Extended Data Fig. 3: Trials with elevated levels of neural engagement also showed increased pupil size.

a-c. In Fig. 2g, we related neural engagement and pupil size by first averaging the pupil size across time points within a trial. To further explore this relationship, here we consider the time course of pupil size within a trial. Trial-averaged pupil sizes are shown for three example sessions after grouping trials separately based on whether neural engagement during the control interval of each trial during Block 2 was above- (dark gray) or below- (light gray) the median across trials during Block 2. Vertical dashed line indicates the time within each trial when the cursor was released (300 ms; see Methods), that is, the beginning of the control interval. Shading indicates mean ± SE across trials (a, n = 456 trials; b, n = 296 trials; c, n = 202 trials). Within each example session, the time course of pupil size was similar for trials with above- versus below-average levels of neural engagement, but with a larger overall pupil size on trials with above-average neural engagement. d. Prior to computing the correlations between neural engagement and pupil size shown in Fig. 2g (and in the previous panel), we first smoothed the trial-by-trial time courses of pupil size and neural engagement with a 30-trial boxcar filter, similar to previous work correlating population activity and pupil size¹². Here we show that neural engagement and pupil size were typically positively correlated even without smoothing. Without smoothing, the median Pearson’s correlation across sessions was ρ = 0.12 (bootstrapped 95% C.I. [0.09, 0.18], n = 44 sessions). Same conventions as Fig. 2g. e. Although the recording of pupil size began part way into Block 1 due to experimental constraints, we computed the trial-by-trial correlation between pupil size and neural engagement during Block 1 for the 13 sessions with a sufficient number of trials (all from monkey J). The median Pearson’s correlation during these sessions was ρ = 0.67 (bootstrapped 95% C.I. [0.41, 0.79], n = 13 sessions). Thus, a positive correlation between neural engagement and pupil size was also present before learning. Same conventions as Fig. 2g.