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Workshop: Symmetry and Geometry in Neural Representations

Emergence of Latent Binary Encoding in Deep Neural Network Classifiers

Luigi Sbailò · Luca Ghiringhelli

Abstract: We observe the emergence of binary encoding within the latent space of deep-neural-network classifiers.Such binary encoding is induced by introducing a linear penultimate layer, which is equipped during training with a loss function that grows as $\exp(\vec{x}^2)$, where $\vec{x}$ are the coordinates in the latent space. The phenomenon we describe represents a specific instance of a well-documented occurrence known as \textit{neural collapse}, which arises in the terminal phase of training and entails the collapse of latent class means to the vertices of a simplex equiangular tight frame (ETF).We show that binary encoding accelerates convergence toward the simplex ETF and enhances classification accuracy.

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