similar data collected by Taylor and Ivry, 2011) was to emphasize that our work is not meant to support an either-or hypothesis between target error and SPE learning, but rather the more pluralistic conclusion that both error sources contribute to implicit learning in a condition-dependent manner.

In our revised manuscript, we now better appreciate this conclusion and its potential limitation in the following passage: “It is important, however, to note a limitation in these analyses. Our earlier study did not employ the standard conditions used to measure implicit aftereffects: i.e., instructing participants to aim directly at the target, and also removing any visual feedback. Thus, the proposed dual-error model relies on the assumption that differences in washout were primarily related to the implicit system. These assumptions need to be tested more completely in future experiments.

In summary, the conditions tested by Mazzoni and Krakauer show that the simplistic idea that adaptation is driven by only one target error, or only one SPE, cannot be true in general⁵⁴. We propose a new hypothesis that when people move a cursor to one visual target, while aiming at another visual target, each target may partly contribute to implicit learning. When these two error sources conflict with one another, the implicit learning system may exhibit an attenuation in total adaptation. Thus, implicit learning modules may compete with one another when presented with opposing errors.”

Fernandez-Ruiz et al. (2011)

As noted by the reviewers, our original manuscript also reported data from a study by Fernandez-Ruiz et al. (2011). Here, we showed that participants in this study who increased their preparation time more upon rotation onset tended to exhibit a smaller aftereffect. We used these data to test the idea that when a participant uses a larger strategy, they inadvertently suppress their own implicit learning. However, we agree with the reviewers that this analysis is problematic because participants were not instructed to stop aiming in this earlier study. Thus, we have removed these data in the revised manuscript. This change has little to no effect on the manuscript, given that individual-level correlations between implicit and explicit learning are tested in Experiments 1, 2, and 3 in the revised paper (Figures 3-5), and are also reported from earlier works (Maresch et al., 2021; Tsay et al., 2021) in Figure 4-Supplements 1GandI, where implicit learning was more appropriately measured via exclusion. Note that all 5 studies support the same ideas suggested by the Fernandez-Ruiz et al. study: increases in explicit strategy suppress implicit learning.

3. All the new experiments limit preparation time (PT) to eliminate explicit learning. In fact, the results are based on the assumption that shortened PT leads to implicit-only learning (e.g., Figure 4). Is the manipulation effective, as claimed? This paradigm needs to be validated using independent measures, e.g., by direct measurement of implicit and/or explicit strategy.

We agree that it is important to test how effectively this condition limits explicit strategy use. Therefore, we have performed two additional control studies to measure explicit strategy in the limited PT condition. First, we added a limited preparation time (Limit PT) group to our laptop-based study in Experiment 3 (Experiment 2 in original manuscript). In Experiment 3, participants in the Limit PT group (n=21) adapted to a 30° rotation but under a limited preparation time condition. As for the Limit PT group in Experiment 2 (Experiment 1 in original paper), we imposed a bound on reaction time to suppress movement preparation time. However, unlike Experiment 2, once the rotation ended, participants were told to stop re-aiming. This permitted us to examine whether limiting preparation time suppressed explicit strategy as intended. Our analysis of these new data is shown in Figures 3K-Q.

In Experiment 3, we now compare two groups: one where participants had no preparation time limit (No PT Limit, Figures 3H-J) and one where an upper bound was placed on preparation time (Limit PT, Figures 3K-M). We measured early and late implicit learning measures over a 20-cycle no feedback and no aiming period at the end of the experiment. The voluntary decrease in reach angle over this no aiming period revealed each participant’s explicit strategy (Figure 3N). When no reaction time limit was imposed (No PT Limit), reaiming totaled approximately 11.86° (Figure 3N, E3, black), and did not differ statistically across Experiments 2 and 3 (t(42)=0.50, p=0.621). Recall that Experiment 2 tested participants using a robotic manipulandum and Experiment 3 tested participants in a similar laptop-based paradigm. As in earlier reports, limiting reaction time dramatically suppressed explicit strategy, yielding only 2.09° of re-aiming (Figure 3N, E3, red). Therefore, our new control dataset suggests that our limited reaction time technique was highly effective at suppressing explicit strategy as initially claimed in our original manuscript.

Since we have now demonstrated that limiting PT is effective at suppressing explicit strategy, we use our new Limit PT group in Experiment 3, to corroborate several key competition model predictions. First, consistent with the competition model, suppressing explicit strategy increased implicit learning by approximately 40% (Figure 3O, No PT Limit vs. Limit PT, two-sample t-test, t(54)=3.56, p<0.001, d=0.98). Second, we used the Limit PT group’s behavior in Experiment 3 to estimate implicit learning parameters (a_i and b_i) as we did in Experiment 1 (now Experiment 2) in our original manuscript. Briefly, the implicit retention factor was estimated during the no feedback and no aiming period, and the implicit error sensitivity was estimated via trial-to-trial changes in reach angle during the rotation period. We used these parameters to specify the unknown implicit learning gain in the competition model (p_i described in Point 1 above). Limit PT group behavior predicted that implicit and explicit learning should be related by the following competition model: x_i = 0.63(30 – x_e). As in Experiment 2, we observed a striking correspondence between this model prediction (Figure 3Q, bottom, model) and the actual implicit-explicit relationship measured across participants in the No PT Limit group (Figure 3Q, bottom, points). The slope and bias predicted by Equation 4 (-0.67 and 20.2°, respectively) differed from the measured linear regression by less than 8% (Figure 3Q, bottom brown line, R²=0.78; slope is -0.63 with 95% CI [-0.74, -0.51] and intercept is 19.7° with 95% CI [18.2°, 21.3°]).

With that said, our new data alone suggest that while explicit strategies are strongly suppressed by limiting preparation time, they are not entirely eliminated; when we limited preparation time in Experiment 3, we observed that participants still exhibited a small decrease (2.09°) in reach angle when we instructed them to aim their hand straight to the target (Figure 3L, no aiming; Figure 3N, E3, red). This ‘cached’ explicit strategy, while small, may have contributed to the 8° reach angle change measured early during the second rotation in our savings experiment (Experiment 4, Figure 8C in revised paper).

