Recurrent neural network models for working memory of continuous variables: activity manifolds, connectivity patterns, and dynamic codes

Many daily activities and psychophysical experiments involve keeping multiple items in working memory. When the items take continuous values (e.g., orientation, direction, contrast, length, weight, loudness) they must be stored in a continuous structure of appropriate dimensions. We investigate how such a structure might be represented in neural circuits by training recurrent networks to report two previously flashed stimulus orientations. We find that the activity manifold for the two orientations resembles a Clifford torus. Although a Clifford torus and a standard torus (the surface of a donut) are topologically equivalent, they have important functional differences. A Clifford torus treats the two orientations equally and keeps them in orthogonal subspaces, as demanded by the task, whereas a standard torus does not. We further find that the Clifford-torus-like manifold is realized by two different sets of locally-excitatory/globally-inhibitory connectivity patterns. Moreover, in addition to attractors that store information via persistent activity, our networks also use a dynamic coding scheme such that many units change their tuning to prevent the new sensory input from overwriting the previously stored one. We argue that such dynamic codes are generally required whenever multiple inputs enter a memory system via shared connections. Finally, we apply our framework to a human psychophysics experiment in which subjects reported two remembered orientations. We demonstrate that not all RNNs reproduce human behavior. By varying the training conditions of the RNNs, we test and support the hypothesis that human behavior is a product of both neural noise and reliance on the more stable and behaviorally relevant memory of the ordinal relationship between the two orientations. This suggests that suitable inductive biases in RNNs are important for uncovering how the human brain implements working memory. Together, these results ∗. Equal contribution. 1 ar X iv :2 11 1. 01 27 5v 2 [ qbi o. N C ] 1 8 D ec 2 02 1 offer an understanding of the neural computations underlying a class of visual decoding tasks, bridging the scales from human behavior to synaptic connectivity.