RT Journal Article
SR Electronic
T1 Manifold-tiling Localized Receptive Fields are Optimal in Similarity-preserving Neural Networks
JF bioRxiv
FD Cold Spring Harbor Laboratory
SP 338947
DO 10.1101/338947
A1 Sengupta, Anirvan M.
A1 Pehlevan, Cengiz
A1 Tepper, Mariano
A1 Genkin, Alexander
A1 Chklovskii, Dmitri B.
YR 2018
UL http://biorxiv.org/content/early/2018/06/04/338947.abstract
AB 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.