For this reason, we consider another important phenomenon in our revised manuscript: time-dependent decay in implicit learning. That is, the 2° decrease in reach angle we observed when participants were told to stop aiming in the PT Limit group in Experiment 3 may be due to time-based decay in implicit learning over the 30 second instruction period, as opposed to a voluntary reduction in strategy. To test this possibility, we tested another limited preparation group (n=12, Figure 8-Supplement 1A, decay-only, black). But this time, participants were instructed that the experiment’s disturbance was still on, and that they should continue to move the ‘imagined’ cursor through the target during the terminal no feedback period. Still, reach angles decreased by approximately 2.1° (Figure 8-Supplement 1B, black). Indeed, we detected no statistically significant difference between the change in reach angle in this decay-only condition, and the Limit PT group in Experiment 3 (Figure 8-Supplement 1B; two-sample t-test, t(31)=0.016, p=0.987).

This control experiment suggested that residual ‘explicit strategies’ we measured in the Limit PT condition, were in actuality caused by time-dependent decay in implicit learning. Thus, our Limit PT protocol appears to almost entirely eliminate explicit strategy. This additional analysis lends further credence to the hypothesis that savings in Experiment 4, was primarily due to changes in the implicit system rather than cached explicit strategies (and also that the impairment in learning observed in Experiment 5, was driven by the implicit system).

Summary

We collected additional experimental conditions in Experiment 3 in the revised manuscript (a Limit PT group and a decay-only group). Data in the Limit PT condition suggested that explicit strategies are suppressed to approximately 2° by our preparation time limit (compared to about 12° under normal conditions). Data in the decay-only group suggest that this 2° change in reach angle was not due to a cached explicit strategy but rather time-dependent implicit decay. Together, these conditions demonstrate that limiting reaction time in our experiments prevents the caching of explicit strategies; our limited preparation time measures do indeed reflect implicit learning.

4. Related to point 3, it is noted that the aiming report produced a different implicit learning estimate than a direct probe in Exp1 (Figure S5E). However, Figure 3 only reported Exp1 data with the probe estimate. What would the data look like with report-estimated implicit learning? Will it show the same negative correlation results with good model matches (Figure 3H)?

We ended Experiment 2 (Experiment 1 in the original manuscript) by asking participants to verbally report where they remembered aiming in order to hit the target. While many studies use similar reports to tease apart implicit and explicit strategy (e.g., McDougle et al., 2015), our probe had important limitations. Normally, participants are probed at various points throughout adaptation by asking them to report where they plan to aim on a given trial, and then allowing them to execute their reaching movement (thus they are able to continuously evaluate and familiarize themselves with their aiming strategy over time). However, we did not use this reporting paradigm given recent evidence (Maresch et al., 2020) that reporting explicit strategies increases explicit strategy use, which we expected would have the undesirable consequence of suppressing implicit learning (given the competition theory). Thus, in Experiment 2, reporting was measured only once; participants tried to recall where they were aiming throughout the experiment.

This methodology may have reduced the reliability in this measure of explicit adaptation. As stated in our Methods, we observed that participants were prone to incorrectly reporting their aiming direction, with several reported angles in the perturbation’s direction, rather than the compensatory direction. In fact, 25% of participant responses were reported in the incorrect direction. Thus, as outlined in our Methods, we chose to take the absolute value of these measures, given recent evidence that strategies are prone to sign errors (McDougle and Taylor, 2019). That is, we assumed that participants remembered their aiming magnitude, but misreported the orientation. In sum, we suspect that our report-based strategy measures are prone to inaccuracies and opted to interpret them cautiously and sparingly in our original manuscript.

Nevertheless, in the revised manuscript, we now also report the individual-level relationships between report-based implicit learning and report-based explicit strategy in Experiment 2 (previously Experiment 1). These are now illustrated in Figure 3-Supplement 2C. While reported explicit strategies were on average greater than our probe-based measure, and report-based implicit learning was smaller than our probe-based measure (Figures 3-Supplement 2AandB; paired t-test, t(8)=2.59, p=0.032, d=0.7), the report-based measures exhibited a strong correlation which aligned with competition model’s prediction (Figure 3-Supplement 2C; R²=0.95; slope is -0.93 with 95% CI [-1.11, -0.75] and intercept is 25.51° with 95% CI [22.69°, 28.34°]).

In summary, we have now added report-based implicit learning and explicit learning measurements to our revised manuscript. We show that these measures also exhibit a strong negative correlation with good agreement to the competition model. However, we still feel that it is important to question the reliability of these report-based measures (given that they were collected only once at the end of the experiment, when no longer in a ‘reaching context’). Our new analysis is described on Lines 319-327 in the paper.

5. Figure 3H is one of the rare pieces of direct evidence to support the model, but we find the estimated slope parameter is based on a B value of 0.35, which is unusually high. How is it obtained? Why is it larger than most previous studies have suggested? In fact, this value is even larger than the learning rate estimated in Exp 3 (Figure 6C). Is it related to the small sample size (see below)?

We can see where there may be confusion concerning how we estimated implicit error sensitivity, b_i in Experiment 1 (now Experiment 2 in the revised manuscript). Note that we use the same procedures to estimate error sensitivity in Experiment 3 (newly collected Limit PT group in laptop-based study). We can explain why the error sensitivity we estimate is appropriate. In Figure 3H (now Figure 3G), as well as throughout our paper, we attempt to understand asymptotic behavior. Therefore, we require error sensitivity during the asymptotic learning phase. In other words, steady-state adaptation will depend on asymptotic implicit error sensitivity, not initial error sensitivity. This subtlety is important because as we and others have shown, error sensitivity increases as errors get smaller (e.g., Marko et al., 2012; Kim et al., 2018, Albert et al., 2021). This was indeed the case in the Limit PT condition in Experiment 2 (previously Experiment 1), as shown in Figure 3-Supplement 1A in the revised manuscript.

To calculate error sensitivity in each cycle, we used its empirical definition (Equation 14 in revised manuscript). To determine the terminal error sensitivity during the adaptation period, we averaged error sensitivity over the last 5 rotation cycles (last 5 cycles in S3-1A). This error sensitivity was approximately 0.346, as shown by the horizontal dashed line in S3-1A. How reasonable is this value? The corresponding terminal error in the Limit PT condition in Experiment 2 (previously Experiment 1) was approximately 7.5° as shown in Figure 3-Supplement 1B (blue horizontal line). Recently Kim et al. (2018) calculated implicit error sensitivity as a function of error size; we show these curves in Figure 3-Supplement 1C in the revised manuscript. The blue line shows the terminal error in the Limit PT condition. As we can see, these earlier works suggested that for this particular error size, implicit error sensitivity varies somewhere between 0.25 and 0.35. Thus, our reported value of 0.346, does indeed appear reasonable. We thank the reviewers for noting this potential point of confusion and now reference our analysis on Lines 304-306 in the revised manuscript. We repeat this analysis for Experiment 3 (Limit PT group in newly added laptop-based study) in Figure 3-Supplements 1D-F.

