An Information-Geometric Formulation of Pattern Separation and Evaluation of Existing Indices

TL;DR

This paper introduces an information-geometric framework for understanding pattern separation in neural systems and evaluates existing similarity indices, revealing their limitations in capturing correlation-based differences.

Contribution

It formulates pattern separation as a geometric problem on a statistical manifold and critically assesses current similarity indices within this framework.

Findings

Existing indices are sensitive to marginal firing rate differences.

Current indices fail to detect differences in spike train correlation.

The geometric formulation provides new insights into neural pattern separation.

Abstract

Pattern separation is a computational process by which dissimilar neural patterns are generated from similar input patterns. We present an information-geometric formulation of pattern separation, where a pattern separator is modelled as a family of statistical distributions on a manifold. Such a manifold maps an input (i.e. coordinates) to a probability distribution that generates firing patterns. Pattern separation occurs when small coordinate changes result in large distances between samples from the corresponding distributions. Under this formulation, we implement a two-neuron system whose probability law forms a 3-dimensional manifold with mutually orthogonal coordinates representing the neurons' marginal and correlational firing rates. We use this highly controlled system to examine the behaviour of spike train similarity indices commonly used in pattern separation research. We found that all indices (except scaling factor) were sensitive to relative differences in marginal firing rates, but no index adequately captured differences in spike trains that resulted from altering the correlation in activity between the two neurons. That is, existing pattern separation metrics appear (A) sensitive to patterns that are encoded by different neurons, but (B) insensitive to patterns that differ only in relative spike timing (e.g. synchrony between neurons in the ensemble).