RNNs perform task computations by dynamically warping neural representations

Arthur Pellegrino, Angus Chadwick

Keywords: RNN, Computational Neuroscience, Dynamical Systems, Neural Representations

TL;DR: RNNs used in computational neuroscience lie on manifolds whose geometry provides insights into their computations.

Abstract: Analysing how neural networks represent data features in their activations can help interpret how they perform tasks. Hence, a long line of work has focused on mathematically characterising the geometry of such "neural representations." In parallel, machine learning has seen a surge of interest in understanding how dynamical systems perform computations on time-varying input data. Yet, the link between computation-through-dynamics and representational geometry remains poorly understood. Here, we hypothesise that recurrent neural networks (RNNs) perform computations by dynamically warping their representations of task variables. To test this hypothesis, we develop a Riemannian geometric framework that enables the derivation of the manifold topology and geometry of a dynamical system from the manifold of its inputs. By characterising the time-varying geometry of RNNs, we show that dynamic warping is a fundamental feature of their computations.

Primary Area: Neuroscience and cognitive science (e.g., neural coding, brain-computer interfaces)

Submission Number: 23781