Categorical Perception: A Groundwork for Deep Learning

TL;DR

This paper investigates how deep neural networks develop categorical perception similar to humans, analyzing the geometry of neural representations and the effects of regularization techniques like dropout.

Contribution

It provides a theoretical and numerical analysis of categorical perception in neural networks, linking neural geometry to perceptual effects and regularization practices.

Findings

Deeper layers exhibit stronger categorical effects.

Category learning induces categorical perception automatically.

Dropout regularization impacts neural geometry and categorical representation.

Abstract

A well-known perceptual consequence of categorization in humans and other animals, called categorical perception, is notably characterized by a within-category compression and a between-category separation: two items, close in input space, are perceived closer if they belong to the same category than if they belong to different categories. Elaborating on experimental and theoretical results in cognitive science, here we study categorical effects in artificial neural networks. We combine a theoretical analysis that makes use of mutual and Fisher information quantities, and a series of numerical simulations on networks of increasing complexity. These formal and numerical analyses provide insights into the geometry of the neural representation in deep layers, with expansion of space near category boundaries and contraction far from category boundaries. We investigate categorical representation by using two complementary approaches: one mimics experiments in psychophysics and cognitive neuroscience by means of morphed continua between stimuli of different categories, while the other introduces a categoricality index that, for each layer in the network, quantifies the separability of the categories at the neural population level. We show on both shallow and deep neural networks that category learning automatically induces categorical perception. We further show that the deeper a layer, the stronger the categorical effects. As an outcome of our study, we propose a coherent view of the efficacy of different heuristic practices of the dropout regularization technique. More generally, our view, which finds echoes in the neuroscience literature, insists on the differential impact of noise in any given layer depending on the geometry of the neural representation that is being learned, i.e. on how this geometry reflects the structure of the categories.