Abstract
Recently multiple models have been proposed to account for behavioral performance in working memory tasks. These include the slot models, variable precision models, resource-based models etc. Each type of model has been shown to account for some behavioral characteristics of working memory. Although some efforts have been made toward unification of these models, so far there remains a substantial conceptual gap. Here we present a theory of working memory that helps to unify various aspects of previous experimental and modeling results. The main new ingredient of the theory is to consider how representational geometry determines behavioral performance in ideal observer models. Using mathematical analysis and numerical simulations, we investigate how the geometry of the representation determines predicted behavior in various psychophysical tasks. Surprisingly, we find that, under some commonly made assumptions, the error distribution in continuous estimation tasks can be well captured by the geometry of the representation and the noise magnitude. Assuming a high dimensional geometry, this relation can naturally account for the heavy tails of working memory error for various stimulus variables. With only two free parameters, the model is able to well account empirically reported error distributions in a number of working memory tasks. In the context of previous models, our theory 1) demystifies results from several different experimental paradigms; 2) provides a potential rationale for the psychological space that is used in the target confusability competition model; 3) differs from the probabilistic population coding model in that representational geometry rather than tuning curves becomes the key ingredient; and 4) requires no additional assumptions on variability in encoding precision. Together our theory provides a novel and simple conceptual framework for working memory tasks based on the geometry of the representation, unifying several key aspects of previous models.