Sensorimotor adaptation refers to the gradual adjustment of movements in response to changes in the environment or body. In laboratory adaptation tasks, the introduction of perturbed sensory feedback results in a sensorimotor prediction error. This error signal is used to update a model of an internal sensorimotor mapping, thus ensuring that the sensorimotor system remains well calibrated (Shadmehr and Krakauer, 2008; Wolpert et al., 1995; Wolpert and Ghahramani, 2000). The integrity of the cerebellum is essential for this form of error-based learning (Donchin et al., 2012; Izawa et al., 2012; Popa et al., 2016; Schlerf et al., 2012) and is thought to play a key role in generating predictions of future states given the current sensory context.

Different contexts may call for the use of different sensorimotor mappings. For instance, distinct motor memories should be retrieved when a skilled tennis player prepares to hit a service return on a clay court vs a grass court. A topic of considerable discussion in the adaptation literature centers on the constraints underlying effective contextual cues (Addou et al., 2011; Addou et al., 2011; Heald et al., 2021; Dawidowicz et al., 2022; Heald et al., 2018; Howard et al., 2012; Howard et al., 2013; Howard et al., 2015; Karniel and Mussa-Ivaldi, 2002; Osu et al., 2004; Schween et al., 2019; Sheahan et al., 2016; Sheahan et al., 2018; Forano and Franklin, 2020; Forano et al., 2021). Contextual cues are highly effective when the cue is directly relevant to properties of the movement. For example, people can simultaneously adapt to competing sensorimotor perturbations if the current context is established by the movement segment that precedes or follows the perturbed segment of a reach (Howard et al., 2012; Howard et al., 2015; Sheahan et al., 2016). In these situations, the contextual cues are hypothesized to be effective because the cues are incorporated into the motor plan (Howard et al., 2012; Howard et al., 2013).

Less clear is the efficacy of arbitrary contextual cues, ones that are not directly related to movement. In general, arbitrary cues do not appear to be effective for defining distinct motor memories. For example, participants show large interference between opposing perturbations that are signaled by color cues (Howard et al., 2012; Howard et al., 2013; Gandolfo et al., 1996; Forano et al., 2021). This interference can be reduced with multiple days of practice, although even after 10 days of training, residual interference remains on trials immediately following a switch in context (Addou et al., 2011; see also Osu et al., 2004).

The ineffectiveness of arbitrary contextual cues in shaping sensorimotor adaptation is surprising when one considers another popular model task of cerebellar-dependent sensorimotor learning – delay eyeblink conditioning. In this form of classical conditioning, a sensory cue (conditioned stimulus [CS], e.g. a tone) is repeatedly paired with an aversive event (unconditioned stimulus [US], e.g. an air puff to the cornea). By itself, the aversive event naturally causes an immediate unconditioned response (UR, e.g. an eye blink in response to the air puff). After just a short training period with a reliable CS, organisms as diverse as turtles and humans produce an adaptive conditioned response (CR, e.g. an eye blink that anticipates the aversive air puff). Notably, there is little constraint on the features of the predictive cues. The CR can be readily acquired in response to arbitrary CSs, such as a tone or a light flash. However, there is an important temporal constraint, at least with respect to cerebellar-dependent eyeblink conditioning. The cue must appear before the aversive event, and the two stimuli must be in close temporal proximity (Schneiderman and Gormezano, 1964; Smith et al., 1969).

In the present study, we set out to re-evaluate the efficacy of arbitrary cues in sensorimotor adaptation, drawing on key theoretical concepts and design features employed in studies of delay eyeblink conditioning. Using a variant of a visuomotor adaptation task, we show that arbitrary stimuli can act as effective contextual cues when a strict temporal relationship is established between those cues and their associated movement-related sensory outcomes. We then take this result a step further by showing that the effect of these arbitrary cues adheres to an established core principle of associative learning – cue additivity. The parallels between adaptation and conditioning observed in our results lay the empirical groundwork for a more parsimonious model of cerebellar-dependent sensorimotor learning.

Our primary goal in the present study was to determine if arbitrary stimuli can serve as effective contextual cues in sensorimotor adaptation. Participants reached from a start location to a target, with movement feedback provided by a cursor (Figure 1A). In typical adaptation tasks, the onset of the target serves as an imperative for movement initiation. When considered through the lens of classical conditioning, the target appearance could be viewed as a CS given that it is presented just before the sensory feedback (the US) resulting from the movement (Figure 1B). To test the efficacy of arbitrary cues as CSs, the onset of the tone or light served as the imperative, with the target visible at its fixed location throughout the experimental session (Figure 1B). For optimal delay eyeblink conditioning, the interval between the CS and the US is relatively narrow, on the order of 100–500 ms (Schneiderman and Gormezano, 1964; Smith et al., 1969). By using a neutral stimulus to cue movement initiation, we imposed a tight temporal link between the CS and the US, requiring the participant to initiate the movement within 400 ms of the onset of the imperative. Participants complied with this requirement, exhibiting rapid response times ([mean ± STD]: 293±49.0 ms).

Figure 1

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A common perturbation technique to elicit sensorimotor adaptation is to introduce a visuomotor rotation, where the movement path of the visual feedback cursor is rotated (about the origin) with respect to the hand’s path. This drives an adaptation process in which the movement heading angle shifts across trials in the direction opposite to the rotated cursor, thus offsetting the error (Krakauer et al., 2000). To continue with our conditioning analogy, the CR would be the movement heading angle elicited by a CS, expressed as a change in heading angle following the pairing of that CS with the visual error, the US (Figure 1B). We note here that the UR in an adaptation task could correspond to an immediate movement correction in response to the perturbation, that is, an ‘online’ correction. Given that we required fast movements to minimize these corrections, this potential form of UR is not observed in our design.

