Interlimb Generalization of Learned Bayesian Visuomotor Prior Occurs in Extrinsic Coordinates

Abstract

Recent work suggests that the brain represents probability distributions and performs Bayesian integration during sensorimotor learning. However, our understanding of the neural representation of this learning remains limited. To begin to address this, we performed two experiments. In the first experiment, we replicated the key behavioral findings of Körding and Wolpert (2004), demonstrating that humans can perform in a Bayes-optimal manner by combining information about their own sensory uncertainty and a statistical distribution of lateral shifts encountered in a visuomotor adaptation task. In the second experiment, we extended these findings by testing whether visuomotor learning occurring during the same task generalizes from one limb to the other, and relatedly, whether this learning is represented in an extrinsic or intrinsic reference frame. We found that the learned mean of the distribution of visuomotor shifts generalizes to the opposite limb only when the perturbation is congruent in extrinsic coordinates, indicating that the underlying representation of learning acquired during training is available to the untrained limb and is coded in an extrinsic reference frame.

Keywords: Bayesian integration; interlimb generalization; motor learning; sensorimotor learning; transfer; visuomotor adaptation.

Graphical abstract

Figure 1.

A–F, Experimental paradigm. G, Experimental workspace with example hand and cursor paths shown for a representative trial when a 2-cm lateral visual shift is applied. Dashed white lines indicate feedback windows. H, Midpoint feedback conditions with different amounts of visual uncertainty. Panels G, H after Körding and Wolpert (2004).

Figure 2.

Experimental design. A, In experiment 1, training and testing phases were nominally defined as the first and last 1080 trials, respectively. B, C, In experiment 2, the training phase consisted of 1080 RH trials followed by a testing phase of 1080 LH trials. In the congruent-extrinsic (CE) condition, the imposed visuomotor perturbation was a rightward lateral shift for both RH and LH trials. In the congruent-intrinsic (CI) condition the imposed visuomotor perturbation was a rightward lateral shift for RH trials and a leftward lateral shift for LH trials, both of which require elbow flexion. Mean endpoint (${\sigma }_{\infty }$) for trials 980–1080 (RH late training) was used to compute the percentage of adaptation. The percentage of IG was computed by dividing the mean endpoint (${\sigma }_{\infty }$) for trials 980–1080 (RH late training) by the mean endpoint (${\sigma }_{\infty }$) for trials 1080–1180 (LH early testing).

Figure 3.

Computational models considered for experiment 1. The average lateral cursor deviation from the target (cursor error) as a function of the imposed shift for the models. Full compensation model (A), minimal mapping model (B), and Bayesian estimation model (C). (Transparent bands indicate the relative degree of variability in estimation.) The colors of the linear fits correspond to the visual condition (matching Fig. 1H), as do the bands of variability in C. D, The experimentally imposed prior distribution of shifts is Gaussian with a mean of 1 cm (in black). The probability distribution of possible visually experienced shifts under the clear, moderate, and large uncertainty conditions are represented with solid lines (colors as in Fig. 1H) for a trial in which the imposed shift is 2 cm. The Bayes-optimal estimate of the shift that combines the prior with the evidence is represented by dashed lines (colors also as in Fig. 1H). After Körding and Wolpert (2004).

Figure 4.

Effect of visual uncertainty. A, Cursor error at the end of the trial as a function of the imposed shift for a representative subject. Colors as in Figure 1H. Values represent Cartesian (screen) coordinates. Horizontal dotted lines indicate the full compensation model prediction and diagonal dashed lines indicate the minimal mapping model prediction. Solid lines provide the Bayesian estimation model fits to the data as a function of sensory uncertainty. Due to trial scheduling statistics, applied shift values differ slightly across each subject. To reflect this difference, error bars denote SD instead of SEM. Importantly, every subject experienced the same overall statistical distribution of shifts during training and testing. B, Slopes of the linear fits for all subjects in experiment 1. The first bar in each grouping corresponds to the subject represented in panel A.

Figure 5.

A comparison of endpoints (${\sigma }_{\infty }$) for all experimental groups. A, Mean endpoint during late RH training. B, Mean endpoints during early LH testing. All p values represent significance levels of independent samples t tests. Error bars denote SEM. Color coding is the same as in Figure 2.

Figure 6.

Moving average plot for early LH (${\mathrm{\sigma }}_{\mathrm{\infty }}$) trials. A, B, A moving average of endpoints across the first 100 trials in the LH testing phase for CE (A) and CI (B). Each bar represents the average across seven subjects using a window size of five trials. Error bars denote SD not SEM to reflect the disparate number of values included in each window. All p values represent significance levels from independent Welch t tests. C, D, Average endpoints for CE (C) and CI (D) conditions for the remaining reaches in the testing phase (1180–2160). In C, D, error bars denote SEM. The dashed line represents the mean across reaches 1180–2160. Color coding is the same as in Figure 2.