Now we should address the inquiry about why this value is larger than the error sensitivity estimated in our Haith et al. (2015) state-space model. This question is actually common to most studies (including our own) in the literature that use state-space models to interrogate sensorimotor adaptation (e.g., Smith et al., 2006; Mawase et al., 2014; Galea et al. 2015; McDougle et al., 2015; Coltman et al., 2019, etc.). This issue arises because in our Haith et al. (2015) model, error sensitivity remains constant within a learning block. Clearly, we know this is not the case: within a single perturbation exposure not only does error sensitivity vary with error size (Figure 3-Supplement 1A, Marko et al., 2012; Kim et al., 2018, Albert et al., 2021), but it also changes with one’s error history (Herzfeld et al., 2014; Gonzalez-Castro and Hadjiosif et al., 2014; Albert et al., 2021). Our simple model does not describe these within-block changes, but instead permits savings by supposing that error sensitivity can differ across Blocks 1 and 2.

Even with this simplification, the model possesses 6 free parameters: b_i in Block 1, b_i in Block 2, b_e in Block 1, b_e in Block 2, a_i, and a_e. If we were to allow error sensitivity to change within each block, the simplest choice would require at least 2-4 free parameters: rate parameters describing how b_i and b_e change within each block. Thus, a simple model of within-block and between-block changes in error sensitivity, would likely require a state-space model with at least 8-10 free parameters. As these models become more complex, the likelihood that they overfit the data increases significantly.

Thus, the common choice is to simplify this complexity, by not permitting b to change within a block. This assumption will cause the model to identify an error sensitivity that is intermediate between its initial value in the block, and its terminal value within a block. Of course, this is an abstraction of reality because b is not constant. Nevertheless, this common assumption still has value, as it provides a means of testing if some “average” error sensitivity differs across two different perturbation exposures. However, because error sensitivity increases over the block, this “average” error sensitivity parameter will be smaller than the terminal error sensitivity reached later in the block. Thus, this is the reason why when we estimate b late during the Limit PT condition, we obtained a sensitivity near 35%, but when we fit a model to the entire exposure period in Haith et al. (2015), the average error sensitivity identified by the model falls far short of this value.

While using a constant b_i value in our Haith et al. (2015) model represents a potential limitation, a more sophisticated state-space model is not needed for our purposes. Here, we compare an SPE model and a TE model, in order to demonstrate the possibility that some “average” implicit error sensitivity is greater during the second rotation. Our main purpose is to raise an alternate hypothesis to our original conclusion in Haith et al., and recent evidence that implicit learning processes do not exhibit savings. Also note that our choice to fix b_i to a constant value within a block is consistent with past studies that have used statespace models to document changes in error sensitivity across perturbation exposures (e.g., Lerner and Albert et al., 2020; Coltman et al., 2019; Mawase et al., 2014).

In summary, we hope that this discussion helps to clarify the error sensitivity estimates in our work. In our revised manuscript we have now added Figure 3-Supplement 1 to show that our asymptotic error sensitivity estimates are consistent with past literature.

6a. The direct evidence supporting a competition of implicit and explicit learning is still weak.

First, we humbly submit that our work provides considerable support for a competition between implicit and explicit learning. Given the large amount of data added to the revised manuscript it seems appropriate to begin with a brief summary of the analyses that support the competition theory over the standard SPEonly learning hypothesis.

A. Saturated learning with increasing rotation size in some experiments, yet an increasing response in others (Figure 1 in revised manuscript), which is inconsistent with generalized SPE-learning.

B. Quadratic responses to rotation size which are inconsistent with generalized SPE-learning (new analysis in Figure 1 in revised manuscript, described more below)

C. Decreases in implicit adaptation due to coaching, with a simultaneous insensitivity to rotation size (Figure 2 in revised manuscript), whose co-occurrence is unexplained by generalized SPE-learning.

D. Increases in implicit learning driven by gradual perturbation onsets (Figure 1 in revised paper) whose subject-to-subject properties are inconsistent with generalization of SPE learning (Figure 5 in revised paper along with several supplements).

E. Increases in implicit learning due to suppressed explicit strategy, consistent with the competition model (Figure 3O in revised manuscript).

F. Negative subject-level correlations between implicit and explicit learning, with properties that are quantitatively predicted by the competition model (Figures 3GandQ).

G. Negative correlations between implicit-total learning that support the competition theory and disprove an SPE-only model (Figure 4H).

H. Positive correlations between explicit-total totaling that support the competition theory and disprove an SPE-only model (Figure 4G).

I. Negative implicit-explicit correlations (Figures 3G, P, and Q) that we have now detected across three additional studies (Figure 4-Supplements 1G-I), whose properties are inconsistent with a generalized SPE learning model (Figure 5).

The totality of this evidence cannot be reconciled by the standard model where implicit learning is solely driven by SPEs. With that said, we wish to restate that despite these points, our paper is intended to show that implicit target error learning exists in addition to, not instead of, the implicit sensory prediction error system. We hope that this pluralistic intention is better emphasized in our revised paper (see for example our text on Lines 787-790 and 1036-1103).

6b. Most data presented here are about the steady-state learning amplitude; the authors suggest that steady-state implicit learning is proportional to the size of the rotation (Equation5). But this is directly contradictory to the experimental finding that implicit learning saturates quickly with rotation size (Morehead et al., 2017; Kim et al., 2018). This prominent finding has been dismissed by the proposed model.

These concerns are critical. We agree with the reviewers that Morehead et al., 2017 and Kim et al., 2018 suggest that implicit learning saturates quickly with rotation size. With that said, these studies both use invariant error-clamp perturbations, not standard visuomotor rotations. We are not sure that the implicit properties observed in an invariant error context apply to the conditions we consider in our manuscript. In our revised manuscript, we consider variations in steady-state implicit learning across two new data sets: (1) stepwise adaptation in Experiment 1 and (2) non-monotonic implicit responses in Tsay et al., 2021. As we will demonstrate below, our data and re-analysis strongly indicate that the implicit system does not always saturate with changes in rotation size. Rather, the implicit system exhibits a complicated response to both rotation size and explicit strategies, which together yield three implicit learning phenotypes:

1. Saturation in steady-state implicit learning despite increasing rotation size (analysis reported in original paper using Neville and Cressman, 2018).

2. Scaling in steady-state implicit learning with increasing rotation size (new analysis using stepwise learning in Experiment 1).