Rather than rotate the position of the feedback cursor with respect to the actual hand position, we opted to use a visual ‘clamp’ where the cursor followed an invariant path with respect to the target (Morehead et al., 2017; Shmuelof et al., 2012). In contrast to traditional movement-contingent feedback, the clamp method eliminates confounding effects that can come about from strategic processes (McDougle et al., 2016; Kim et al., 2020), and the size of the error can be controlled on every trial. The participant was fully informed of this manipulation and was instructed to ignore the task-irrelevant cursor and always reach straight to the target. Despite these instructions, participants’ reach angles gradually shift in the direction opposite the error clamp, showing the key signatures of implicit sensorimotor adaptation (Morehead et al., 2017; Kim et al., 2018; Tsay et al., 2020a; Tsay et al., 2021; Avraham et al., 2021; Poh et al., 2021; Vandevoorde and Orban de Xivry, 2019; Yin and Wei, 2020).

Sensorimotor adaptation is modulated by arbitrary sensory cues

In a standard differential conditioning design, one CS is paired with the US (CS+) and another CS is presented without the US (CS−). Thus, only the CS+ should become associated with the US and result in a CR. To implement this in Experiment 1, we used two arbitrary cues for the CSs – a tone or a light cue (Figures 1A, 2A). For the CS+ condition, the feedback cursor followed a clamped path that was rotated from the target by 15°. Rather than eliminate the US on CS− trials, we used a 0° clamp in which the feedback cursor always moved directly to the target. Thus, there was always a US on each trial, with the 15° US creating an error signal (paired with the CS+) and the 0° US signaling the absence of error (paired with the CS-).

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During a 600-trial acquisition phase, CS+ and CS− trials were randomly interleaved. Participants exhibited a marked change in movement direction during this phase, reaching an asymptote of ~15° (Figure 2B). The observed rapid adaptation is consistent with previous adaptation studies, particularly those in which the target appears at a single fixed location (Bond and Taylor, 2015; Day et al., 2016; McDougle et al., 2015; McDougle et al., 2017; Poh et al., 2021).

The main analysis centered on trial-by-trial changes in heading angle. The change in heading angle from trial n−1 to trial n is normally dictated by the feedback experienced in trial n−1. Thus, following experience with an error on CS+ trials, participants should show increased adaptation (a positive change in heading angle), and following no error on CS− trials, decreased adaptation (i.e. extinction). We refer to these trial-by-trial changes as the ‘adaptation effect,’ the standard measure of learning in sensorimotor adaptation tasks. There was a robust adaptation effect (Figure 2C, left panel). Trial-by-trial changes in reaching direction (Δ heading angle) were significantly affected by the CS presented on the previous trial (F[1, 15]=13.4, p=0.002, BF₁₀=41.45, and η_p²=0.47) such that the change in heading angle was larger after CS+ trials compared to after CS− trials (mean difference: 1.50°, 95% CI: [0.70° 2.30°]). That is, the error occurring on CS+ trials resulted in learning that carried over to the next trial, whereas the absence of an error on a previous CS− trial resulted in a relative reversion to baseline (extinction). This is the canonical signature of incremental sensorimotor adaptation.

Importantly, the conditioning framework makes a critical prediction. The CS+ and CS− should differentially modulate the hand’s heading angle on trial n itself. That is, the presentation of the light or tone should produce a CR associated with that cue, leading to a difference in heading angle on trials with different cues that is independent of the feedback received on the previous trial. We refer to this as the ‘Pavlovian effect.’ As shown in Figure 2C (both panels), the results revealed clear Pavlovian effects during the acquisition phase. The heading angle increased in the direction of adaptation on CS+ trials (i.e. a positive change in heading angle relative to previous trials) and decreased on CS− trials (mean difference: 0.82°, 95% CI: [0.13° 1.51°]; F[1, 15]=5.37, p=0.035, BF₁₀=2.89, and η_p²=0.26). This effect provides a novel demonstration that arbitrary sensory cues can lawfully influence implicit sensorimotor adaptation.

We also observed an interaction between CS identity on trials n−1 and n (F[1, 15]=4.70, p=0.047, BF₁₀=2.21, and η_p²=0.24). That is, the difference between CS+ and CS− was larger on trials following a CS− (mean: 1.05°, 95% CI: [0.20° 1.89°]) compared to trials following a CS+ (0.58°, [–0.13° 1.30°]). This interaction effect may reflect an asymmetry between the rate of the acquisition and extinction processes once CS-US associations are established. That is, the state following a CS+ trial may be closer to its asymptotic limit than after a CS− trial and is thus more limited in its potential for further change.

We note that the visual feedback was different on CS+ and CS− trials, with the cursor deviating from the target in the former and moving in a straight line to the target in the latter. This raises the possibility that the heading angle differences on CS+ and CS− trials could be affected by online feedback corrections. This explanation is unlikely given that the movements were quite rapid (mean movement time [MT] ± STD, 103±31.2 ms). To assess the online correction hypothesis more directly, we calculated the difference in heading angle 50 ms after movement initiation and at the radial distance of the target. There was no overall change in heading angle between the time points (–0.32°±2.92°) and no significant difference between CS+ and CS− trials on this metric (mean difference: –0.04°, 95% CI: [–0.19° 0.12°]; t[15]=−0.47, p=0.640, BF₁₀=0.28, and d=−0.12). Thus, our results appear to pertain exclusively to feedforward learning.

Following the acquisition phase, participants completed a probe phase in which CS+ and CS− trials were randomly presented in the absence of any visual feedback (no US). This phase provides a clean test for associative learning effects since it removes trial-by-trial effects that arise from the differential feedback given during CS+ and CS− acquisition trials. Here too, we observed a clear Pavlovian effect. Although there was an overall decrease in heading angle across the probe phase (i.e. a partial washout of adaptation, Figure 2B), there was a significant main effect of the CS presented on trial n (1.06°, [0.53° 1.59°]; F[1, 15]=15.45, p=0.001, BF₁₀=72.15, and η_p²=0.51; Figure 2D), with a relative increase in heading angle on CS+ trials and a decrease on CS− trials.

