Dynamical Archetype Analysis: Autonomous Computation

TL;DR

This paper introduces a novel method for classifying neural systems based on their asymptotic dynamical behavior using archetypes and a new dissimilarity measure, improving understanding of neural computation.

Contribution

It proposes a library of archetypical computations and a dissimilarity measure that groups systems by effective behavior, extending to biological and artificial neural systems.

Findings

Method overcomes fragility of existing measures for attractors and high-dimensional networks.

Numerical experiments demonstrate effective grouping of neural systems based on dynamics.

Approach extends to general interpretation of recurrent neural dynamics.

Abstract

The study of neural computation aims to understand the function of a neural system as an information processing machine. Neural systems are undoubtedly complex, necessitating principled and automated tools to abstract away details to organize and incrementally build intuition. We argue that systems with the same effective behavior should be abstracted by their ideal representative, i.e., archetype, defined by its asymptotic dynamical structure. We propose a library of archetypical computations and a new measure of dissimilarity that allows us to group systems based on their effective behavior by explicitly considering both deformations that break topological conjugacy as well as diffeomorphisms that preserve it. The proposed dissimilarity can be estimated from observed trajectories. Numerical experiments demonstrate our method's ability to overcome previously reported fragility of existing (dis)similarity measures for approximate continuous attractors and high-dimensional recurrent neural networks. Although our experiments focus on working memory systems, our theoretical approach naturally extends to general mechanistic interpretation of recurrent dynamics in both biological and artificial neural systems. We argue that abstract dynamical archetypes, rather than detailed dynamical systems, offer a more useful vocabulary for describing neural computation.