“What” × “When” working memory representations using Laplace Neural Manifolds

Working memory—the ability to remember recent events as they recede continuously into the past—requires the ability to represent any stimulus at any time delay. This property requires neurons coding working memory to show mixed selectivity, with conjunctive receptive fields (RFs) for stimuli and time, forming a representation of ‘what’ x ‘when’ for the recent past. We study the properties of such a working memory in experiments where a single stimulus must be remembered for a short time. Conjunctive receptive fields allows the covariance matrix of the network to decouple neatly, allowing an understanding of the low-dimensional dynamics of the population. We study a specific choice—a Laplace space with exponential basis functions for time coupled to an “Inverse Laplace” space with circumscribed basis functions in time. We refer to this choice with basis functions that evenly tile log time as a Laplace Neural Manifold for time. Despite being related by a linear projection, the Laplace population shows a stable stimulus-specific subspace whereas the Inverse Laplace population shows rotational dynamics. The rank of the covariance matrix with time grows logarithmically in good agreement with data. We sketch a continuous attractor network that constructs a Laplace Neural Manifold for time. The attractor in the Laplace space appears as an edge; the attractor for the inverse space as a bump. This work provides a bridge between abstract cognitive models of WM and circuit-level continuous attractor neural networks.