Probing Biological and Artificial Neural Networks with Task-dependent Neural Manifolds

TL;DR

This paper explores the internal organization of biological and artificial neural networks using neural population geometry, providing insights into how different learning objectives shape neural representations and their decodability.

Contribution

It introduces a geometric framework combining manifold capacity theory and alignment analysis to bridge mechanistic and normative understanding of neural networks.

Findings

Different learning objectives lead to distinct neural organization strategies.

Geometric properties correlate with the decodability of task-relevant information.

Analysis applies to both deep neural networks and macaque neural recordings.

Abstract

Recently, growth in our understanding of the computations performed in both biological and artificial neural networks has largely been driven by either low-level mechanistic studies or global normative approaches. However, concrete methodologies for bridging the gap between these levels of abstraction remain elusive. In this work, we investigate the internal mechanisms of neural networks through the lens of neural population geometry, aiming to provide understanding at an intermediate level of abstraction, as a way to bridge that gap. Utilizing manifold capacity theory (MCT) from statistical physics and manifold alignment analysis (MAA) from high-dimensional statistics, we probe the underlying organization of task-dependent manifolds in deep neural networks and macaque neural recordings. Specifically, we quantitatively characterize how different learning objectives lead to differences in the organizational strategies of these models and demonstrate how these geometric analyses are connected to the decodability of task-relevant information. These analyses present a strong direction for bridging mechanistic and normative theories in neural networks through neural population geometry, potentially opening up many future research avenues in both machine learning and neuroscience.