Code and data from: Representational geometry explains puzzling error distributions in behavioral tasks

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 challenge the dominant view in the
 mechanisms and capacity constraints of working memory systems,
and instead suggest that the Bayesian framework, which explains various
aspects of perceptual behavior, also provides an excellent account of
working memory.Overall, our results establish a new and direct connection
between neural manifold geometry and behavior, and call attention to the
geometry of the representation as a critically important, yet
underappreciated factor in determining the character of errors in human
behavior.