A ‘demixing’ model explains repulsive biases in visual working memory and perception

Abstract

Humans often err consistently in estimating what they see or have seen before. For example, when trying to remember one of the two similar items, the estimates of this item’s features are “repulsed” away from the other item, while for dissimilar items there is sometimes an attraction effect. This is highly reminiscent of a tilt illusion and similar biases in perception. How to explain such biases? Many models have been suggested at the mechanistic level (in Marr’s classification) but at the computational level, their rationale remains elusive. Such biases are baffling for standard Bayesian (ideal) observer models, prompting theorists to add extra components (e.g., asymmetric likelihoods or non-uniform priors). I propose an alternative based on the simple idea that observers acquire many sensory samples for each of the presented items and have to determine their causes. In other words, the observers are presented with a mixture of samples and have to ‘demix’ them to find out what the stimuli are. The mixture models are well-known in statistics, yet, their biases are seldom described, and their implications in vision science have not been explored in detail. By simulating the ideal observer behaviour, I show that the ‘demixing’ model can readily explain the repulsive-then-attractive bias pattern when the similarity between the test item and the bias inducer decreases as exemplified above. Notably, this result does not require complex priors or asymmetric likelihoods. Interestingly, depending on sensory noise levels, the observed bias pattern could change to purely repulsive or purely attractive, matching bias patterns observed in different experimental paradigms (e.g., serial dependence). This model, beautiful in its simplicity, provides a formal grounding for the intuition that repulsive biases stem from the observer’s attempt to differentiate between the items, as well as a potential way to explain other kinds of biases.