3. Non-monotonic (quadratic) steady-state implicit behavior due to increases in rotation magnitude (new analysis added which uses data from Tsay et al., 2021).

We explore these three phenotypes in Figure 1 in the revised paper. Below, we provide an overview of these phenotypes, and make references to our revised text and Figure 1 where appropriate.

To begin with, we discuss cases where implicit learning appears to remain constant over large changes in rotation magnitude. This analysis is the same as the Neville and Cressman (2018) analysis described in our original manuscript (though the way we present certain aspects has been updated). Recall that Neville and Cressman (2018) examined how both implicit and explicit systems responded to changes in rotation size.

Participants adapted to a 20° (n=11), 40° (n=10), or 60° (n=10) visuomotor rotation (Figure 1C). Figures 1D and 1E show exclusion-based measures for implicit and explicit learning across all 3 rotations. Unsurprisingly, strategies increased proportionally with the rotation’s size (Figure 1E). On the other hand, implicit learning was insensitive to the rotation magnitude; it reached only 10° and remained constant despite tripling the perturbation’s size (Figure 1D).

As the reviewers note, on its face, this implicit saturation appears in line with an upper bound on implicit learning, as in Morehead et al., 2017 and Kim et al., 2018 (with the exception that here implicit learning was limited to 10° which falls short of the 15-25° limits observed in the invariant error-clamp paradigm).

Here, however, we propose another way that implicit learning might exhibit this saturation phenotype: not due to an upper bound on its compensation, but instead, competition.

In the competition model, the implicit system is driven by the residual error between the rotation and explicit strategy (r – x_e^ss in Equation 4). As a result, this model predicts that when an increase in rotation magnitude is matched by an equal change in explicit strategy (Figure 1-Supplement 1A, same), the implicit learning system’s driving force will remain constant (Figure 1-Supplement 1B, same). This constant driving input leads to a phenotype where implicit learning appears to “saturate” with increases in rotation size (Figure 1-Supplement 1C, same).

To investigate this possibility, we measured the rate at which explicit strategy increased with rotation size in the measured behavior. Rapid increases in explicit strategy (Figure 1E) limited changes in the competitive driving force; whereas the rotation increased by 40°, the driving force changed by less than 2.5° (Figure 1F). Thus, the competition model (Figure 1G, competition) yielded a close correspondence to the measured data (Figure 1G, data); when the driving input remains the same across rotation sizes, implicit learning will remain the same.

This model suggested that the implicit system’s response saturated not due to an intrinsic upper limit in implicit learning, but due to a constant driving input. The key prediction is that the implicit system should be ‘released’ from this saturation phenotype by weakening the explicit system’s response to the rotation. That is, when a change in rotation size is accompanied by a smaller change in explicit strategy (Figure 1-Supplement 1A, slower), the competitive driving input to the implicit system should increase (Figure 1Supplement 1B, slower). In the revised manuscript, we have added a new dataset (n=37) to test this idea. In this new experiment, we probed implicit and explicit learning across similar rotation sizes (15-60°) but using a stepwise perturbation. In Experiment 1, participants (n=37) adapted to a stepwise perturbation which started at 15°, but increased to 60° in 15° increments (Figure 1H). Towards the end of each learning block, we assessed implicit and explicit adaptation by instructing participants to aim directly to the target (Figure 1H, implicit learning shown in black shaded regions).

Stepwise rotation onset muted the explicit system’s gain, relative to the abrupt rotation conditions used by Neville and Cressman (2018); explicit strategies increased with a 94.9% gain (change in strategy divided by change in rotation) across the abrupt groups in Figure 1E, but only a 55.5% gain in the stepwise condition shown in Figure 1J. This suppression in the explicit response caused the competition model’s implicit driving input (Figure 1K) to increase with rotation magnitude. Remarkably, this increasing driving input predicted a “scaling” phenotype in steady-state learning (Figure 1L, competition) that precisely matched the measured implicit response (Figures 1I; 1L, data).

Thus, steady-state implicit learning can exhibit a saturation phenotype (Figure 1G) and a scaling phenotype (Figure 1L), as predicted by the competition model. But recent work in Tsay et al., 2021, suggests a third steady-state implicit phenotype: non-monotonicity. We have now added an analysis of these data to the revised manuscript. In this study, the authors probed a wider range in rotation size, 15° to 90° (Figure 1M). A terminal no aiming period was used to measure steady-state implicit learning levels (n=25/group). Curiously, whereas implicit learning increased across the 15° and 30° rotations, it remained the same in the 60° rotation group, and then decreased in the 90° rotation group (Figure 1N).

To determine whether this non-monotonicity could be captured by the competition model, we considered again how explicit re-aiming increased with rotation size (Figure 1O). We observed an intriguing pattern. When the rotation increased from 15° to 30°, explicit strategy responded with a very low gain (4.5%, change in strategy divided by change in rotation). An increase in rotation size to 60° was associated with a medium-sized gain (80.1%). The last increase to 90° caused a marked change in the explicit system: a 53.3° increase in explicit strategy (177.7% gain). Thus, explicit strategy increased more than the rotation had. Critically, this condition produces a decrease in the implicit driving input in the competition model (Figure 1-Supplement 1, faster). Overall, this large modulation in explicit learning gain (4.5% to 80.1% to 177.7%) yielded non-monotonic behavior in the implicit driving input (Figure 1P) which increased between 15° and 30°, changed little between 30° and 60°, and then dropped between 60° and 90°. As a result, the competition model (Figure 1Q, competition) exhibited a non-monotonic envelope, which closely tracked the measured implicit steady-states (Figure 1Q, data).

Together, these studies demonstrate that the implicit system exhibits at least 3 steady-state phenomena: saturation, scaling, and non-monotonicity. In abrupt conditions, the implicit response saturated. In a more gradual condition, the implicit response scaled. When the rotation increased to an orthogonal extreme (90° rotation), implicit learning showed a non-monotonic decrease. A model where implicit learning is driven solely by SPEs could only produce the scaling phenotype (Figures 1G, 1L, and 1Q, independence, not shown here but provided in the revised manuscript). The competition model, however, predicted that the implicit system should respond not only to the rotation, but also changes in explicit strategy. This additional dimension yielded a match to the data across all 3 implicit learning phenotypes (Figures 1G, 1L, and 1Q, competition). Thus, the implicit system appeared to compete with explicit strategy, in their shared response to target error.

