Low Tensor Rank Learning of Neural Dynamics

• URL: http://arxiv.org/abs/2308.11567v2
• Date: Sat, 4 Nov 2023 11:47:43 GMT
• Title: Low Tensor Rank Learning of Neural Dynamics
• Authors: Arthur Pellegrino, N Alex Cayco-Gajic, Angus Chadwick
• Abstract summary: We show that low-tensor-rank weights emerge naturally in RNNs trained to solve low-dimensional tasks. Our findings provide insight on the evolution of population connectivity over learning in both biological and artificial neural networks.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Learning relies on coordinated synaptic changes in recurrently connected populations of neurons. Therefore, understanding the collective evolution of synaptic connectivity over learning is a key challenge in neuroscience and machine learning. In particular, recent work has shown that the weight matrices of task-trained RNNs are typically low rank, but how this low rank structure unfolds over learning is unknown. To address this, we investigate the rank of the 3-tensor formed by the weight matrices throughout learning. By fitting RNNs of varying rank to large-scale neural recordings during a motor learning task, we find that the inferred weights are low-tensor-rank and therefore evolve over a fixed low-dimensional subspace throughout the entire course of learning. We next validate the observation of low-tensor-rank learning on an RNN trained to solve the same task. Finally, we present a set of mathematical results bounding the matrix and tensor ranks of gradient descent learning dynamics which show that low-tensor-rank weights emerge naturally in RNNs trained to solve low-dimensional tasks. Taken together, our findings provide insight on the evolution of population connectivity over learning in both biological and artificial neural networks, and enable reverse engineering of learning-induced changes in recurrent dynamics from large-scale neural recordings.

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