Perceptual error based on Bayesian cue combination drives implicit motor adaptation

Reviewer #1 (Public Review):

This valuable study demonstrates a novel mechanism by which implicit motor adaptation saturates for large visual errors in a principled normative Bayesian manner. Additionally, the study revealed two notable empirical findings: visual uncertainty increases for larger visual errors in the periphery, and proprioceptive shifts/implicit motor adaptation are non-monotonic, rather than ramp-like. This study is highly relevant for researchers in sensory cue integration and motor learning. However, I find some areas where statistical quantification is incomplete, and the contextualization of previous studies to be puzzling.

Issue #1: Contextualization of past studies.

While I agree that previous studies have focused on how sensory errors drive motor adaptation (e.g., Burge et al., 2008; Wei and Kording, 2009), I don't think the PReMo model was contextualized properly. Indeed, while PReMo should have adopted clearer language - given that proprioception (sensory) and kinaesthesia (perception) have been used interchangeably, something we now make clear in our new study (Tsay, Chandy, et al. 2023) - PReMo's central contribution is that a perceptual error drives implicit adaptation (see Abstract): the mismatch between the felt (perceived) and desired hand position. The current paper overlooks this contribution. I encourage the authors to contextualize PReMo's contribution more clearly throughout. Not mentioned in the current study, for example, PReMo accounts for the continuous changes in perceived hand position in Figure 4 (Figure 7 in the PReMo study).

There is no doubt that the current study provides important additional constraints on what determines perceived hand position: Firstly, it offers a normative Bayesian perspective in determining perceived hand position. PReMo suggests that perceived hand position is determined by integrating motor predictions with proprioception, then adding a proprioceptive shift; PEA formulates this as the optimal integration of these three inputs. Secondly, PReMo assumed visual uncertainty to remain constant for different visual errors; PEA suggests that visual uncertainty ought to increase (but see Issue #2).

Issue #2: Failed replication of previous results on the effect of visual uncertainty.

2a. A key finding of this paper is that visual uncertainty linearly increases in the periphery; a constraint crucial for explaining the non-monotonicity in implicit adaptation. One notable methodological deviation from previous studies is the requirement to fixate on the target: Notably, in the current experiments, participants were asked to fixate on the target, a constraint not imposed in previous studies. In a free-viewing environment, visual uncertainty may not attenuate as fast, and hence, implicit adaptation does not attenuate as quickly as that revealed in the current design with larger visual errors. Seems like this current fixation design, while important, needs to be properly contextualized considering how it may not represent most implicit adaptation experiments.

2b. Moreover, the current results - visual uncertainty attenuates implicit adaptation in response to large, but not small, visual errors - deviates from several past studies that have shown that visual uncertainty attenuates implicit adaptation to small, but not large, visual errors (Tsay, Avraham, et al. 2021; Makino, Hayashi, and Nozaki, n.d.; Shyr and Joshi 2023). What do the authors attribute this empirical difference to? Would this free-viewing environment also result in the opposite pattern in the effect of visual uncertainty on implicit adaptation for small and large visual errors?

2c. In the current study, the measure of visual uncertainty might be inflated by brief presentation times of comparison and referent visual stimuli (only 150 ms; our previous study allowed for a 500 ms viewing time to make sure participants see the comparison stimuli). Relatedly, there are some individuals whose visual uncertainty is greater than 20 degrees standard deviation. This seems very large, and less likely in a free-viewing environment.

2d. One important confound between clear and uncertain (blurred) visual conditions is the number of cursors on the screen. The number of cursors may have an attenuating effect on implicit adaptation simply due to task-irrelevant attentional demands (Parvin et al. 2022), rather than that of visual uncertainty. Could the authors provide a figure showing these blurred stimuli (gaussian clouds) in the context of the experimental paradigm? Note that we addressed this confound in the past by comparing participants with and without low vision, where only one visual cursor is provided for both groups (Tsay, Tan, et al. 2023).

Issue #3: More methodological details are needed.

3a. It's unclear why, in Figure 4, PEA predicts an overshoot in terms of perceived hand position from the target. In PReMo, we specified a visual shift in the perceived target position, shifted towards the adapted hand position, which may result in overshooting of the perceived hand position with this target position. This visual shift phenomenon has been discovered in previous studies (e.g., (Simani, McGuire, and Sabes 2007)).