Despite the absence of feedback in the probe phase, the change in heading angle on trial n (CS+ or CS−) should also depend on the CS presented on trial n−1. After an association is formed, the motor state, namely the actual heading angle, fluctuates as a function of the presented CS, decreasing on CS− trials (due to extinction) and increasing on CS+ trials (due to conditioning). As such, the heading angle on a CS+ trial should increase more if it follows a CS− trial than if it follows a CS+ trial. Similarly, the heading angle on a CS− trial should decrease more if it follows a CS+ trial than if it follows a CS− trial. While the data appeared to follow this pattern, there was no main effect of the trial n−1 CS (–0.44°, [–1.11° 0.24°]; F[1, 15]=1.61, p=0.224, BF₁₀=0.56, and η_p²=0.10). This may be because, statistically, the main effect of trial n−1 considers consecutive trials with a repeated CS (CS+ that follows CS+, and CS− that follows CS−) where the change in heading angle is minimal. Crucially, the Pavlovian effect (the difference between the change in heading angle on CS+ and CS− trials on trial n) should not depend on the previous trial. Consistent with this prediction, the trial n−1 CS × trial n CS interaction was not significant (F[1, 15]=2.03, p=0.175, BF₁₀=0.69, and η_p²=0.12).

The Pavlovian effect did not appear to be driven by explicit awareness of the CS-US contingency. A post-experiment survey was used to classify participants as either aware or unaware of the CS-US associations (see Materials and methods). Participants who reported being aware of the contingencies (N=7) did not show a different Pavlovian effect compared to those who reported being unaware (N=9) in either the acquisition (–0.34°, [–1.90° 1.22°]; t[14]=−0.470, p=0.647, BF₁₀=0.46, and d=−0.24) or probe (–0.14°, [–1.34° 1.07°]; t[14]=−0.242, p=0.813, BF₁₀=0.44, and d=−0.12) phases. A similar null effect of awareness on the strength of conditioning has also been reported in studies of human delay eyeblink conditioning (Clark and Squire, 1998).

In summary, the observed effects of context on implicit sensorimotor adaptation in both the acquisition and probe phases in Experiment 1 are consistent with differential conditioning effects. Feedforward implicit sensorimotor adaptation – here operationalized as a type of CR – was differentially modulated by arbitrary sensory CSs, with a greater response to the CS+, the cue that was paired with a visuomotor error.

The Rescorla-Wagner model for context-dependent sensorimotor adaptation

One influential model that has been used to describe contextual effects in associative learning tasks is the Rescorla-Wagner model (Rescorla and Wagner, 1972). This model formalizes changes in CRs via the modulation of learned associations. Here, the associative strengths, V, of the conditioning stimuli are updated according to the learning rule (Equation 1):

(1) $V^{[n]}=V^{[n-1]}+\alpha \cdot \beta \cdot SP{E}^{[n-1]};SP{E}^{\left[n-1\right]}=\lambda -V^{\left[n-1\right]}$

where V represents the associative strengths between the US and the CS. It is updated based on the sensory prediction error (SPE) presented on trial n−1. The SPE is defined as the difference between the maximum conditioning (asymptotic) level for the US (λ) and the associative strength on the given trial. β is the learning rate parameter of the US, and α represents the salience of the CS. We note that the Rescorla-Wagner model is one of many computational frameworks for associative learning (Courville et al., 2006; Gershman, 2015) and does not provide a mechanistic account for the error-correction process itself (e.g. the fact that the motor system ‘knows’ to update movements in the direction opposite of the error). For simplicity, we assume that the sign of the change in movement direction is coded in specialized neural mechanisms for reducing motor error (Hadjiosif et al., 2021; Herzfeld et al., 2018; Wolpert et al., 1998).

To examine whether the Rescorla-Wagner model can capture differential conditioning behavior similar to the results observed in Experiment 1, we performed model simulations. The simulation results demonstrated both the adaptation effect and Pavlovian effect for the acquisition phase (Figure 2E), as well as a clear Pavlovian effect for the probe phase (Figure 2F). Importantly, the behavioral signature of differential conditioning – the larger changes in heading angle on CS+ trials compared to CS− trials – holds for essentially all combinations of parameters in the Rescorla-Wagner model (Figure 3, left side).

Figure 3

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Sensorimotor adaptation is typically described by a ‘state-space’ model in which the motor state (x) is updated according to the following learning rule (Equation 2):

(2) $x^{\left[n\right]}=A\bullet x^{\left[n-1\right]}+B\bullet {SPE}^{\left[n-1\right]}$

where SPE is the sensory prediction error – the difference between the predicted and the actual sensory feedback – experienced on trial n−1, A is the retention factor, and B is the learning rate. The state-space model is broadly similar to the Rescorla-Wagner (e.g. both models share the Markov property, produce exponential-family learning curves, etc.). However, the basic state-space model is unable to account for context effects. Unlike the Rescorla-Wagner model, it does not include parameters that allow the updating of separate states that are associated with distinct contexts. It predicts the change in behavior based on the outcome of the previous trial (i.e. the adaptation effect); it cannot account for variation in heading angle due to the CS on the current trial (i.e. the Pavlovian effect; Figure 3, right side).

To formally compare the Rescorla-Wagner and state-space models in terms of the observed results, we conducted a model comparison by fitting each participant’s time course data with the two models. The Rescorla-Wagner model provided a better fit to the data than a standard state-space model, underscoring the significant role of the Pavlovian effect (Figure 4; t test comparing sum of squared residuals, –6.61×10⁴, [–1.05×10⁵ –2.72×10⁴]; t[15]=–3.62, p=0.003, and d=−0.90; t test comparing Akaike information criterion (AIC) values, –430, [–572 –288]; t[15]=–6.44, p<0.001, and d=−1.61).

