Linear Readout of Object Manifolds

TL;DR

This paper develops a theoretical framework to understand how the geometry of neural response manifolds affects the ability of a linear perceptron to classify objects invariantly, providing insights into sensory representation efficiency.

Contribution

It introduces a theory linking object manifold geometry to perceptron classification capacity, advancing understanding of neural coding and invariant object recognition.

Findings

Perceptron capacity depends on manifold dimensionality and size.

Shape of object manifolds influences classification performance.

Theoretical predictions align with neural response data.

Abstract

Objects are represented in sensory systems by continuous manifolds due to sensitivity of neuronal responses to changes in physical features such as location, orientation, and intensity. What makes certain sensory representations better suited for invariant decoding of objects by downstream networks? We present a theory that characterizes the ability of a linear readout network, the perceptron, to classify objects from variable neural responses. We show how the readout perceptron capacity depends on the dimensionality, size, and shape of the object manifolds in its input neural representation.