3b. The extent of implicit adaptation in Experiment 2, especially with smaller errors, is unclear. The implicit adaptation function seems to be still increasing, at least by visual inspection. Can the authors comment on this trend, and relatedly, show individual data points that help the reader appreciate the variability inherent to these data?

3c. The same participants were asked to return for multiple days/experiments. Given that the authors acknowledge potential session effects, with attenuation upon re-exposure to the same rotation (Avraham et al. 2021), how does re-exposure affect the current results? Could the authors provide clarity, perhaps a table, to show shared participants between experiments and provide evidence showing how session order may not be impacting results?

3d. The number of trials per experiment should be detailed more clearly in the Methods section (e.g., Exp 4). Moreover, could the authors please provide relevant code on how they implemented their computational models? This would aid in future implementation of these models in future work. I, for one, am enthusiastic to build on PEA.

3f. In addition to predicting a correlation between proprioceptive shift and implicit adaptation on a group level, both PReMo and PEA (but not causal inference) predict a correlation between individual differences in proprioceptive shift and proprioceptive uncertainty with the extent of implicit adaptation (Tsay, Kim, et al. 2021). Interestingly, shift and uncertainty are independent (see Figures 4F and 6C in Tsay et al, 2021). Does PEA also predict independence between shift and uncertainty? It seems like PEA does predict a correlation.

References:

Avraham, Guy, Ryan Morehead, Hyosub E. Kim, and Richard B. Ivry. 2021. "Reexposure to a Sensorimotor Perturbation Produces Opposite Effects on Explicit and Implicit Learning Processes." PLoS Biology 19 (3): e3001147.
Makino, Yuto, Takuji Hayashi, and Daichi Nozaki. n.d. "Divisively Normalized Neuronal Processing of Uncertain Visual Feedback for Visuomotor Learning."
Parvin, Darius E., Kristy V. Dang, Alissa R. Stover, Richard B. Ivry, and J. Ryan Morehead. 2022. "Implicit Adaptation Is Modulated by the Relevance of Feedback." BioRxiv. https://doi.org/10.1101/2022.01.19.476924.
Shyr, Megan C., and Sanjay S. Joshi. 2023. "A Case Study of the Validity of Web-Based Visuomotor Rotation Experiments." Journal of Cognitive Neuroscience, October, 1-24.
Simani, M. C., L. M. M. McGuire, and P. N. Sabes. 2007. "Visual-Shift Adaptation Is Composed of Separable Sensory and Task-Dependent Effects." Journal of Neurophysiology 98 (5): 2827-41.
Tsay, Jonathan S., Guy Avraham, Hyosub E. Kim, Darius E. Parvin, Zixuan Wang, and Richard B. Ivry. 2021. "The Effect of Visual Uncertainty on Implicit Motor Adaptation." Journal of Neurophysiology 125 (1): 12-22.
Tsay, Jonathan S., Anisha M. Chandy, Romeo Chua, R. Chris Miall, Jonathan Cole, Alessandro Farnè, Richard B. Ivry, and Fabrice R. Sarlegna. 2023. "Implicit Motor Adaptation and Perceived Hand Position without Proprioception: A Kinesthetic Error May Be Derived from Efferent Signals." BioRxiv. https://doi.org/10.1101/2023.01.19.524726.
Tsay, Jonathan S., Hyosub E. Kim, Darius E. Parvin, Alissa R. Stover, and Richard B. Ivry. 2021. "Individual Differences in Proprioception Predict the Extent of Implicit Sensorimotor Adaptation." Journal of Neurophysiology, March. https://doi.org/10.1152/jn.00585.2020.
Tsay, Jonathan S., Steven Tan, Marlena Chu, Richard B. Ivry, and Emily A. Cooper. 2023. "Low Vision Impairs Implicit Sensorimotor Adaptation in Response to Small Errors, but Not Large Errors." Journal of Cognitive Neuroscience, January, 1-13.

