Linear Readout of Neural Manifolds with Continuous Variables

TL;DR

This paper develops a statistical-mechanical theory linking the geometric properties of neural manifolds to the linear decoding capacity of continuous variables, improving understanding of neural representations in brains and artificial networks.

Contribution

It introduces a novel theoretical framework that relates neural manifold geometry to regression capacity, applicable to complex neural variability and real data.

Findings

Decoding capacity increases for object position and size along the visual stream.

The theory effectively handles complex neural variability.

Applicable to both biological and artificial neural systems.

Abstract

Brains and artificial neural networks compute with continuous variables such as object position or stimulus orientation. However, the complex variability in neural responses makes it difficult to link internal representational structure to task performance. We develop a statistical-mechanical theory of regression capacity that relates linear decoding efficiency of continuous variables to geometric properties of neural manifolds. Our theory handles complex neural variability and applies to real data, revealing increasing capacity for decoding object position and size along the monkey visual stream.