Data set #1: Cue-target 2AFC task and results.

(A) Events during a single trial. While pupil dilation was recorded, participants predicted the orientation (left/right) of the upcoming target (Gabor patch) based on the visual and/or auditory cues (in the data analyzed here, only the visual cue had predictive validity). Predictions were given by a button press with the corresponding finger on the left or right hand. Two mapping conditions (condition 1 or condition 2) were counterbalanced across participants such that a participant in condition 1 was shown the square cue followed by a left-oriented target on 80% of the trials, while the square cue was followed by a right-oriented target on 20% of the trials. Gray box indicates the feedback event of interest. (B) Accuracy (fraction of correct responses) as a function of cue-target frequency. Data points are individual participants; stats, paired-samples Wilcoxon signed-rank t-test. (C) RT as a function of both cue-target frequency and accuracy (error/correct); stats, repeated-measures ANOVA. (D) Feedback-locked pupil response time course, plotted as a function of cue-target frequency and accuracy. Shading represents the standard error of the mean. Gray boxes, time windows of interest; early time window, [0.75, 1.25]; late time window, [2.5, 3.0]. The black horizontal bar indicates a significant interaction term (cluster-corrected, permutation test). (E) Early time window, average feedback-locked pupil response as a function of cue-target frequency and accuracy. stats, repeated-measures ANOVA. (F) As E, for the late time window. ANOVA results (multiple panels): top, main effect of frequency; middle, main effect of accuracy; bottom, frequency x accuracy interaction. Error bars, standard error of the mean. *p < 0.05, **p < 0.01, *** p < 0.001.

Data set #2: Letter-color 2AFC task and results.

(A) Left, an independent learning phase was administered in the form of an odd-ball detection task during which six letters together with six shades of green colors as background (squares) were presented in three frequency conditions (33%, 50%, and 84%) on most trials (91%). Participants had to quickly respond to odd-ball targets (numbers and/or non-green color, 9% of trials). Letter-color mapping conditions were randomized per participant. Right, events during a single trial of the subsequent letter-color decision 2AFC task. While pupil dilation was recorded, participants indicated whether the letter “matched” the colored square with a button press. A match was correct when the letter and color had occurred most often together in the preceding odd-ball task. Gray box indicates the feedback event of interest. (B) Accuracy (fraction of correct responses) as a function of letter-color frequency. Dashed line represents chance level. Data points are individual participants; stats, paired-samples t-test. (C) RT as a function of both letter-color frequency and accuracy; stats, repeated-measures ANOVA. (D) Feedback-locked pupil response time course, plotted as a function of letter-color frequency and accuracy. Shading represents the standard error of the mean. Gray boxes, time windows of interest; early time window, [0.75, 1.25]; late time window, [2.5, 3.0]. The purple horizontal bar indicates a significant two-way interaction effect (uncorrected for multiple comparisons). No significant time points remained after correction using the false discovery rate (FDR). (E) Early time window, average feedback-locked pupil response as a function of letter-color frequency and accuracy. (F) As E, for the late time window. ANOVA results (multiple panels): top, main effect of frequency; middle, main effect of accuracy; bottom, frequency x accuracy interaction. Error bars, standard error of the mean. *p < 0.05, **p < 0.01, *** p < 0.001.

Results of the three-way repeated-measures ANOVA on the feedback-locked pupil response in the cue-target 2AFC task (data set #1).

The three-way repeated-measures ANOVA included factors: time window (levels: early vs. late), frequency (levels: 20% vs. 80%) and accuracy (levels: error vs. correct).

Results of the three-way repeated-measures ANOVA on the feedback-locked pupil response in the letter-color 2AFC task (data set #2).

The three-way repeated-measures ANOVA included factors: time window (levels: early vs. late), frequency (levels: 33%, 50%, and 84%) and accuracy (levels: error vs. correct). Greenhouse-Geisser statistics are reported when assumptions of sphericity were violated.

Correlations between the feedback-locked pupil response time course and the information-theoretic variables.

