Do place cells dream of conditional probabilities? Learning Neural Nystr\"om representations

TL;DR

This paper proposes a biologically-inspired neural network based on Nyström kernel approximations that models hippocampal place cells as encoding transition distributions, with applications to both spatial and conceptual representations.

Contribution

It introduces a novel neural network architecture inspired by Nyström kernel methods that captures transition distributions and generates sparse, localized place cell-like representations.

Findings

Successfully approximates transition distributions

Produces sparse, localized receptive fields similar to place cells

Extends to supervised learning with class-specific place cells

Abstract

We posit that hippocampal place cells encode information about future locations under a transition distribution observed as an agent explores a given (physical or conceptual) space. The encoding of information about the current location, usually associated with place cells, then emerges as a necessary step to achieve this broader goal. We formally derive a biologically-inspired neural network from Nystr\"om kernel approximations and empirically demonstrate that the network successfully approximates transition distributions. The proposed network yields representations that, just like place cells, soft-tile the input space with highly sparse and localized receptive fields. Additionally, we show that the proposed computational motif can be extended to handle supervised problems, creating class-specific place cells while exhibiting low sample complexity.