The relationship between precision-weighted prediction errors and pupil size reported in the main text (Figure 5b), links pupil size to behaviour indirectly via the HGF model, since the precision-weighted prediction errors are estimated for each participant on the basis of their trial-wise RT. However, we conducted an additional regression analysis to investigate the relationship between basic behaviour (trial-wise RT) and pupil size directly. As RT increases, post-outcome pupil size shows an initial decrease from baseline followed by an increase towards the end of the trial. Crucially, there are no time points in which the relationship between RT and pupil size is significantly different between the ASD and NT groups. Notably, trial-wise RT is included as a control regressor in the results reported in the main text (Figure 5), and in the analyses reported above (Figure S9 & S10), so where there is a significant relationship between pupil size and the trial-wise model parameters this exists over and above any effect of RT on pupil size. Blue and yellow bars indicates where the relationship between RT and pupil size significantly differed from zero in the ASD and NT participants, respectively. As for the results reported in the main text (see online methods) this regression analysis included, trial type (face, house), fixation compliance and UE-E ground truth contrasts, as control regressors. Shaded region represents standard error of the mean.