In sum, we now add two additional datasets to the revised manuscript: data collected using a stepwise rotation in Experiment 1, and data recently collected by Tsay et al., 2021. Collectively, these new data show that steady-state implicit learning is complex, exhibiting at least three contrasting phenotypes: saturation, scaling, and non-monotonicity. Remarkably, the competition theory provides a way to account for each of these patterns. Thus, the competition model does accurately describe how implicit learning varies due to both changes in rotation size and explicit strategy, at least in standard rotation paradigms. However, these rules do not explain implicit behavior in invariant error-clamp paradigms. In the revised manuscript, we delve further into a comparison between standard rotation learning and invariant error learning in our Discussion (Lines 911-941). The relevant passage is provided below:

“Although the implicit system is altered in many experimental conditions, one commonly observed phenomenon is its invariant response to changes in rotation size^{3,31,35,36,40}. For example, in the Neville and Cressman³¹ dataset examined in Figure 1, total implicit learning remained constant despite tripling the rotation’s magnitude. While this saturation in implicit learning is sometimes interpreted as a restriction in implicit adaptability, this rotation-insensitivity may have another cause entirely: competition. That is, when rotations increase in magnitude, rapid scaling in the explicit response may prevent increases in total implicit adaptation. Critically, in the competition theory, implicit learning is driven not by the rotation, but by the residual error that remains between the rotation and explicit strategy. Thus, when we used gradual rotations to reduce explicit adaptation (Experiment 1), prior invariance in the implicit response was lifted: as the rotation increased, so too did implicit learning³⁷ (Figure 1I). The competition theory could readily describe these two implicit learning phenotypes: saturation and scaling (Figures 1GandL). Furthermore, it also provided insight as to why implicit learning can even exhibit a non-monotonic response, as in Tsay et al. (2021)³⁶. All in all, our data suggest that implicit insensitivity to rotation size is not due to a limitation in implicit learning, but rather a suppression created by competition with explicit strategy.

With that said, this competitive saturation in implicit adaptation should not be conflated with the upper limits in implicit adaptation that have been measured in response to invariant errors^3,11,40. In this latter condition, implicit adaptation reaches a ceiling whose value varies somewhere between 15 degrees³ and 25 degrees⁴⁰ across studies. In these experiments, participants adapt to an error that remains constant and is not coupled to the reach angle (thus, the competition theory cannot apply). While the state-space model naturally predicts that total adaptation can exceed the error size which drives learning in this errorclamp condition (as is observed in response to small error-clamps), it cannot explain why asymptotic learning is insensitive to the error’s magnitude. One idea is that proprioceptive signals^40,83 may eventually outweigh the irrelevant visual errors in the clamped-error condition, thus prematurely halting adaptation. Another possibility is that implicit learning obeys the state-space competitive model described here, but only up until a ceiling that limits total possible implicit corrections. Indeed, in Experiment 1, we produced scaling in the implicit system in response to rotation size, but never evoked more than about 22° of implicit learning. However, when we used similar gradual conditions in the past to probe implicit learning³⁷, we observed about 32° implicit learning in response to a 70° rotation. Further, in a recent study by Maresch and colleagues⁴⁷, where strategies were probed only intermittently, implicit learning reached nearly 45°. Thus, there remains much work to be done to better understand variations in implicit learning across errorclamp conditions, and standard rotation conditions.”

6c. On the other hand, one classical finding for conventional VMR is that explicit learning would gradually decrease after its initial spike, while implicit learning would gradually increase. The competition model appears unable to account for this stereotypical interaction. How can we account for this simple pattern with the new model or its possible extensions?

As the reviewers note, some studies have observed an initial spike in explicit strategy which then gradually declines over adaptation (e.g., McDougle et al., 2015; some groups in Yin and Wei, 2020) – though it should be noted that in other cases, this does not appear to occur (e.g., most cases in Morehead et al., 2015; multi-day training in Wilterson et al., 2021). While we opted not to investigate these dynamic phenomena in our paper, it should be noted that the competition model can produce this explicit phenotype.

In the simplest case where adaptation depends solely on a target error shared between the implicit and explicit systems, this gives rise to the competitive state-space system given by:

This is the competition model we use in our Haith et al. (2015) simulations. In this model, the rise and fall in explicit strategy can occur due to the way that both systems interact through e_target in these equations. An example can even be observed in our manuscript, in our Haith et al. (2015) analysis (Figure 6D).

Note how explicit adaptation predicted by the competition model (magenta curves) rises during the first 20 rotation trials on both Day 1 and Day 2, and then declines over the rest of adaptation. Thus, clearly the competition model naturally describes such waxing and waning in the explicit response; high explicit error sensitivity initially causes increases in explicit learning, but then as the implicit process develops, errors are siphoned away from the explicit system causing it to gradually decline.

Altogether, these simulations illustrate that the competition model can indeed account for the explicit and implicit phenotypes described by the reviewers. With that said, there is another potential culprit in the rise-and-fall explicit learning phenotype. In some cases where aiming landmarks are provided during adaptation, target errors can be eliminated, but implicit learning persists with a concomitant decrease in explicit strategy (e.g., Taylor et al., 2014; McDougle et al., 2011). We suspect in these cases that persistent implicit learning is due to errors between the cursor and the aiming landmarks, as demonstrated by Taylor and Ivry (2011). Thus, in order to maintain the cursor on the target without overcompensating for the rotation, explicit strategies must decline.

In sum, in the revised manuscript we note that the competition model can produce the implicit-explicit learning phenotype noted by the reviewers: rising-and-falling explicit strategy accompanied by persistent implicit learning, as demonstrated in Figure 5D. However, we also recognize that in aiming landmark studies, this behavior can be driven by a second error (an SPE and/or target error between the cursor and aiming landmark). In our revised paper, we have added a passage concerning these matters:

“…For example, early during learning, it is common that explicit strategies increase, peak, and then decline. That is, when errors are initially large, strategies increase rapidly. But as implicit learning builds, the explicit system’s response can decline in a compensatory manner^1,9,12. This dynamic phenomenon can also occur in the competition theory, where both implicit and explicit systems respond to target error (Figure 6D). But in many cases, a second error source may drive this behavioral phenotype. That is, in cases with aiming landmarks ^1,9,12, errors between the cursor and primary target can be eliminated, but implicit learning persists. This implicit learning is likely driven by the SPEs and target errors that remain between the cursor and the aiming landmark, as in Taylor and Ivry (2011)⁹. This persistent implicit adaptation must be counteracted by decreasing explicit strategy to avoid overcompensation. In sum, competition between implicit learning and explicit strategy is complex. Both systems can respond to one another in ways that change with experimental conditions.”