Reviewer #2 (Public Review):

Summary:
The authors present the Perceptual Error Adaptation (PEA) model, a computational approach offering a unified explanation for behavioral results that are inconsistent with standard state-space models. Beginning with the conventional state-space framework, the paper introduces two innovative concepts. Firstly, errors are calculated based on the perceived hand position, determined through Bayesian integration of visual, proprioceptive, and predictive cues. Secondly, the model accounts for the eccentricity of vision, proposing that the uncertainty of cursor position increases with distance from the fixation point. This elegantly simple model, with minimal free parameters, effectively explains the observed plateau in motor adaptation under the implicit motor adaptation paradigm using the error-clamp method. Furthermore, the authors experimentally manipulate visual cursor uncertainty, a method established in visuomotor studies, to provide causal evidence. Their results show that the adaptation rate correlates with perturbation sizes and visual noise, uniquely explained by the PEA model and not by previous models. Therefore, the study convincingly demonstrates that implicit motor adaptation is a process of Bayesian cue integration

Strengths:
In the past decade, numerous perplexing results in visuomotor rotation tasks have questioned their underlying mechanisms. Prior models have individually addressed aspects like aiming strategies, motor adaptation plateaus, and sensory recalibration effects. However, a unified model encapsulating these phenomena with a simple computational principle was lacking. This paper addresses this gap with a robust Bayesian integration-based model. Its strength lies in two fundamental assumptions: motor adaptation's influence by visual eccentricity, a well-established vision science concept, and sensory estimation through Bayesian integration. By merging these well-founded principles, the authors elucidate previously incongruent and diverse results with an error-based update model. The incorporation of cursor feedback noise manipulation provides causal evidence for their model. The use of eye-tracking in their experimental design, and the analysis of adaptation studies based on estimated eccentricity, are particularly elegant. This paper makes a significant contribution to visuomotor learning research.

Weaknesses:
The paper provides a comprehensive account of visuomotor rotation paradigms, addressing incongruent behavioral results with a solid Bayesian integration model. However, its focus is narrowly confined to visuomotor rotation, leaving its applicability to broader motor learning paradigms, such as force field adaptation, saccadic adaptation, and de novo learning paradigms, uncertain. The paper's impact on the broader fields of neuroscience and cognitive science may be limited due to this specificity. While the paper excellently demonstrates that specific behavioral results in visuomotor rotation can be explained by Bayesian integration, a general computational principle, its contributions to other motor learning paradigms remain to be explored. The paper would benefit from a discussion on the model's generality and its limitations, particularly in relation to the undercompensating effects in other motor learning paradigms.

Reviewer #3 (Public Review):

Summary
In this paper, the authors model motor adaptation as a Bayesian process that combines visual uncertainty about the error feedback, uncertainty about proprioceptive sense of hand position, and uncertainty of predicted (=planned) hand movement with a learning and retention rate as used in state space models. The model is built with results from several experiments presented in the paper and is compared with the PReMo model (Tsay, Kim, et al., 2022) as well as a cue combination model (Wei & Körding, 2009). The model and experiments demonstrate the role of visual uncertainty about error feedback in implicit adaptation.

In the introduction, the authors notice that implicit adaptation (as measured in error-clamp-based paradigms) does not saturate at larger perturbations, but decreases again (e.g. Moorehead et al., 2017 shows no adaptation at 135{degree sign} and 175{degree sign} perturbations). They hypothesized that visual uncertainty about cursor position increases with larger perturbations since the cursor is further from the fixated target. This could decrease the importance assigned to visual feedback which could explain lower asymptotes.

The authors characterize visual uncertainty for 3 rotation sizes in the first experiment, and while this experiment could be improved, it is probably sufficient for the current purposes. Then the authors present a second experiment where adaptation to 7 clamped errors is tested in different groups of participants. The models' visual uncertainty is set using a linear fit to the results from experiment 1, and the remaining 4 parameters are then fit to this second data set. The 4 parameters are 1) proprioceptive uncertainty, 2) uncertainty about the predicted hand position, 3) a learning rate, and 4) a retention rate. The authors' Perceptual Error Adaptation model ("PEA") predicts asymptotic levels of implicit adaptation much better than both the PReMo model (Tsay, Kim et al., 2022), which predicts saturated asymptotes, or a causal inference model (Wei & Körding, 2007) which predicts no adaptation for larger rotations. In a third experiment, the authors test their model's predictions about proprioceptive recalibration, but unfortunately, compare their data with an unsuitable other data set. Finally, the authors conduct a fourth experiment where they put their model to the test. They measure implicit adaptation with increased visual uncertainty, by adding blur to the cursor, and the results are again better in line with their model (predicting overall lower adaptation) than with the PReMo model (predicting equal saturation but at larger perturbations) or a causal inference model (predicting equal peak adaptation, but shifted to larger rotations). In particular, the model fits experiment 2 and the results from experiment 4 show that the core idea of the model has merit: increased visual uncertainty about errors dampens implicit adaptation.

