Title: Latent Point Collapse on a Low Dimensional Embedding in Deep Neural Network Classifiers
Primary area: optimization
Keywords: Classification, Latent Space, Neural Collapse

Abstract: The topological properties of latent representations play a critical role in determining the performance of deep neural network classifiers. In particular, the emergence of well-separated class embeddings in the latent space has been shown to improve both generalization and robustness. In this paper, we propose a method to induce the collapse of latent representations belonging to the same class into a single point, which enhances class separability in the latent space while making the network Lipschitz continuous.
We demonstrate that this phenomenon, which we call \textit{latent point collapse} (LPC), is achieved by adding a strong $L_2$ penalty on the penultimate-layer representations and is the result of a push-pull tension developed with the cross-entropy loss function.
In addition, we show the practical utility of applying this compressing loss term to the latent representations of a low-dimensional linear penultimate layer.
LPC can be viewed as a stronger manifestation of \textit{neural collapse} (NC): while NC entails that within-class representations converge around their class means, LPC causes these representations to collapse in absolute value to a single point. As a result, the network improvements typically associated with NC—namely better generalization and robustness—are even more pronounced when LPC develops.

TL;DR: We characterize latent point collapse, a stronger manifestation of neural collapse that is is achieved by adding a strong $L_2$ penalty on the penultimate-layer representations making the network Lipschitz continuous.