7. General comments about the data:

Experiments 3 and 4 (Figures 6 and 7) do not contribute to the theorization of competition between implicit and explicit learning. The authors appear to use them to show that implicit learning properties (error sensitivity) can be modified, but then this conclusion critically depends on the assumption that the limit-PT paradigm produces implicit-only learning, which is yet to be validated.

Figure 4 is not a piece of supporting evidence for the competition model since those obtained parameters are based on assumptions that the competition model holds and that the limit-PT condition "only" has implicit learning.

We agree with these points. Yes, we do not intend for Experiments 3 and 4 (now Experiments 4 and 5) to directly contribute to the competition theory’s experimental evidence. We have made changes to our revised manuscript to make this clearer. First, our Results are now divided in 4 sections. Sections 1 and 2 present evidence that supports the competition theory. The savings and interference studies are included in a separate section (Part 3). We expect that these analyses will be important to the reader, as they provide new ideas about how the implicit system may exhibit changes that are masked by explicit strategy.

Secondly, we have now added new analysis to the Haith et al. (2015) dataset, so that it better recognizes and contrasts competition and independence model predictions. In the original Figure 4, we solely fit the competition model to the Haith et al. dataset and highlighted the implicit and explicit error sensitivities predicted by the model. In the revised manuscript, we now also fit the independence model to the Haith et al. dataset and include its error sensitivity estimates in Figure 6 (previously Figure 4) as well. We hope that this inclusion better illustrates that these model fits are not meant as evidence for one model or the other, but rather two contrasting interpretations of the same data.

In the revised paper we explain the competition model predicts that both the implicit system and explicit system exhibited a statistically significant error sensitivity increase (Figure 6D, right; two-way rm-ANOVA, within-subject effect of exposure number, F(1,13)=10.14, p=0.007, η_p²=0.438; within-subject effect of preparation time, F(1,13)=0.051, p=0.824, η_p²=0.004; exposure by preparation interaction, F(1,13)=1.24, p=0.285). The independence model suggested only the explicit system exhibited a statistically significant increase in error sensitivity (Figure 5E; 2-way rm-ANOVA, learning process by exposure number interaction, F(1,13)=7.016, p=0.02; significant interaction followed by 1-way rm-ANOVA across exposures: explicit system with F(1,13)=9.518, p=0.009, η_p²=0.423; implicit system with F(1,13)=2.328, p=0.151, η_p²=0.152).

In the revised manuscript we conclude these results with: “In summary, when we reanalyzed our earlier data, the competition and independence theories suggested that our data could be explained by two contrasting hypothetical outcomes. If we assumed that implicit and explicit systems were independent, then only explicit learning contributed to savings, as we concluded in our original report. However, if we assumed that the implicit and explicit systems learned from the same error (competition model), then both implicit and explicit systems contributed to savings. Which interpretation is more parsimonious with measured behavior?”

We hope that these additions and revisions to the manuscript better illustrate that our analysis is not meant to support one model over the other, but rather to illustrate their contrasting implications about the implicit system.

Finally, the reviewers also note in their concern, that our analyses in Figures 7, 8, and 9 (previously Figures 4, 6, and 7) depend on the assumption that limited preparation time trials isolate implicit learning. We responded to similar concerns in Point 3 above. We will reiterate this discussion here. In the revised paper, we have added 2 additional experiments to confirm that the limited preparation time conditions we use in our studies accurately isolate implicit learning. First, we have now added a limited preparation time (Limit PT) group to our laptop-based study in Experiment 3 (Experiment 2 in original manuscript). In Experiment 3, participants in the Limit PT group (n=21) adapted to a 30° rotation but under a limited preparation time condition. As for the Limit PT group in Experiment 2, we imposed a strict bound on reaction time to suppress movement preparation time. However, unlike Experiment 2 (Experiment 1 in original manuscript) once the rotation ended, participants were told to stop re-aiming. This no-aiming instruction allowed us to examine whether limiting preparation time suppressed explicit strategy as intended. Our analysis of these new data is shown in Figures 3K-N.

In Experiment 3, we now compare two groups: one where participants had no preparation time limit (No PT Limit, Figures 3H-J) and one where an upper bound was placed on preparation time (Limit PT, Figures 3K-M). We measured early and late implicit learning measures over a 20-cycle no feedback and no aiming period at the end of the experiment. The voluntary decrease in reach angle over this no aiming period revealed each participant’s explicit strategy (Figure 3N). When no reaction time limit was imposed (No PT Limit), reaiming totaled approximately 11.86° (Figure 3N, E3, black), and did not differ statistically across Experiments 2 and 3 (t(42)=0.50, p=0.621). Recall that Experiment 2 tested participants with a robotic arm and Experiment 3 tested participants in a similar laptop-based paradigm. As in earlier reports, limiting reaction time dramatically suppressed explicit strategy, yielding only 2.09° of re-aiming (Figure 3N, E3, red).

Therefore, our new control dataset suggest that our limited reaction time technique was highly effective at suppressing explicit strategy as initially claimed in our original manuscript. However, this experiment alone suggests that while explicit strategies are strongly suppressed by limiting preparation time, they are not entirely eliminated; when we limited preparation time in Experiment 3, we observed that participants still exhibited a small decrease (2.09°) in reach angle when we instructed them to aim their hand straight to the target (Figure 3L, no aiming; Figure 3N, E3, red). This ‘cached’ explicit strategy, while small, may have contributed to the 8° reach angle change measured early during the second rotation in our savings experiment (Experiment 4, Figure 7C in revised paper).

For this reason, it was critical to consider whether this 2° change in reach angle was indeed due to explicit strategy or instead caused by time-based decay in implicit learning over the 30 sec instruction period. To test this possibility, we collected another limited preparation group (n=12, Figure 7-Supplement 1A, decay-only, black). But this time, participants were instructed that the experiment’s disturbance was still on, and that they should continue to move the ‘imagined’ cursor to the target during the no feedback period. Even though participants were instructed to continue using their strategy, their reach angles decreased by approximately 2.1° (Figure 7-Supplement 1, black decay-only). Indeed, we detected no statistically significant difference between the change in reach angle in this decay-only condition, and the Limit PT group in Experiment 3 (Figure 7-Supplement 1B; two-sample t-test, t(31)=0.016, p=0.987).

This control experiment suggested that residual ‘explicit strategies’ we measured in the Limit PT condition, were caused by time-dependent decay in implicit learning. Thus, our Limit PT exhibits a near-complete suppression of explicit strategy.

