Procedures of the experimental paradigm.

We employed a cursor shift perturbation paradigm to reinvestigate the relationship between feedback responses (FBRs) and learning responses (LRs). A, Participants repeatedly performed a block consisting of one baseline trial, one perturbation trial, one probe trial followed by two null trials. B, Baseline trials. Forces exerted against the force channel were measured to quantify baseline motor output. C, In perturbation trials, the cursor was shifted laterally by manipulating both location and magnitude of the shift. This manipulation allowed the imposition of arbitrary temporal patterns of visual error. Hand trajectories were constrained using the force channel. D, Probe trials were used to measure the LR elicited for the visual error imposed in the preceding perturbation trial. Temporal patterns of FBRs and LRs were baseline-subtracted using forces measured during baseline trials. E, Temporal profiles of responses to rightward and leftward cursor shift perturbations were collapsed (left) to enable direct comparison of the motor commands underlying FBRs and LRs for a given temporal pattern of visual error.

Relationship between feedback and learning responses in Experiment 1.

a, In the perturbation trial, the cursor shift location was manipulated from 1 cm to 16 cm from the starting position, while the cursor shift magnitude was fixed at 3 cm. b, Temporal profiles of the feedback responses (FBRs) in Experiment 1, aligned to movement onset. c, FBRs emerged with a latency of approximately 160 ms relative to movement onset. Latencies were estimated using receiver operating characteristic (ROC) analysis. d, Temporal profiles of learning responses (LRs) in Experiment 1. e-g, Cross-correlation analysis was used to evaluate temporal similarity and relative timing between FBRs and LRs (e). The temporal shift between the FBRs and LRs was defined as the time lag that maximized the individual cross-correlation (f), and temporal similarity was quantified as the cross-correlation coefficient at this optimal time lag (g). Shaded areas represent the standard error of the mean across participants. Asterisks indicate statistically significant effects (* p < 0.05, ** p < 0.01, *** p < 0.001).

Temporal patterns of feedback and learning responses across different cursor shift magnitudes in Experiment 2.

a, In perturbation trials, the shift magnitude was varied from 0.4 cm to 3 cm. b, Temporal patterns of the feedback responses (FBRs) in Experiment 2. c, Temporal profiles of learning responses (LRs) in Experiment 2. d, Cross-correlation analysis between FBRs and LRs used to evaluate their temporal similarity. The plot shows the cross-correlation coefficient as a function of time lag. e, Cross-correlation coefficient at the time lag that maximized the average cross-correlation function in Experiment 1 (−238 ms). f, Cross-correlation coefficient at a fixed time lag of -500 ms. A significant modulation of correlation coefficients was observed across error magnitudes. Shaded areas represent the standard error of the mean across participants.

Decomposition of feedback and learning response temporal profiles.

a, Temporal profiles of feedback responses (FBRs) were decomposed into two components: an early phasic component and a late tonic component. b, Decomposition model reproduced the temporal profiles of FBRs in Experiment 2. c-d, The same decomposition procedure was applied to the temporal profiles of the learning responses (LRs). e, Modulation of the amplitudes of the phasic and tonic components of the FBR as a function of error magnitude. f, Modulation of the amplitudes of the phasic and tonic components of the LR as a function of error magnitude. Error bars represent the standard error of the mean across the participants. g-h, Linear regression analyses examining the quantitative relationship between FBRs and LRs using the model y = ax, where x represents the amplitude of the phasic (g) and tonic components (h) of the FBR, and y represents the amplitude of the corresponding phasic (left) and tonic components (right) of the LR. Error bars represent the standard error of the mean across the participants.

