Representational geometry explains puzzling error distributions in behavioral tasks

Abstract

Measuring and interpreting errors in behavioral tasks is critical for understanding cognition. Conventional wisdom assumes that encoding/decoding errors for continuous variables in behavioral tasks should naturally have Gaussian distributions, so that deviations from normality in the empirical data indicate the presence of more complex sources of noise. This line of reasoning has been central for prior research on working memory. Here we re-assess this assumption, and find that even in ideal observer models with Gaussian encoding noise, the error distribution is generally non-Gaussian, contrary to the commonly held belief. Critically, we find that the shape of the error distribution is determined by the geometrical structure of the encoding manifold via a simple rule. In the case of a high-dimensional geometry, the error distributions naturally exhibit flat tails. Using this novel insight, we apply our theory to visual short-term memory tasks, and find that it can account for a large array of experimental data with only two free parameters. Our results call attention to the geometry of the representation as a critically important, yet underappreciated factor in determining the character of errors in human behavior.