Figure 4

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An additional analysis provided further support for an associative learning account of the results of Experiment 1. The Rescorla-Wagner model not only provides a framework for understanding how associations can be formed with arbitrary stimuli, but it can also capture how the strength of these associations is constrained by the relevance of the cues. For instance, gustatory cues are much more likely to be associated with an internal bodily state (e.g. nausea) than a visual cue (Garcia and Koelling, 1966). In the current study, the clamped feedback (the US) is a highly relevant stimulus for reaching; as such, we should expect it to have an immediate strong influence on motor behavior. In contrast, the imperative cues (the tone and light CSs) have no natural relevance for reaching; as such, their contribution to the CR should initially be quite modest but gradually increase with experience (Figure 5A). To test this prediction, we examined the time course of the adaptation and Pavlovian effects during acquisition using a linear mixed model analysis. As expected, at early stages of acquisition, the adaptation effect emerged rapidly, whereas the contribution of the Pavlovian effect was small. Over experience, the relative contribution of the two effects reversed (type X time bin interaction effect: F[1, 365]=16.7, p<0.001). The Pavlovian effect gradually grew (mean slope: 0.14, 95% CI: [0.04 0.24]) at the expense of the adaptation effect, which eventually exhibited a reduced contribution (–0.15, [–0.25 –0.05]; Figure 5B). We note that both the decrease in the adaptation effect and the increase in the Pavlovian effect are not captured by a typical state-space model (Figure 5A).

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Pavlovian effects in sensorimotor adaptation are sensitive to the CS-US interval

The Pavlovian effects observed in Experiment 1 provide evidence that sensorimotor adaptation can be shaped by arbitrary contextual cues. These results stand in contrast to previous work showing that arbitrary cues are ineffective for separating competing motor memories (e.g. differential responses to clockwise [CW] and counterclockwise [CCW] rotations). This null result has been taken to reflect the irrelevance of such cues to the motor state (Gandolfo et al., 1996; Karniel and Mussa-Ivaldi, 2002; Howard et al., 2012; Howard et al., 2013).

Why were the arbitrary cues effective in Experiment 1? Inspired by studies of eyeblink conditioning, we opted to impose a strong temporal constraint on the CS-US interval. The contextual cues served as the imperative signals, and we required that the participants respond quickly to the imperative, resulting in a mean CS-US interval of around 300 ms. The timing of events was somewhat more relaxed in prior studies. For example, in Howard et al., 2013, the color cues (which could be seen as CSs for differential conditioning) were presented 1000 ms before the imperative. When adding in the reaction time (RT), the CS-US interval may lie beyond the optimal value for cerebellar-dependent learning (Brudner et al., 2016; Kitazawa et al., 1995; Schneiderman and Gormezano, 1964; Smith et al., 1969). Thus, the reported ineffectiveness of arbitrary cues in separating motor memories may be related to the failure to meet the temporal requirements for forming associations between these cues and their associated feedback signals.

In Experiment 2, we tested the hypothesis that extending the temporal interval between arbitrary cues and sensorimotor feedback would attenuate or abolish the Pavlovian effect in visuomotor adaptation. To extend the interval, we opted to have the CSs no longer serve as the movement imperative; rather, a new cue, a color change of the target, served as the imperative signal (Figure 6A). To extend the CS-US interval, we imposed a delay between the onsets of the CS and the imperative. The mean of the delay was set to 1000 ms, with the actual value selected from a distribution ranging from 800 to 1200 ms to maintain unpredictability of the imperative timing (see Materials and methods for details).

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During the acquisition phase of Experiment 2, participants exhibited a marked change in movement direction, opposite to the direction of the clamped feedback (adaptation effect: F[1, 63]=47.3, p<0.001, BF₁₀=7.58×10⁶, η_p²=0.43, mean difference, 95% CI; 1.80°, [1.29° 2.31°]), reaching a mean asymptote of ~25° (Figure 6B). The asymptotic values in this experiment were higher than those seen in Experiment 1, possibly due to differences in the experimental setup (see Discussion). Despite this increase in overall adaptation, a Pavlovian differential conditioning effect was not detected (F[1, 63]=0.54, p=0.465, BF₁₀=0.16, η_p²=0.01, mean difference: 0.17°, 95% CI: [–0.29° 0.63°]), and there was no trial n−1 × n interaction (F[1, 63]=0.60, p=0.442, BF₁₀=0.17, and η_p²=0.01; Figure 6C). During the probe phase, the trial n−1 effect disappeared with the removal of the visual feedback (F[1, 63]=1.01, p=0.319, BF₁₀=0.21, η_p²=0.02, mean difference: –0.22°, 95% CI: [–0.65° 0.21°]). Importantly, and consistent with the results from the acquisition phase, we again found no reliable Pavlovian effect (F[1, 63]=1.36, p=0.248, BF₁₀=0.25, η_p²=0.02, mean difference: 0.28°, 95% CI: [–0.19° 0.75°]) and no trial n−1 × n interaction (F[1, 63]=0.42, p=0.517, BF₁₀=0.16, and η_p²=0.01; Figure 6D). These results suggest that extending the CS-US interval by approximately 1000 ms rendered arbitrary sensory contextual cues ineffective in separating distinct motor memories.