Strengths
In this study, the authors propose a Perceptual Error Adaptation model ("PEA") and the work combines various ideas from the field of cue combination, Bayesian methods, and new data sets, collected in four experiments using various techniques that test very different components of the model. The central component of visual uncertainty is assessed in the first experiment. The model uses 4 other parameters to explain implicit adaptation. These parameters are 1) learning and 2) retention rate, as used in popular state space models, and the uncertainty (variance) of 3) predicted and 4) proprioceptive hand position. In particular, the authors observe that asymptotes for implicit learning do not saturate, as claimed before, but decrease again when rotations are very large and that this may have to do with visual uncertainty (e.g. Tsay et al., 2021, J Neurophysiol 125, 12-22). The final experiment confirms predictions of the fitted model about what happens when visual uncertainty is increased (overall decrease of adaptation). By incorporating visual uncertainty depending on retinal eccentricity, the predictions of the PEA model for very large perturbations are notably different from and better than, the predictions of the two other models it is compared to. That is, the paper provides strong support for the idea that visual uncertainty of errors matters for implicit adaptation.

Weaknesses
Although the authors don't say this, the "concave" function that shows that adaptation does not saturate for larger rotations has been shown before, including in papers cited in this manuscript.

The first experiment, measuring visual uncertainty for several rotation sizes in error-clamped paradigms has several shortcomings, but these might not be so large as to invalidate the model or the findings in the rest of the manuscript. There are two main issues we highlight here. First, the data is not presented in units that allow comparison with vision science literature. Second, the 1 second delay between the movement endpoint and the disappearance of the cursor, and the presentation of the reference marker, may have led to substantial degradation of the visual memory of the cursor endpoint. That is, the experiment could be overestimating the visual uncertainty during implicit adaptation.

The paper's third experiment relies to a large degree on reproducing patterns found in one particular paper, where the reported hand positions - as a measure of proprioceptive sense of hand position - are given and plotted relative to an ever-present visual target, rather than relative to the actual hand position. That is, 1) since participants actively move to a visual target, the reported hand positions do not reflect proprioception, but mostly the remembered position of the target participants were trying to move to, and 2) if the reports are converted to a difference between the real and reported hand position (rather than the difference between the target and the report), those would be on the order of ~20{degree sign} which is roughly two times larger than any previously reported proprioceptive recalibration, and an order of magnitude larger than what the authors themselves find (1-2{degree sign}) and what their model predicts. Experiment 3 is perhaps not crucial to the paper, but it nicely provides support for the idea that proprioceptive recalibration can occur with error-clamped feedback.

Perhaps the largest caveat to the study is that it assumes that people do not look at the only error feedback available to them (and can explicitly suppress learning from it). This was probably true in the experiments used in the manuscript, but unlikely to be the case in most of the cited literature. Ignoring errors and suppressing adaptation would also be a disastrous strategy to use in the real world, such that our brains may not be very good at this. So the question remains to what degree - if any - the ideas behind the model generalize to experiments without fixation control, and more importantly, to real-life situations.

Specific comments:
A small part of the manuscript relies on replicating or modeling the proprioceptive recalibration in a study we think does NOT measure proprioceptive recalibration (Tsay, Parvin & Ivry, JNP, 2020). In this study, participants reached for a visual target with a clamped cursor, and at the end of the reach were asked to indicate where they thought their hand was. The responses fell very close to the visual target both before and after the perturbation was introduced. This means that the difference between the actual hand position, and the reported/felt hand position gets very large as soon as the perturbation is introduced. That is, proprioceptive recalibration would necessarily have roughly the same magnitude as the adaptation displayed by participants. That would be several times larger than those found in studies where proprioceptive recalibration is measured without a visual anchor. The data is plotted in a way that makes it seem like the proprioceptive recalibration is very small, as they plot the responses relative to the visual target, and not the discrepancy between the actual and reported hand position. It seems to us that this study mostly measures short-term visual memory (of the target location). What is astounding about this study is that the responses change over time to begin with, even if only by a tiny amount. Perhaps this indicates some malleability of the visual system, but it is hard to say for sure.