Relationship between the temporal patterns of feedback and learning responses in Experiment 3.

a, In perturbation trials, the cursor was shifted laterally twice during a single movement. Three temporal patterns of visual error were tested, and the location of the second shift was varied from 6 cm to 16 cm from the starting position. b-d, Temporal profiles of the feedback responses (FBRs) when the second shift occurred at 16 cm (b), 11 cm (c), and 6 cm (d). e-g, Temporal patterns of the learning responses (LRs) when the second shift occurred at 16 cm (e), 11 cm (f), and 6 cm (g). h, Cross-coefficient function showing the relationship between the cross-correlation coefficient and time lag between FBRs and LRs when the second shift occurred at 16 cm (left), 11 cm (middle), and 6 cm (right). i, Cross-correlation coefficient evaluated at the time lag that maximized the cross-correlation function in Experiment 1 (−238 ms). Shaded areas represent the standard error of the mean across participants. Asterisks indicate statistically significant effects (* p < 0.05, ** p < 0.01, *** p < 0.001).

Temporal relationship between feedback and learning responses in Experiment 3.

a-b, To isolate the effect of the second cursor shift on feedback (FBRs) and learning responses (LRs), differential force profiles were computed by subtracting the responses in the maintained condition from those in the removed and reversed conditions (insets). The decomposition model successfully reproduced the differential force profiles of the feedback response (a) and learning response (b) for the second shift when it occurred at 16 cm (left), 11 cm (middle), and 6 cm (right). Solid lines indicate model predictions, and dashed lines indicate experimental data. c, Linear regression analysis examining the quantitative relationship between the phasic component of the FBR and the amplitudes of the phasic (left) and tonic (right) components of the LR for the second cursor shift, following the same procedure as in Experiment 2. d, Linear regression analysis examining the relationship between the tonic component of the FBR and the amplitudes of the phasic (left) and tonic (right) components of the LR for the second cursor shift. Error bars represent the standard error of the mean across participants.

The tonic component of the feedback response predicts between-subject variability in learning response amplitude.

a, Across Experiments 1–3, all participants experienced an identical temporal pattern of visual error, in which the cursor was shifted laterally by 3 cm at a location 1 cm from the starting position. b-c, Temporal profiles of the feedback response (FBR) (b) and learning response (LR) (c) elicited by this perturbation. Each trace represents an individual participant and the thick black trace represents the average across participants. Participants are ordered according to the amplitude of the tonic component of the FBR, with colors closer to magenta indicating larger tonic feedback responses. d-g, Relationships between the amplitudes of the phasic and tonic components of the FBRs and LRs across participants.

The tonic component of the feedback response predicts trial-by-trial variability in learning response amplitude.

Trial triplets obtained under an identical cursor shift perturbation (see Fig. 7a) were split into two datasets based on the amplitude of either phasic (a-d) and tonic (e-h) components of the feedback response (FBR). a, Temporal profiles of the FBR for datasets split according to the tonic FBR component and averaged across participants. b, Difference in the amplitudes of the phasic and tonic components of the FBR between the High and Low tonic FBR datasets. c-d, Temporal profiles (c) and difference in the amplitudes of the phasic and tonic components (d) of the learning response (LR) for datasets split based on the tonic FBR component. e, Temporal profiles of the FBR for the datasets split according to the phasic FBR magnitude. f, Amplitudes of the phasic and tonic FBR components for the High- and Low phasic FBR datasets. g–h, Temporal profiles (g) and component amplitudes (h) of the LR for datasets split according to the phasic FBR amplitude.

Robustness of the quantitative relationship between feedback and learning responses to model parameterization in Experiment 2.

Even when additional fitting parameters were introduced for the model (Eq. 1), the quantitative relationship between the feedback response (FBR) and the learning response (LR) remained unchanged. a-b, The decomposition model (Eq. 1) was fitted to individual participants’ FBRs (a) and LRs (b) while allowing not only component amplitudes but also onset timing and temporal dispersion to vary as free parameters. The fitted parameter values across participants were distributed around those obtained from the grand-averaged responses. This distribution was relatively narrow for the FBR, indicating high consistency across participants, whereas the LR showed a broader distribution, reflecting greater inter-individual variability. c-f, Using this extended fitting procedure, the model successfully reproduced the modulation of FBR and LR amplitudes as a function of visual error magnitude, consistent with the results shown in Fig.4.