One possible concern with our method of increasing the CS-US interval is that, by using a different stimulus as the imperative (the target color change), the salience of the tone and light CSs may have been reduced since the task no longer required the participants to attend to these cues. To address this, in Experiment 3, we used the same CSs (tone and light) and imperative signal (color change of the target) as in Experiment 2 but now made the onsets of the CS and imperative simultaneous on each trial (Figure 7A). In this way, the CS-US interval is much shorter ([mean reaction time (RT) ± STD]: 306±57.9 ms), similar to Experiment 1. We also increased the inter-trial interval in Experiment 3 to roughly match that of Experiment 2 given evidence showing that the rate of associative events impacts classical conditioning (Gallistel and Gibbon, 2000).

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The time course of adaptation in Experiment 3 was similar to that observed in Experiment 2, with a mean asymptote around ~25° (Figure 7B). During the acquisition phase, trial-by-trial changes in heading angle showed the standard adaptation (trial n−1) effect (F[1, 63]=101.6, p<0.001, BF₁₀=2.77×10¹², η_p²=0.62, mean difference, 95% CI; 1.46°, [1.17° 1.74°]). However, unlike Experiment 2, we now observed a significant Pavlovian effect (F[1, 63]=6.05, p=0.017, BF₁₀=2.35, η_p²=0.09, mean difference, 95% CI; 0.34°, [0.07° 0.61°]; Figure 7C). Consistent with the Rescorla-Wanger predictions (see Figure 2E), there was no significant interaction between trial n−1 and trial n effects (F[1, 63]=1.30, p=0.258, BF₁₀=0.24, and η_p²=0.26). The Pavlovian effect was also significant in the probe phase (F[1, 63]=25.6, p<0.001, BF₁₀=6.88×10³, η_p²=0.29, mean difference, 95% CI; 0.77°, [0.47° 1.07°]) with neither trial n−1 (F[1, 63]=2.37, p=0.129, BF₁₀=0.41, η_p²=0.04, mean difference, 95% CI; –0.28°, [–0.63° 0.08°]) nor interaction effects (F[1, 63]=0.86, p=0.358, BF₁₀=0.19, and η_p²=0.01; (Figure 7D)).

Taken together, the results of Experiments 2 and 3 support our conjecture that the efficacy of arbitrary stimuli in serving as contextual cues for sensorimotor conditioning is subject to strong temporal constraints, a key feature of cerebellar-dependent learning. Even when the tone and light no longer required attention, they proved effective for differential conditioning when the interval between these CSs and the US was short (around 300 ms) but not when the interval was extended (around 1000 ms).

Additivity principle in response to compound stimuli is observed in sensorimotor adaptation

The results of Experiments 1–3 demonstrate that implicit sensorimotor adaptation displays two prominent features of associative learning – the associability of sensorimotor feedback with arbitrary sensory cues, and the key role of CS-US timing in the formation of those associations. In Experiment 4, we tested another core feature of associative learning, the principle of additivity (Mackintosh, 1976; Pavlov, 1927; Rescorla and Wagner, 1972). This principle is based on the idea that there is an associative capacity for a given US – the V term in the Rescorla-Wagner equation. That is, multiple CSs can become associated with a given US, but the combined associative strength is bounded by V. As a result of this capacity constraint, CSs effectively compete with one another, with the associative strength split among multiple cues.

The classic method to examine additivity is compound conditioning, where two or more stimuli are presented simultaneously to form a ‘compound’ CS (Equation 3). When paired with a US, this compound CS will come to elicit CRs. Importantly, the associative strength of the compound CS (V_comp) is the sum of the associative strengths of the elemental CSs (V_i), where nS in Equation 3 represents the number of elements forming the compound. Consequently, each element of the compound, when presented alone, elicits a proportionally weaker CR, with the degree of attenuation being a function of the associative strength of that CS.

(3) $V_i^{[n]}=V_i^{[n-1]}+\alpha \cdot \beta \cdot (\lambda -V_{comp}^{\left[n-1\right]});V_{comp}^{\left[n-1\right]}=\sum _{i=1}^{nS}{V}_i^{\left[n-1\right]}$

The additivity principle has received ample support in behavioral and neural studies of associative learning (Giurfa, 2007; Kehoe et al., 1994; Kehoe and Schreurs, 1986; Rescorla and Wagner, 1972; Weiss, 1972) but has not, to our knowledge, been tested in sensorimotor adaptation. In Experiment 4, we used a compound conditioning design, pairing a 15° error clamp stimulus with a compound CS (simultaneous presentation of the tone and light; Figure 8A) on all trials of the acquisition phase. As in Experiments 1–3, we again observed robust adaptation in the acquisition phase, manifesting as a change in heading angle in the direction opposite the clamp (Figure 8B).

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The critical test in this experiment comes from the probe phase. Here, the visual feedback was eliminated, and the presented imperative was either the original compound CS or just the tone or light alone. We observed a significant Pavlovian effect of CS type on these no-feedback trials (Friedman test: χ²[2]=9.82, p=0.007, and W=0.223), with larger changes in heading angles on compound CS trials (median: 0.39°, interquartile range: [–0.05° 0.49°]) relative to the tone-alone (–0.15°, [–0.47° 0.18°], p=0.020) or light-alone (–0.22°, [–0.52° 0.34°]p=0.020) trials, conforming to the first prediction of the additivity principle (Figure 8C and D).

We note that the median trial-by-trial change in heading angle for the tone- and light-alone trials is negative. This is because this measure reflects modulations in behavior around the mean heading angle, and this mean decreases over time due to extinction given the absence of the error feedback. This general trend should also vary for the different CSs depending on their relative salience (Equation 3; Kamin, 1967). Crucially, the additivity principle posits that there should be a negative correlation between the associative strengths of competing CSs (Rescorla and Wagner, 1972). That is, if a strong associative bond is formed between one CS and the US, this will come at the expense of the associative strength accrued by competing CSs (Equation 3) given the capacity limit on associability (V). This prediction was strikingly confirmed in an analysis of the heading angle changes on tone- and light-alone trials. Participants who were more sensitive to the tone stimulus were less sensitive to the light stimulus and vice versa (Figure 8E, Pearson correlation: r=−0.72, p<0.001, and BF₁₀=163.2).

