Efficient, probabilistic analysis of combinatorial neural codes

TL;DR

This paper introduces a more efficient algebraic approach to analyze high-dimensional combinatorial neural codes in both artificial and biological networks, revealing insights into their structure and learning processes.

Contribution

It significantly reduces the computational complexity of analyzing neural codes and applies these methods to large-scale neural data from ANNs and BNNs.

Findings

Quadratic time analysis of neural codes achieved

Identified neural code structure and dimensionality in experiments

Tracked internal representation changes during learning

Abstract

Artificial and biological neural networks (ANNs and BNNs) can encode inputs in the form of combinations of individual neurons' activities. These combinatorial neural codes present a computational challenge for direct and efficient analysis due to their high dimensionality and often large volumes of data. Here we improve the computational complexity -- from factorial to quadratic time -- of direct algebraic methods previously applied to small examples and apply them to large neural codes generated by experiments. These methods provide a novel and efficient way of probing algebraic, geometric, and topological characteristics of combinatorial neural codes and provide insights into how such characteristics are related to learning and experience in neural networks. We introduce a procedure to perform hypothesis testing on the intrinsic features of neural codes using information geometry. We then apply these methods to neural activities from an ANN for image classification and a BNN for 2D navigation to, without observing any inputs or outputs, estimate the structure and dimensionality of the stimulus or task space. Additionally, we demonstrate how an ANN varies its internal representations across network depth and during learning.