Summary

In our revised manuscript, we have added the independence model’s predictions to Figure 6 (previously Figure 4) and have altered our text to better explain that our Haith et al. analysis is not intended to support the competition model, but to compare each models’ implications. In addition, we add two new experiments to corroborate our assumption that limited preparation time trials reveal implicit learning in our tasks. Data in the Limit PT condition in Experiment 3 suggest that explicit strategies are suppressed to approximately 2° by our preparation time limit (compared to about 12° under normal conditions). Data in the decay-only group suggest that this 2° change in reach angle was not due to a cached explicit strategy but rather time dependent decay in implicit learning. Together, these conditions demonstrate that limiting reaction time in our experiments almost completely prevents the caching of explicit strategies; our limited preparation time measures do indeed reflect implicit learning.

8a. Concerns about data handling:

All the experiments have a limited number of participants. This is problematic for Exp1 and 2, which have correlation analysis. Note Fig3H contains a critical, quantitative prediction of the model, but it is based on a correlation analysis of n=9. This is an unacceptably small sample. Experiment 3 only had 10 participants, but its savings result (argued as purely implicit learning-driven) is novel and the first of its kind.

We agree with these points. Yes, we do not intend for Experiments 3 and 4 (now Experiments 4 and 5) to directly contribute to the competition theory’s experimental evidence. We have made changes to our revised manuscript to make this clearer. First, our Results are now divided in 4 sections. Sections 1 and 2 present evidence that supports the competition theory. The savings and interference studies are included in a separate section (Part 3). We expect that these analyses will be important to the reader, as they provide new ideas about how the implicit system may exhibit changes that are masked by explicit strategy.

Secondly, we have now added new analysis to the Haith et al. (2015) dataset, so that it better recognizes and contrasts competition and independence model predictions. In the original Figure 4, we solely fit the competition model to the Haith et al. dataset and highlighted the implicit and explicit error sensitivities predicted by the model. In the revised manuscript, we now also fit the independence model to the Haith et al. dataset and include its error sensitivity estimates in Figure 6 (previously Figure 4) as well. We hope that this inclusion better illustrates that these model fits are not meant as evidence for one model or the other, but rather two contrasting interpretations of the same data. Below we reproduce the relevant changes to Figure 6 (previously Figure 4).

In the revised paper we explain the competition model predicts that both the implicit system and explicit system exhibited a statistically significant error sensitivity increase (Figure 6D, right; two-way rm-ANOVA, within-subject effect of exposure number, F(1,13)=10.14, p=0.007, η_p²=0.438; within-subject effect of preparation time, F(1,13)=0.051, p=0.824, η_p²=0.004; exposure by preparation interaction, F(1,13)=1.24, p=0.285). The independence model suggested only the explicit system exhibited a statistically significant increase in error sensitivity (Figure 5E; 2-way rm-ANOVA, learning process by exposure number interaction, F(1,13)=7.016, p=0.02; significant interaction followed by 1-way rm-ANOVA across exposures: explicit system with F(1,13)=9.518, p=0.009, η_p²=0.423; implicit system with F(1,13)=2.328, p=0.151, η_p²=0.152).

In the revised manuscript we conclude these results with: “In summary, when we reanalyzed our earlier data, the competition and independence theories suggested that our data could be explained by two contrasting hypothetical outcomes. If we assumed that implicit and explicit systems were independent, then only explicit learning contributed to savings, as we concluded in our original report. However, if we assumed that the implicit and explicit systems learned from the same error (competition model), then both implicit and explicit systems contributed to savings. Which interpretation is more parsimonious with measured behavior?”

We hope that these additions and revisions to the manuscript better illustrate that our analysis is not meant to support one model over the other, but rather to illustrate their contrasting implications about the implicit system.

Finally, the reviewers also note in their concern, that our analyses in Figures 7, 8, and 9 (previously Figures 4, 6, and 7) depend on the assumption that limited preparation time trials isolate implicit learning. We responded to similar concerns in Point 3 above. We will reiterate this discussion here. In the revised paper, we have added 2 additional experiments to confirm that the limited preparation time conditions we use in our studies accurately isolate implicit learning. First, we have now added a limited preparation time (Limit PT) group to our laptop-based study in Experiment 3 (Experiment 2 in original manuscript). In Experiment 3, participants in the Limit PT group (n=21) adapted to a 30° rotation but under a limited preparation time condition. As for the Limit PT group in Experiment 2, we imposed a strict bound on reaction time to suppress movement preparation time. However, unlike Experiment 2 (Experiment 1 in original manuscript) once the rotation ended, participants were told to stop re-aiming. This no-aiming instruction allowed us to examine whether limiting preparation time suppressed explicit strategy as intended. Our analysis of these new data is shown in Figures 3K-N.

In Experiment 3, we now compare two groups: one where participants had no preparation time limit (No PT Limit, Figures 3H-J) and one where an upper bound was placed on preparation time (Limit PT, Figures 3K-M). We measured early and late implicit learning measures over a 20-cycle no feedback and no aiming period at the end of the experiment. The voluntary decrease in reach angle over this no aiming period revealed each participant’s explicit strategy (Figure 3N). When no reaction time limit was imposed (No PT Limit), reaiming totaled approximately 11.86° (Figure 3N, E3, black), and did not differ statistically across Experiments 2 and 3 (t(42)=0.50, p=0.621). Recall that Experiment 2 tested participants with a robotic arm and Experiment 3 tested participants in a similar laptop-based paradigm. As in earlier reports, limiting reaction time dramatically suppressed explicit strategy, yielding only 2.09° of re-aiming (Figure 3N, E3, red).

Therefore, our new control dataset suggest that our limited reaction time technique was highly effective at suppressing explicit strategy as initially claimed in our original manuscript. However, this experiment alone suggests that while explicit strategies are strongly suppressed by limiting preparation time, they are not entirely eliminated; when we limited preparation time in Experiment 3, we observed that participants still exhibited a small decrease (2.09°) in reach angle when we instructed them to aim their hand straight to the target (Figure 3L, no aiming; Figure 3N, E3, red). This ‘cached’ explicit strategy, while small, may have contributed to the 8° reach angle change measured early during the second rotation in our savings experiment (Experiment 4, Figure 7C in revised paper).

For this reason, it was critical to consider whether this 2° change in reach angle was indeed due to explicit strategy or instead caused by time-based decay in implicit learning over the 30 sec instruction period. To test this possibility, we collected another limited preparation group (n=12, Figure 7-Supplement 1A, decay-only, black). But this time, participants were instructed that the experiment’s disturbance was still on, and that they should continue to move the ‘imagined’ cursor to the target during the no feedback period. Even though participants were instructed to continue using their strategy, their reach angles decreased by approximately 2.1° (Figure 7-Supplement 1, black decay-only). Indeed, we detected no statistically significant difference between the change in reach angle in this decay-only condition, and the Limit PT group in Experiment 3 (Figure 7-Supplement 1B; two-sample t-test, t(31)=0.016, p=0.987).