As in Experiments 1–3, since the probe phase of Experiment 4 consisted of different types of CSs presented randomly across trials, the behavior for a given trial should reflect not only the CS on trial n but also the motor state on trial n−1 (which is itself also influenced by the CS on that trial). As a further test of compound conditioning, we pooled the two single-CS conditions to measure the effects of the previous and current CS type (singleton vs compound) on the observed changes in heading angle during the probe phase. We again observed the Pavlovian effect (mean: 0.42°, 95% CI: [0.24° 0.59°]; F[1, 21]=21.2, p<0.001, BF₁₀=459.9, and η_p²=0.50). There was a relative increase in heading angle for the compound CS (0.24°, [0.13° 0.35°]) and a relative decrease for the singleton CSs (–0.18°, [–0.28° –0.07°]; Figure 8F). The main effect of the CS on trial n−1 was neither significant (–0.01°, [–0.27° 0.24°]; F[1, 21]=0.012, p=0.915, BF₁₀=0.21, and η_p²=5.58×10^–4) nor was the trial n−1 × trial n interaction (F[1, 21]=0.276, p=0.605, BF₁₀=0.25, and η_p²=0.01), presumably due to the elimination of adaptation effects given the absence of visual feedback in the probe phase.

Sensorimotor adaptation and delay eyeblink conditioning are foundational paradigms for studying error-based sensorimotor learning. They have yielded a rich empirical foundation in the development of theoretical and neural models of learning and memory, particularly with respect to cerebellar function (Albus, 1971; Ito, 1984; Marr, 1969; Wolpert et al., 1998). Adaptation has typically been modeled from a control engineering perspective, centered on the idea that changes in behavior are driven by sensory prediction errors that arise when experienced feedback deviates from that predicted by a forward model operating on an efference copy of the motor command (Krakauer et al., 2019; Shadmehr and Krakauer, 2008; Wolpert and Flanagan, 2001). In contrast, eyeblink conditioning is treated as an associative learning process that can be shaped by arbitrary sensory context cues.

The present study takes a first step toward a more parsimonious framework that might account for these two canonical forms of cerebellar-dependent motor learning. We were motivated by the apparent paradox concerning whether arbitrary stimuli can act as sufficient contextual cues for the establishment of distinct motor memories during sensorimotor adaptation. In attempting to resolve this paradox, we conceptualized adaptation as analogous to associative learning. Seen from this perspective, we recognized that prior studies failing to observe adaptation in response to arbitrary context cues had not considered the short, precise temporal relationship between these cues and sensorimotor feedback. By modifying a visuomotor adaptation task to conform to timing constraints similar to those required for delay eyeblink conditioning, we showed that adaptation exhibited the hallmarks of both differential conditioning (Experiments 1 and 3) and compound conditioning (Experiment 4). These results provide the first evidence, to our knowledge, that pairing neutral stimuli (i.e. tones and lights) with distinct visuomotor outcomes can differentially influence implicit feedforward sensorimotor adaptation in a manner consistent with core principles of associative learning.

The role of context in sensorimotor adaptation has been the subject of considerable debate, with a large body of empirical studies asking whether different sensory cues are sufficient to ‘tag’ different motor memories. Postural and movement-related variables, such as different lead-in and follow-through movements, are very effective contextual cues and allow participants to respond to interleaved, opposing perturbations with minimal interference (Howard et al., 2012; Howard et al., 2013; Howard et al., 2015; Sheahan et al., 2016; Schween et al., 2019). In contrast, arbitrary visual features, such as color cues, have been generally ineffective (Gandolfo et al., 1996; Karniel and Mussa-Ivaldi, 2002; Howard et al., 2012; Howard et al., 2013; Krouchev and Kalaska, 2003; Osu et al., 2004; Addou et al., 2011; Forano et al., 2021). To account for this discrepancy, it has been proposed that movement-related cues are dynamically incorporated into the motor state, allowing for the separation of distinct internal models, whereas arbitrary cues are not sufficiently relevant to the motor state (Howard et al., 2012; Howard et al., 2013).

In the current study, we found compelling contextual effects using arbitrary sensory cues. Importantly, like delay eyeblink conditioning, these effects were subject to strong temporal constraint on the interval between the CS and US, similar to what is observed in other forms of cerebellar-dependent sensorimotor learning. Robust differential conditioning behavior was observed when the CS-US interval was short (Experiments 1 and 3); increasing the interval by just ~1000 ms abolished the Pavlovian effect (Experiment 2). These results are also consistent with prior evidence showing that the efficacy of movement-related cues is highly sensitive to timing (Howard et al., 2012).

These temporal constraints are likely built into standard adaptation tasks. The target is a salient stimulus that defines the task goal and movement plan, and its onset usually serves as the imperative for movement initiation. RTs in these tasks are typically below 500 ms (Kim et al., 2018; Kim et al., 2019; Avraham et al., 2021). As such, a tight temporal link is established between target appearance and movement, echoing (perhaps inadvertently) the CS-US temporal constraints essential for cerebellar-dependent conditioning. Under these conditions, the target can be viewed as a highly effective contextual cue.