Regardless, the results of that study do not form a solid basis for the current work and they should be removed. We would recommend making use of the dataset from the same authors, who improved their methods for measuring proprioception shifts just a year later (Tsay, Kim, Parvin, Stover, and Ivry, JNP, 2021). Although here the proprioceptive shifts during error-clamp adaptation (Exp 2) were tiny, and not quite significant (p<0.08), the reports are relative to the actual location of the passively placed unseen hand, measured in trials separate from those with reach adaptation and therefore there is no visual target to anchor their estimates to.

Experiment 1 measures visual uncertainty with increased rotation size. The authors cite relevant work on this topic (Levi & Klein etc) which has found a linear increase in uncertainty of the position of more and more eccentrically displayed stimuli.

First, this is a question where the reported stimuli and effects could greatly benefit from comparisons with the literature in vision science, and the results might even inform it. In order for that to happen, the units for the reported stimuli and effects should (also) be degrees of visual angle (dva).

As far as we know, all previous work has investigated static stimuli, where with moving stimuli, position information from several parts of the visual field are likely integrated over time in a final estimate of position at the end of the trajectory (a Kalman filter type process perhaps). As far as we know, there are no studies in vision science on the uncertainty of the endpoint of moving stimuli. So we think that the experiment is necessary for this study, but there are some areas where it could be improved.

Then, the linear fit is done in the space of the rotation size, but not in the space of eccentricity relative to fixation, and these do not necessarily map onto each other linearly. If we assume that the eye-tracker and the screen were at the closest distance the manufacturer reports it to work accurately at (45 cm), we would get the largest distances the endpoints are away from fixation in dva. Based on that assumed distance between the participant and monitor, we converted the rotation angles to distances between fixation and the cursor endpoint in degrees visual angle: 0.88, 3.5, and 13.25 dva (ignoring screen curvature, or the absence of it). The ratio between the perturbation angle and retinal distance to the endpoint is roughly 0.221, 0.221, and 0.207 if the minimum distance is indeed used - which is probably fine in this case. But still, it would be better to do fit in the relevant perceptual coordinate system.

The first distance (4 deg rotation; 0.88 dva offset between fixation and stimulus) is so close to fixation (even at the assumed shortest distance between eye and screen) that it can be considered foveal and falls within the range of noise of eye-trackers + that of the eye for fixating. There should be no uncertainty on or that close to the fovea. The variability in the data is likely just measurement noise. This also means that a linear fit will almost always go through this point, somewhat skewing the results toward linearity. The advantage is that the estimate of the intercept (measurement noise) is going to be very good. Unfortunately, there are only 2 other points measured, which (if used without the closest point) will always support a linear fit. Therefore, the experiment does not seem suitable to test linearity, only to characterize it, which might be sufficient for the current purposes. We'd understand if the effort to do a test of linearity using many more rotations requires too much effort. But then it should be made much clearer that the experiment assumes linearity and only serves to characterize the assumed linearity.

Final comment after the consultation session:
There were a lot of discussions about the actual interpretation of the behavioral data from this paper with regards to past papers (Tsay et al. 2020 or 2021), and how it matches the different variables of the model. The data from Tsay 2020 combined both proprioceptive information (Xp) and prediction about hand position (Xu) because it involves active movements. On the other hand, Tsay et al. 2021 is based on passive movements and could provide a better measure of Xp alone. We would encourage you to clarify how each of the variables used in the model is mapped onto the outcomes of the cited behavioral experiments.

The reviewers discussed this point extensively during the consultation process. The results reported in the Tsay 2020 study reflect both proprioception and prediction. However, having a visual target contributes more than just prediction, it is likely an anchor in the workspace that draws the response to it. Such that the report is dominated by short-term visual memory of the target (which is not part of the model). However, in the current Exp 3, as in most other work investigating proprioception, this is calculated relative to the actual direction.

The solution is fairly simple. In Experiment 3 in the current study, Xp is measured relative to the hand without any visual anchors drawing responses, and this is also consistent with the reference used in the Tsay et al 2021 study and from many studies in the lab of D. Henriques (none of which also have any visual reach target when measuring proprioceptive estimates). So we suggest using a different data set that also measures Xp without any other influences, such as the data from Tsay et al 2021 instead.

