Latent Point Collapse on a Low Dimensional Embedding in Deep Neural Network Classifiers

• URL: http://arxiv.org/abs/2310.08224v5
• Date: Sat, 08 Feb 2025 11:34:08 GMT
• Title: Latent Point Collapse on a Low Dimensional Embedding in Deep Neural Network Classifiers
• Authors: Luigi Sbailò, Luca Ghiringhelli,
• Abstract summary: We propose a method to induce the collapse of latent representations belonging to the same class into a single point. The proposed approach is straightforward to implement and yields substantial improvements in discnative feature embeddings.
• Score: 0.0
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• Abstract: The configuration of latent representations plays 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 enforcing Lipschitz continuity in the network. We demonstrate that this phenomenon, which we call \textit{latent point collapse}, 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. The proposed approach is straightforward to implement and yields substantial improvements in discriminative feature embeddings, along with remarkable gains in robustness to input perturbations.

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