RNNs perform task computations by warping neural representations
Arthur Pellegrino, Angus Chadwick
How networks internally encode variables of the world in their activity is a fundamental question in both neuroscience and machine learning. Characterising such "neural representations" has reshaped our understanding of computation in biological and artificial neural networks. In parallel, there is mounting interest in understanding how dynamical systems perform computations on task variables through their internal dynamics. Yet, the link between computation-through-dynamics and representational geometry is poorly understood. Here, we hypothesise that recurrent neural networks (RNNs) perform computations by dynamically warping their internal representation of task variables. To test this hypothesis, we develop a Riemannian geometric framework which 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 task-trained RNNs, we show that dynamic warping is a fundamental feature of their computations.