%0 Journal Article
%A Sengupta, Anirvan M.
%A Pehlevan, Cengiz
%A Tepper, Mariano
%A Genkin, Alexander
%A Chklovskii, Dmitri B.
%T Manifold-tiling Localized Receptive Fields are Optimal in Similarity-preserving Neural Networks
%D 2018
%R 10.1101/338947
%J bioRxiv
%P 338947
%X 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.
%U https://www.biorxiv.org/content/biorxiv/early/2018/06/04/338947.full.pdf