Efficient coding of ensemble stimuli relative to a dynamic reference

When discriminating the average of a stimulus ensemble against a reference, observers often overweigh those stimuli in the ensemble that have feature values similar to the reference—a behavior known as ‘robust averaging’. We previously proposed that this behavior can be explained by a Bayesian decision model constrained by efficient coding. Assuming our visual system rapidly forms efficient representations of ensemble stimuli relative to a dynamic reference, our model captured multiple existing datasets showing robust averaging of low-level stimulus ensembles. Here, we provide further evidence for two key predictions of the model: robust averaging should 1) become progressively more pronounced the longer the visual system is exposed to the ensemble stimuli statistics and 2) be reduced when the distribution of the ensemble stimuli is uniform. To test the first prediction, we had subjects discriminate the average orientation of 12 gratings displayed on a virtual circle against a central reference grating during three sessions. In every trial, ensemble orientations were drawn from a Gaussian distribution with various means relative to the (variable) reference orientation, overall creating an approximately Gaussian distribution of ensemble orientations around the reference. Across the three sessions, subjects’ discrimination accuracy continuously improved and the weighting kernel became increasingly non-uniform, attributed by our model to a reduction in internal noise and a progressively better adaptation to the ensemble statistics. We tested the second prediction by sampling orientations from two oppositely ‘skewed’ linear distributions, resulting in an overall uniform distribution centered at the reference. Subjects completed three sessions each under both Gaussian and uniform conditions. While accuracy was similar in both, robust averaging was largely absent in the uniform condition. The alignment between our model’s predictions and empirical data validates our hypothesis that the visual system can dynamically create efficient sensory representations of ensemble stimuli relative to a trial-by-trial varying reference.