This control experiment suggested that residual ‘explicit strategies’ we measured in the Limit PT condition, were caused by time-dependent decay in implicit learning. Thus, our Limit PT exhibits a near-complete suppression of explicit strategy.

Summary

In our revised manuscript, we have added the independence model’s predictions to Figure 6 (previously Figure 4) and have altered our text to better explain that our Haith et al. analysis is not intended to support the competition model, but to compare each models’ implications. In addition, we add two new experiments to corroborate our assumption that limited preparation time trials reveal implicit learning in our tasks. Data in the Limit PT condition in Experiment 3 suggest that explicit strategies are suppressed to approximately 2° by our preparation time limit (compared to about 12° under normal conditions). Data in the decay-only group suggest that this 2° change in reach angle was not due to a cached explicit strategy but rather timedependent decay in implicit learning. Together, these conditions demonstrate that limiting reaction time in our experiments almost completely prevents the caching of explicit strategies; our limited preparation time measures do indeed reflect implicit learning.

8b. Experiment 2: This experiment tried to decouple implicit and explicit learning, but it is still problematic. If the authors believe that the amount of implicit adaptation follows a state-space model, then the measure of early implicit is correlated to the amount of late implicit because Implicit_late = (ai)^N * Implicit_early where N is the number of trials between early and late. Therefore the two measures are not properly decoupled. To decouple them, the authors should use two separate ways of measuring implicit and explicit. To measure explicit, they could use aim report (Taylor, Krakauer and Ivry 2011), and to measure implicit independently, they could use the after-effect by asking the participants to stop aiming as done here. They actually have done so in experiment 1 but did not use these values.

One reason we conducted Experiment 2 (now Experiment 3) was to examine whether the implicit-explicit relationships were due to spurious correlations (e.g., implicit is compared to explicit, which is total learning minus implicit). While we appreciate the reviewers’ suggestion, we still maintain that the late implicit learning measure in Experiment 2 eliminates spurious correlation as intended.

To illustrate this, imagine that implicit and explicit learning have no relationship. Let’s represent these as random variables I and E. Supposing I and E are independent this implies that cov(I,E) = 0. Now let’s introduce a third random variable, T, which represents total learning. Suppose that we measure total adaptation on the last several cycles. This total adaptation will be equal to the sum of I and E. So total adaptation, T is given by T = I + E. Now, we the experimenter cannot measure I, E, and T. We can only measure these variables corrupted by motor execution noise, M. A reasonable assumption is that M is a zero-mean random variable, that is independently distributed across each reach.

At the end of adaptation, the measured total adaptation is thus T_measure = T + M₁ = I + E + M₁. Now, on the next cycle, we do exclusion trials. These reveal I, but this is also corrupted by motor execution noise. Thus, the I that we measure is given by: I_measure = I + M₂. Now, in Experiment 1, we derived E by subtracting I_measure from T_measure. This is given by: E_estimate = T_measure – I_measure = I + E + M₁ – (I + M₂) = E + M₁ – M₂. Now, we can see the issue when we correlate I_measure with E_estimate:This assumes as we said that I and E are independent.

This clearly illustrates the issue of spurious correlation. Even though I and E are independent, the way we measured I and E results in a non-zero misleading correlation.

Our late implicit measure in Experiment 3 prevents this spurious correlation. Suppose we measure I again on the second cycle in the no-aiming aftereffect period. As noted in the criticism, I here will relate to the previous I, but will be scaled by the retention factor a. Thus, the second I that we measure is given by: I₂ = aI + M₃ where M₃ is now motor execution noise on the 2^nd no-aiming cycle. Now let us determine the covariance between I₂ and E_estimate: cov(I₂, E_estimate) = cov(aI + M₃, E + M₁ – M₂). Noting that I, E, M₁, M₂, and M₃ are all independent, this covariance will be equal to 0.

What does this mean? Even though E_estimate is based on the initial ‘early I’ measurement, the second ‘late I’ that we measure (even though it is related to the first I via a) is no longer correlated with E_estimate. This is the type of spurious correlation we avoid with our late implicit measure in Experiment 2. Thus, the only way for E_estimate to be correlated with any later I measurement (apart from the initial one) requires that the original E and I are not in fact independent (as posited by the competition model).

In our revised manuscript we have increased the number of participants in Experiment 3 to n=35. Below, we show the early implicit-explicit relationship in Figure 3Q and the decoupled late implicit-explicit relationship in Figure 3P in the revised manuscript.

Second, though our late implicit measure does decouple implicit and explicit learning we have added the report-based measures requested by the reviewers to the paper. We also check the relationship between implicit and explicit learning using the aiming reports collected in the experiment. This correlation is now provided in Figure 3-Supplement 2C. In addition, we compare report and exclusion-based implicit and explicit measures in Figure 3-Supplements 2AandB. Note, we are not highly confident in these report measures, given that we collected them only one time and 25% were reported in the incorrect direction (see Point 4).

Thirdly, the revised paper includes new analyses that corroborate the competition model while avoiding spurious implicit-explicit correlations. Recall that spurious correlations can arise between exclusion-based implicit learning and explicit strategy. To avoid this potential issue, the competition model can be restated in another way. As we discussed in Point 1 above, the competition model predicts that x_i^ss = p_i(r – x_e^ss), where π is a gain that depends on implicit error sensitivity and retention. In our manuscript we investigate whether x_i^ss and x_e^ss vary according to this relationship. Note, however, that total adaptation is equal to x_T^ss = x_i^ss + x_e^ss. By combining these two equations, we can relate implicit learning to total adaptation via the equation: x_T^ss = r + (p_i – 1)p_i^-1x_i^ss (see Lines 1576-1620 in revised paper). This equation predicts that total learning will be negatively correlated to implicit learning. This counterintuitive relationship, that greater overall adaptation will be supported by reduced implicit learning, is opposite to that predicted by an SPE learning model like the independence equation. Supposing that implicit learning responds only to SPE, but strategies respond to variations in implicit learning yields: x_e^ss = p_e(r – x_i^ss) where p_e is the gain in the explicit response. Combining this with x_T^ss = x_i^ss + x_e^ss yields a positive linear relationship between total adaptation and implicit learning: x_T^ss = p_er + (1 – p_e)x_i^ss.