Pupil size variations reveal Bayesian inference in cognitive arithmetic

The assumption that the brain relies on Bayesian inference has been successful in accounting for many behavioural and neurophysiological observations, but the dependence on such a mechanism in arithmetic remains unknown. Bayesian inference implies the representation of uncertainty and reliance on prior beliefs. In arithmetic problem-solving, it would consist of refining priors over the response range as the system progressively integrates information conveyed by the operands. To test this hypothesis, we designed three experiments in which participants computed the sum of two numbers presented sequentially through headphones. The first operand was either highly informative and contributed to narrowing down the response range or poorly informative and conveyed little information about plausible responses. Throughout all experiments, pupil-related arousal signalled the information gain associated with the first operand, indicating that participants updated the probability distribution of responses upon hearing that first stimulus. Moreover, when participants received more informative operands and when their pupils dilated more during this presentation, they were also faster to respond, indicating that greater initial information processing facilitated quicker problem-solving. These findings show that Bayesian inference is central to arithmetic problem-solving and that information gains consequent to the integration of the operands can be tracked over time through pupillometry.