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 to date, dependence on such mechanism has not been assessed in the context of arithmetic. Bayesian inference implies the representation of uncertainty and reliance on prior beliefs. In arithmetic problem solving, it would consist in refining prior knowledge about the response range as the system progressively integrates the numerical information conveyed by the operands. Within this framework, the amount of information needed to progress from a prior to a posterior probability distribution over responses can be quantified by the information gain, which would relate to the cognitive workload of the task. To test this hypothesis, we designed three experiments in which participants computed the sum of two numbers presented one after another through headphones. In each experiment, the information about response predictability conveyed by the first operand was manipulated. The first operand was either highly informative and contributed to narrow down the response range, or poorly informative and conveyed little information about a plausible response. Throughout all experiments, we found that pupil-related arousal signalled the information gain associated with the first operand, indicating that participants already updated the probability distribution of possible responses upon hearing that first stimulus. This finding shows that Bayesian inference is central to arithmetic problem solving and that information gains consecutive to the integration of the operands can be tracked over time through pupillometry. Public significance statement- This study suggests that when we do arithmetic, our brain uses Bayesian inference, a method similar to how scientists update their theories based on new evidence. This means that when doing math, we start with hypotheses about the result and progressively narrow down possible solutions. - By observing the eye of the participants while they were solving arithmetic problems, the authors showed that their pupil size increased in proportion to the amount of processed information. - The authors also found that when participants received more informative first operands in the math problem, and when their pupil size increased more during this presentation, they were also faster to respond, indicating that greater initial information processing facilitated quicker problem-solving.