These issues with the data are not superficial and can not be solved within the model. Data with correctly measured biases (relative to the hand) that are not dominated by irrelevant visual attractors would actually be informative about the validity of the PEA model. Dr. Tsay has so much other that we recommend using a more to-the-point data set that could actually validate the PEA model.

Author Response:

We take the liberty to thank all of you for your constructive and inspiring comments, which will help us substantially improve the final version of the paper. Before our final revision with details, I am writing this provisional letter to have a quick response to our reviewers’ comments.

I first give a quick and short summary for your public reviews, then respond point-by-point.

Editors:

1. More discussion is needed.

2. More discussion about eye fixation during adaptation. Discuss why increasing visual uncertainty by blurring the cursor in the present study produces the opposite findings of previous studies (Tsay et al., 2021; Makino et al., 2023).

3. Discuss the broad impact of the current model.

4. Share the codes and the metadata (instead of the current data format).

Response: This is a concise summary of the major concerns listed in the public review. Given these concerns are easy to address, we are giving a quick but point-to-point response for now. The elaborate version will be put into our formal revision.

**Reviewer 1: **

1. More credit should be given to the PReMo model: a) The PReMo model also proposes that perceptual error drives implicit adaptation, as in a new publication in Tsay et al., 2023, which was not public at the time of the current writing; and b) The PReMo model can account for some dataset, e.g. Fig 4A.

Response: We will add this new citation and point out that the new paper also uses the term perceptual error. We will also point out that the PReMo model has the potential to explain Fig 4A, though for now, it assumes an additional visual shift to explain the positive proprioceptive changes relative to the target. We would expand the discussion about the comparison between the two models.

1. The present study produced an opposite finding of a previous finding, i.e., upregulating visual uncertainty (by cursor blurring here) decreases adaptation for large perturbations but less so for small perturbations, while previous studies have shown the opposite (by using a cursor cloud; Tsay et al., 2021; Makino et al., 2023). This needs explanation.

Response: Using the cursor cloud (Tsay et al., 2021, Makino et al., 2023) to modulate visual uncertainty has inherent drawbacks that make it unsuitable for testing the sensory uncertainty effect for visuomotor rotation. For the error clamp paradigm, the error is defined as angular deviation. The cursor cloud consists of multiple cursors spanning over a range of angles, which affects both the sensory uncertainty (the intended outcome) AND the sensory estimate of angles (the error itself, the undesired outcome). In Bayesian terms, the cursor cloud aims to modulate the sigma of a distribution (sigma_v in our model), but it additionally affects the mean of the distribution (mu). This unnecessary confound is avoided by using cursor blurring, which is still a cursor with its center (mu) unchanged from an un-blurred cursor. Furthermore, as correctly pointed out in the original paper by Tsay et al., 2021, the cursor cloud often overlaps with the visual target. This “target hit” would affect adaptation, possibly via a reward learning mechanism (See Kim et al., 2019 eLife). This is a second confound that accompanies the cursor cloud. We will expand our discussion to explain the discrepancy between our findings and previous findings.

1. The estimation of visual uncertainty (our exp1) required people to fixate on the target, while this might not reflect the actual scenario during adaptation where people are free to look wherever they want.

Response: Our data shows otherwise: in a typical error-clamp setting, people fixate on the target for the majority of the time. For our Exp1, the fixation on the straight line between the starting position and the target is 86%-95% (as shown in Figure S1). We also collected eye-tracking data in our Exp4, which is a typical error-clamp experiment. More than 95% of gaze falls with +/- 50 pixels around the center of the screen, even slightly higher than Exp1. We will provide this part of the data in the revision. In fact, we designed our Exp1 to mimic the eye-tracking pattern as in typical error-clamp learning with carefully executed pilot experiments.

This high percentage of fixating on the target is not surprising: the error-clamp task requires participants to use their hands to move towards the target and to ignore the cursor. In fact, we would also like to point out that the high percentage of fixation on the aiming target is also true for conventional visuomotor rotation, which involves strategic re-aiming (shown in de Brouwer et al. 2018; Bromberg et al. 2019; we have an upcoming paper to show this). This is one reason that our new theory would also apply to other types of motor adaptation.

1. More methodology details are needed. E.g., a figure showing the visual blurring, a figure showing individual data, a table showing data from individual sessions, code sharing, and a possible new correlational analysis.

