Manifold-tiling Localized Receptive Fields are Optimal in Similarity-preserving Neural Networks

Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)

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Authors

Anirvan Sengupta, Cengiz Pehlevan, Mariano Tepper, Alexander Genkin, Dmitri Chklovskii

Abstract

<p>Many neurons in the brain, such as place cells in the rodent hippocampus, have localized receptive fields, i.e., they respond to a small neighborhood of stimulus space. What is the functional significance of such representations and how can they arise? Here, we propose that localized receptive fields emerge in similarity-preserving networks of rectifying neurons that learn low-dimensional manifolds populated by sensory inputs. Numerical simulations of such networks on standard datasets yield manifold-tiling localized receptive fields. More generally, we show analytically that, for data lying on symmetric manifolds, optimal solutions of objectives, from which similarity-preserving networks are derived, have localized receptive fields. Therefore, nonnegative similarity-preserving mapping (NSM) implemented by neural networks can model representations of continuous manifolds in the brain.</p>