More precisely, we propose that it is the movement plan itself that constitutes the primary, strongest CS. While the movement plan and target appearance usually coincide spatially (i.e. people aim to the target), this is not always the case. For example, with a standard visuomotor rotation, participants often deliberately aim away from the target, especially when the perturbation is large (Hegele and Heuer, 2010; Taylor et al., 2014). Recognizing this ‘re-aimed’ plan as behaving like a CS may provide a parsimonious account of several phenomena. First, generalization of adaptation appears to be centered around the direction of the movement plan, not the target (Day et al., 2016; McDougle et al., 2017). Speculatively, this mirrors generalization effects seen in eyeblink conditioning, where variations on the learned CS (e.g. altering a tone’s frequency) lead to parametric changes in CR probability (Siegel et al., 1968). These changes produce a similar Gaussian generalization function as that seen in adaptation generalization. Second, even in the absence of distinct contextual movements (e.g. follow-throughs), the mere activation of different motor plans can serve as efficient contextual cues, negating interference effects from opposing perturbations (Sheahan et al., 2016; Sheahan et al., 2018). Third, an emphasis on the movement plan is in accord with theoretical models of cerebellar-dependent adaptation, where the prediction that constitutes the basis for the sensory prediction error is computed using an efference copy of the movement intention (Blakemore et al., 2001; Gao et al., 2016; Kawato and Gomi, 1992; Kim et al., 2022; Wolpert et al., 1998).

We considered the possibility that the movement plan is a highly salient CS when designing the task. Participants were always moving to a single target location. Studies of motor adaptation commonly use multiple targets that span the entire workspace. However, the use of multiple targets could effectively increase the number of CSs in the task. By the additivity principle, these would compete with the arbitrary tone and light CSs, making it harder to observe their contribution to the Pavlovian effect. In addition, using a single target location allowed us to have the target remain on the screen throughout the entire experiment, eliminating any temporal linkage between the onset of the target and the feedback. While a single target may facilitate the use of simple explicit strategies (McDougle and Taylor, 2019), empirically, there is considerable evidence demonstrating that the clamp method effectively isolates implicit adaptation (Morehead et al., 2017; Tsay et al., 2020c; Avraham et al., 2021). Moreover, the Pavlovian effects were similar for the subset of participants who recognized the contingency between the CS and the US as for those who did not (see Results). Thus, while explicit strategies cannot be completely ruled out, we do not believe they significantly drove the observed effects.

Our focus in this study was on features of sensorimotor adaptation that map onto a CS, US, and CR. The UR in this context could be defined as an automatic action that is immediately triggered by the US, such as an online correction to the perceived error. While there is a rich literature showing the automatic and relatively fast latency of this corrective response (e.g. around 150 ms; Carroll et al., 2019; Franklin and Wolpert, 2008), to isolate feedforward adaptation, we opted to use rapid shooting movements that precluded online corrections (see Results). We recognize that a feedback response potentiated by the perturbation might be utilized for feedforward learning (Albert and Shadmehr, 2016). However, a UR is not always required for conditioning processes arising from volitional behaviors (e.g. Cartoni et al., 2016). Future work is needed to better understand the role of URs within our framework.

In terms of the feedforward response, there were notable differences in the extent of adaptation across the four experiments. Overall heading angle reached asymptotic values of ~15° in Experiments 1 and 4 and ~25° in Experiments 2 and 3. These differences are likely due to changes in the experimental platform. Experiments 1 and 4 were conducted in our laboratory, using a tablet and digitizing pen setup in which the movements involve arm movements of at least 8 cm. In contrast, Experiments 2 and 3 were conducted via a web-based platform, with each participant using their personal computer with a mouse or a trackpad to produce wrist or finger movements of ~2 cm (depending on the sensitivity of the device). Although basic phenomena of visuomotor adaptation are similar between lab- and web-based platforms (Tsay et al., 2021), there may be mechanistic differences. For example, with our laboratory setup, the monitor is positioned just above the hand. As such, the stimuli and movement are in parallel planes, and there is a 1:1 correspondence between the distance moved and the extent of the cursor movement. For the web-based platform, the stimuli and movement occur in roughly orthogonal planes, and there is a gain factor such that the cursor movement is larger than the hand movement. We expect that the laboratory setup may be much better suited for providing reliable information concerning proprioception, information that may limit the extent of adaptation (Salomonczyk et al., 2011; Tsay et al., 2022). Given that proprioceptive and visual signals are not aligned in the web-based studies, proprioception may have a reduced effect in limiting adaptation, leading to a higher asymptote.

To formally relate eyeblink conditioning and adaptation, we implemented the Rescorla-Wagner model, a classic associative learning model that has been widely employed in the classical and operant conditioning literature (Rescorla and Wagner, 1972). The success of this model to capture the general features of the current datasets should not be surprising since the model was developed to account for phenomena such as differential conditioning and compound conditioning. Thus, it was somewhat overdetermined that the Rescorla-Wagner model would provide better fits than the standard state-space model in our study, given that the latter cannot capture contextual effects. In theory, a standard state-space model could be modified such that different sensory cues become associated with different independent states to allow for context-dependent learning (Heald et al., 2018). However, we emphasize that to account for compound conditioning, and in particular the additivity principle (i.e. overshadowing), a state-space model would essentially have to be transformed into a facsimile of a Rescorla-Wagner model, supporting our key conclusions.

The Rescorla-Wagner model offers an account of how arbitrary sensory cues, visual targets, and movement plans can serve as CSs for adaptation. There are, however, some notable phenomena in the sensorimotor adaptation literature that are neither accounted for by our application of the Rescorla-Wagner model nor by the basic state-space model. Given the prominent role of the state-space model in the sensorimotor adaptation literature, variants of this model were developed to capture these observations. One such effect is spontaneous recovery, the re-manifestation of a previously adapted state in the absence of error feedback. A variant of the state-space model, one that allows for multiple states with different learning and forgetting rates, can capture spontaneous recovery (Smith et al., 2006). A second example is the relationship between learning rate and environmental consistency; learning is faster in response to a consistent vs inconsistent perturbation (Albert et al., 2021; Avraham et al., 2020; Gonzalez Castro et al., 2014; Herzfeld et al., 2014; Hutter and Taylor, 2018). To account for this effect, the state-space model can be modified to allow the learning rate to vary with experience (Herzfeld et al., 2014). A third example is savings upon relearning, where faster adaptation is observed upon a second exposure to the same perturbation (Huang et al., 2011; Krakauer et al., 2005). Studies have modeled savings using multi-rate state-space models (Smith et al., 2006), learning rate modulation (Herzfeld et al., 2014), or a combination of these factors (Zarahn et al., 2008; Mawase et al., 2014).

