Top-down meets bottom-up: How sensory reliability shapes the influence of number magnitude on size perception Author Accepted Manuscript

A previous study (Shams et al., 2023) found that observers judged computer-generated football players with higher jersey numbers as physically larger than those with lower numbers, suggesting that implicitly learned associations between numerical magnitude and size can bias visual perception. This aligns with Bayesian models of perception, which posit that perceptual estimates arise from a weighted integration of sensory input (likelihood) and prior expectations. In the present study, we investigated how the influence of such priors varies with sensory reliability, manipulated through stimulus duration. Replicating prior results, we found that participants rated players with higher jersey numbers as larger during a baseline condition (500 ms). This jersey number effect persisted at longer durations (750 ms and 1000 ms), but with diminishing effect sizes, consistent with reduced reliance on priors when sensory evidence is more reliable. In contrast, the effect disappeared at the shortest duration (250 ms), likely because numeric magnitude could not be processed in the limited time available. Prior research suggests that number cognition requires at least 350 ms, supporting this interpretation. Overall, our findings demonstrate that the influence of high-level semantic priors on perception is not fixed but dynamically modulated by both the reliability of the sensory input and the temporal availability of prior knowledge, consistent with Bayesian perceptual inference.