Uncertainty in State Estimate and Feedback Determines the Rate of Motor Adaptation Kunlin Wei & Konrad Koerding Rehabilitation Institute of Chicago At any point of time, the nervous system has uncertainty about our state. We do not know all the properties of our body and the environment. At the same time all feedback is noisy, even foveal vision is not perfect. The combination of noisy feedback with our noisy state estimate is thus necessary during motor adaptation to allow us to move precisely. We want to quantitatively understand how uncertainty in the state and in the feedback affects motor adaptation. The Bayesian predictions of motor adaptation are rather intuitive: the nervous system relies less on sensory feedback and exhibits slower adaptation when feedback is more uncertain, whereas it will adapt faster when state estimate is more uncertain [1-3]. For example, if a basketball player is making a jump shot but his view of the basket is blocked by the opponent (high feedback uncertainty), he should rely less on vision but more on the remembered body orientation to adjust his shot. On the other hand, if the player is making the first shot in a ball game (high state estimate uncertainty), the visual feedback of this shot (movement outcome) is critical for him to update his control strategy and he should adapt more to this feedback. In our experiment, subjects repeatedly reached for a target in a virtual reality setting while visual feedback was spatially perturbed randomly from trial to trial. The responses in the subsequent trials (trialto-trial adaptation) were then evaluated. In the first experiment, we conditioned state estimate uncertainty by asking subjects performing the task with veridical visual feedback or without visual feedback for 1 minute, or simply sitting idle in the dark for 1 minute (Fig 1). Subjects had both visual and proprioceptive feedback, or only proprioceptive feedback, or no feedback at all in these three kinds of conditioning, respectively. We expected subjects were increasingly uncertain about the relationship between motor commands and movement outcomes after conditioning. Following each conditioning block, subjects were exposed to random visual perturbations for 30s (test block) and their adaptation evaluated. Each type of conditioning block was randomly presented 10 times but always followed by a test block. In the second experiment, we systematically manipulated feedback uncertainty by blurring the visual feedback of the hand at the end of reach (Fig. 1): the hand is either represented by a single cursor (no blur), or by 5 cursors randomly drawn from a normal distribution with SD of 2cm (small blur) or 3cm (large blur). Results indicated that the average adaptation rate was significantly faster with more state estimate uncertainty (Exp 1) and with less feedback uncertainty (Exp 2), as predicted by the Bayesian model (Fig 2). We fitted the time-series data (Exp 2) to a Kalman filter model whose only free parameters were the covariance of the observation matrix, which captures how uncertain the system is about the observation. The estimated covariance was indeed scaled with the blurring level, indicating the system was increasingly more uncertain about the feedback (Fig 3). The present study explores how state estimate uncertainty and feedback uncertainty influence motor adaptation. Though subjects’ uncertainty about their body can not be directly measured, we manipulated its degree by a novel experimental design and provided behavioral evidence that it impact the control of action in the Bayes’ optimal sense. Feedback uncertainty has been investigated in a previous study where motor adaptation was assessed in blocks of trials [3]. However, such a blocked design can not distinguish between a model in which adaptation is truly Bayesian and a simple state-space model that adapts its learning rate. We provided direct evidences via our trial-to-trial adaptation paradigm that adaptive responses relates to feedback uncertainty; however, this relationship do not require prolonged exposure to perturbations as humans consider feedback uncertainty on an instance-by-instance basis.

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Fig 1: Typical trajectory and experiment designs. The cursor representing the hand position is perturbed 0 or ±2 cm randomly in Y direction at the end of the reach. In Exp 1, subjects, before performing the perturbation test, practice with or without cursor, or simply sitting in the dark for 1 min. In Exp 2 the visual feedback of the hand is blurred to different degrees using representation of a single cursor, or 5 scattered cursors. −0.1

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(B). The slope of hand deviation vs visual disturbances (as in A) is plotted as a function of conditioning (Exp 1). Pair-t test shows that the more state estimate uncertainty, the faster the adaptation. Covariance of Observation Matrix

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Fig 2: (A). Hand deviations in the trials following visual disturbances. Dash line shows the linear regression whose slope is an indicator of adaptation rate.

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(C). Adaptation slope is plotted as a function of blurring level (Exp 2). Pair-t test indicates that the more feedback uncertainty, the slower the adaptation.

Fig 3: (A). The actual hand deviation and the corresponding Kalman model estimates are shown for a typical subject. (B). The estimated covariance of observation matrix (only free parameters) is plotted as a function of blurring level. Plots are based on data from Exp 2.

Reference 1. 2. 3.

Korenberg, A.T. and Z. Ghahramani, A Bayesian view of motor adaptation. Current Psychology of Cognition, 2002. 21 (4-5): p. 537-564. Kording, K.P., J.B. Tenenbaum, and R. Shadmehr, The dynamics of motor memory are a consequence of optimal adaptation to a changing body. Nat Neurosci, 2007. 10(6). Burge, J., M.O. Ernst, and M.S. Banks, The statistical determinants of adaptation rate in human reaching. Journal of Vision, 2008. 8(4): p. 1-19.