Response: All these additional methodological/analysis information will be provided. We were self-limited by writing a short paper, but the revision would be extended for all these details.

Reviewer 2:

1. More discussions are needed since the focus of this study is narrowly confined to visuomotor rotation. “A general computational principle, and its contributions to other motor learning paradigms remain to be explored”.

Response: This is a great suggestion since we also think our original Discussion has not elaborated on the possible broad impact of our theory. Our model is not limited to the error-clamp adaptation, where the participants were explicitly told to ignore the rotated cursor. The error-clamp paradigm is one rare example that implicit motor learning can be isolated in a nearly idealistic way. Our findings thus imply two key aspects of implicit adaptation: 1) localizing one’s effector is implicitly processed and continuously used to update the motor plan; 2) Bayesian cue combination is at the core of integrating multimodal feedback and motor-related cues (motor prediction cue in our model) when forming procedural knowledge for action control.

We will propose that the same two principles should be applied to various kinds of motor adaptation and motor skill learning, which constitutes motor learning in general. Most of our knowledge about motor adaptation is from visuomotor rotation, prism adaptation, force field adaptation, and saccadic adaptation. The first three types all involve localizing one’s effector under the influence of perturbed sensory feedback, and they also have implicit learning. We believe they can be modeled by variants of our model, or at least we should consider using the two principles above to think of their computational nature. For skill learning, especially for de novo learning, the area still lacks a fundamental computational model that accounts for the skill acquisition process on the level of relevant movement cues. Our model suggests a promising route, i.e., repetitive movements with a Bayesian cue combination of movement-related cues might underlie the implicit process of motor skills.

We will add more discussion on the possible broad implications of our model in the revision.

Reviewer 3:

1. Similar to Reviewer 1, raised the concern about whether people’s fixation in typical motor adaptation settings is similar to the fixation that we instructed in our Exp1.

Response: see above.

1. Similar to Reviewer 2, the concern was raised about whether our new theory is applicable to a broad context. Especially, error clamp appears to be a strange experimental manipulation that has no real-life appeal, “(i)Ignoring errors and suppressing adaptation would also be a disastrous strategy to use in the real world”.

Response: about the broad impact of our model, please see responses to Reviewer 2 above. We agree that ignoring errors (and thus “trying” to suppress adaptation) should not be a movement strategy for real-world intentional tasks. However, even in real life, we constantly attend to one thing and do the other thing; that’s when implicit motor processes are in charge. Furthermore, it is this exact “ignoring” instruction that elicits the implicit adaptation that we can work on. In this sense, the error-clamp paradigm is a great vehicle to isolate implicit adaptation and allows us to unpack its cognitive mechanism.

1. In Exp1, the 1s delay between the movement end and the presentation of the reference cursor might inflate the actual visual uncertainty.

Response: The 1s delay of the reference cursor would not inflate the estimate of visual uncertainty. Our Exp1 used a similar paradigm by visual science (e.g., White, Levi, and Aitsebaomo, Vision Research, 1992), which shows that delay does not lead to an obvious increase in visual uncertainty over a broad range of values (from 0.2s to >1s, see their Figure 5-6). We will add more methodology justifications in our revision.

1. Our Fig4A used Tsay et al., 2021 data, which, in the reviewer’s view, is not an appropriate measure of proprioceptive bias. The reason is that in this dataset, “participants actively move to a visual target, the reported hand positions do not reflect proprioception, but mostly the remembered position of the target participants were trying to move to.”

Response: We agree that Tsay et al., 2021 study used an unconventional way to measure the influence of implicit adaptation on proprioception. And, their observed “proprioceptive changes” should not be called “proprioceptive bias” which is conventionally a reserved term for measuring the difference between the estimated hand location relative to the actual hand location (and better to be a passively moved hand). However, we think their dataset is still subject to the same Bayesian cue combination principle and thus can be modeled. Our modeling of this dataset includes all relevant cues: the implicitly perceived hand position and the proprioceptive cue (given that the hand stays at the movement end). Both cues are in the extrinsic coordinates, which happened to set the target position as zero. But where to set the zero (whether it is the target or the actual hand location) does not matter for the model fitting. Note that our Exp4 is also based on PEA modeling of proprioceptive bias, and this time the data is presented relative to the actual location.

In the revision, we would keep the current Fig4A and start to call the data as proprioceptive change as opposed to proprioceptive bias to follow the convention.