These higher-order phenomena have also been addressed in a new model of sensorimotor learning, one that takes a Bayesian inference approach (Heald et al., 2021). The contextual inference (COIN) model posits that motor adaptation arises from two interacting mechanisms: proper learning, which involves the creation and updating of context-specific memories, and apparent learning, a process of inferring the current context to determine which memory to express (recall). Unlike conventional context-independent models of motor adaptation, the COIN model stresses the importance of the environment in guiding memory retrieval. In one sense, our implementation of the Rescorla-Wagner model follows a similar philosophy. However, it maps to the proper learning component of the COIN model since we assume that the current context is determined by the actual properties of the environment in an all-or-none manner (e.g. the CS presented by the experimenter). The COIN model suggests that spontaneous recovery, consistency effects, and savings may emerge due to contextual inferences; these inferences likely involve cognitive systems related to executive function and non-motor memory systems (Collins and McDougle, 2021). Consistent with this view, growing evidence shows that these phenomena are, in large degree, the result of strategic changes (Haith et al., 2015; Morehead et al., 2015; Leow et al., 2020; Avraham et al., 2020; Avraham et al., 2021; Wang et al., 2022).

While the basic Rescorla-Wagner model is unable to account for higher order effects such as spontaneous recovery or savings, we envision that complimenting it with more sophisticated, Bayesian inference models could readily accommodate these phenomena. In fact, models that combine associative mechanisms with some form of a Bayesian inference process that carves the world into distinct contexts have successfully captured a range of complex phenomena in classical conditioning and reinforcement learning (Collins and Frank, 2013; Courville et al., 2006; Gershman, 2015; Kruschke, 2008). We believe that our results lay the foundation for adopting a similar approach to study implicit sensorimotor adaptation and perhaps a more general account that captures the operation and interaction of multiple learning processes.

Motivated by the cerebellar literature, we limited our focus to delay eyeblink conditioning in considering how associative learning mechanisms can account for contextual effects in sensorimotor adaptation. We recognize that conditioning effects can be much more complex than the behavioral changes that arise from the pairing of two stimuli (Rescorla, 1988). These include associations between a CS and an action (Skinner, 1938), learning that does not abide by strict timing requirements (Gallistel and Gibbon, 2000), and other conditioning processes (e.g. trace conditioning) that rely on brain structures outside the cerebellum (Clark et al., 2002; Clark and Squire, 1998). Multiple learning processes allow the organism to build a comprehensive representation of the world, with the ability to flexibly modify behavior at many levels of control in response to changes in the contingencies between the body and environment (McDougle et al., 2016; Kim et al., 2020). Nonetheless, by showing that core constraints of delay eyeblink conditioning are relevant for sensorimotor adaptation, our study may inform a formal framework that looks at these two domains in a more unified manner.

Although our results highlight principles that address context-dependent sensorimotor adaptation, they do not speak to the error-correcting adaptation algorithm itself. Conventional models of this algorithm focus on the role of forward models in predicting future sensory states and updating motor commands to reduce sensory prediction errors (Wolpert and Ghahramani, 2000; but see Hadjiosif et al., 2021). Associative learning alone does not provide a mechanism for the error-correction process (e.g. the directional change of reaching movements given rotated feedback or the precise timing of an eyeblink response to a predicted air puff). Rather, it describes the association between a contextual cue and a salient event (e.g. shock, reward, etc.). Speculatively, an alternative idea is that sensorimotor adaptation may operate as a lookup table of context-outcome associations learned by a system designed to keep the sensorimotor system calibrated. A model-free conception like this could bring sensorimotor adaptation closer to classical associative models of cerebellar learning and plasticity (Albus, 1971; Ito, 1984; Marr, 1969).

All data generated or analysed during this study are included in the manuscript; Source Data files have been provided for Figures 2B, 2C, 2D, 5B, 6B, 6C, 6D, 7B, 7C, 7D, 8B, 8C, 8E and 8F. All raw data files and codes for data analysis and simulations are available from the GitHub repository: https://github.com/guyavr/AssociativeMotorAdaptation.git (copy archived at swh:1:rev:f0c5c7cb930dc7952c24021113edac8be7e4bf32).

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Author details

1. Guy Avraham

   1. Department of Psychology, University of California, Berkeley, Berkeley, United States
   2. Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, United States

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing – original draft, Project administration, Writing – review and editing

   For correspondence

   guyavraham@berkeley.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-6170-1041

2. Jordan A Taylor

   Department of Psychology, Princeton University, Princeton, United States

   Contribution

   Conceptualization, Supervision, Methodology, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-9300-1229

3. Assaf Breska

   1. Department of Psychology, University of California, Berkeley, Berkeley, United States
   2. Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, United States
   3. Max Planck Institute for Biological Cybernetics, Tübingen, Germany

   Contribution

   Conceptualization, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-6233-073X

4. Richard B Ivry

   1. Department of Psychology, University of California, Berkeley, Berkeley, United States
   2. Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, United States

   Contribution

   Conceptualization, Resources, Supervision, Funding acquisition, Project administration, Writing – review and editing

   Competing interests

   Senior editor, eLife

   "This ORCID iD identifies the author of this article:" 0000-0003-4728-5130

5. Samuel D McDougle

   Department of Psychology, Yale University, New Haven, United States

   Contribution

   Conceptualization, Software, Supervision, Methodology, Writing – original draft, Project administration, Writing – review and editing

   For correspondence

   samuel.mcdougle@yale.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-8100-4238

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