Left column, results for the cue-target 2AFC task. Right column, results for the letter-color 2AFC task. (A) The KL divergence, surprise, and entropy parameters are shown as a function of task trial. Model parameter units are in bits. (B) The mean KL divergence, surprise, and entropy parameters are shown as a function of frequency condition. (C) Trial-by-trial correlations between the ideal learner model parameters (KL divergence, surprise, and entropy) at each time point in the feedback-locked pupil response. Shading represents the standard error of the mean. Gray boxes, time windows of interest; early time window, [0.75, 1.25]; late time window, [2.5, 3.0]. (D) Trial-by-trial correlations between the KL divergence parameter and the feedback-locked pupil response separately for the error and correct trials. (E) As C, for the surprise parameter. (F) As D, for the entropy parameter. (G-L) As A-F for the letter-color 2AFC task. All panels, the colored horizontal bars indicate time periods of significant correlation coefficients tested against zero for each model parameter or condition of interest (cluster-corrected, permutation test). The black horizontal bar indicates a difference between conditions (cluster-corrected, permutation test).

Control tasks for data set #2: letter-color 2AFC task.

Left column, results from the control task for colors. Right column, results from the control task for feedback tones. (A) Mean tone-locked pupil response across all trials. (B) Feedback-locked pupil response time course plotted as a function of color used in the main letter-color 2AFC task (hexadecimal codes are given in the legend). (C) as A, for the control task for feedback tones. (D) Pupil response time courses plotted as a function of feedback tone used for error and correct trials in the main letter-color 2AFC task. In C, D, Gray boxes, time windows of interest; early time window, [0.75, 1.25]; late time window, [2.5, 3.0]. Shading represents the standard error of the mean. The black and green horizontal bars indicate a significant effect of interest (cluster-corrected for multiple comparisons).

Main effects of frequency and accuracy in the feedback-locked pupil time courses.

Left column, results from the cue-target 2AFC task. Right column, results from the letter-color 2AFC task. (A) Mean feedback-locked pupil response across all trials. (B) Feedback-locked pupil response time course plotted as a function of accuracy. (C) Feedback-locked pupil response time course plotted as a function of stimulus-pair frequency. (D, E, F) as A, B, C for the letter-color 2AFC task. Gray boxes, time windows of interest; early time window, [0.75, 1.25]; late time window, [2.5, 3.0]. Shading represents the standard error of the mean. The black horizontal bars indicate a significant effect of interest (panels A-E were cluster-corrected for multiple comparisons; panel F, a one-way repeated-measures ANOVA was conducted on each time point and corrected for multiple comparisons with the false discovery rate).

Individual differences analysis between accuracy and pupil responses. Top row, cue-target 2AFC task. Bottom row, letter-color 2AFC task. Left column, early time window. Right column, late time window. The average feedback-locked pupil response difference (80-20% frequency conditions) are plotted against the difference in accuracy (80-20%). Data points, individual participants.

Correlations between the feedback-locked pupil response time course and the information-theoretic variables using a uniform prior distribution in the letter-color 2AFC task.

(A) The KL divergence, surprise, and entropy parameters are shown as a function of task trial. Model parameter units are in bits. (B) The mean KL divergence, surprise, and entropy parameters are shown as a function of frequency condition. (C) Trial-by-trial correlations between the ideal learner model parameters (KL divergence, surprise, and entropy) at each time point in the feedback-locked pupil response. Shading represents the standard error of the mean. Gray boxes, time windows of interest; early time window, [0.75, 1.25]; late time window, [2.5, 3.0]. (D) Trial-by-trial correlations between the KL divergence parameter and the feedback-locked pupil response separately for the error and correct trials. (E) As C, for the surprise parameter. (F) As D, for the entropy parameter. All panels, the colored horizontal bars indicate time periods of significant correlation coefficients tested against zero for each model parameter or condition of interest (cluster-corrected, permutation test). No differences between error and correct trials were obtained (cluster-corrected, permutation test).