Why Self-Supervised Encoders Want to Be Normal

• URL: http://arxiv.org/abs/2604.27743v2
• Date: Sun, 03 May 2026 18:27:16 GMT
• Title: Why Self-Supervised Encoders Want to Be Normal
• Abstract summary: We show that the preference for normal distributions in self-supervised encoders is a direct consequence of the Information Bottleneck (IB) principle.<n>Under this framework, we show that latent representations correspond to soft clustering of inputs sharing similar predictive distributions.<n>This perspective unifies a wide range of existing supervised and less-supervised objectives and provides a principled explanation for commonly used regularization schemes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Self-supervised learning has achieved remarkable empirical success in learning robust representations without explicit labels, most recently demonstrated within the framework of Joint-Embedding Predictive Architectures (JEPA). However, a fundamental question remains: what analytical principles drive these encoders toward specific distributional states? In this paper, we demonstrate that the preference for normal distributions in self-supervised encoders is a direct consequence of the Information Bottleneck (IB) principle. By recasting the IB objective as a rate-distortion problem over the predictive manifold, we provide a theoretical basis for why optimal, target-neutral, latent representations should tend towards isotropic Gaussian states. Under this framework, we show that latent representations correspond to soft clustering of inputs sharing similar predictive distributions, organized within a natural simplex structure. This perspective unifies a wide range of existing supervised and less-supervised objectives and provides a principled explanation for commonly used regularization schemes. Furthermore, we derive practical loss objectives that approximate this structure and demonstrate their effectiveness on standard benchmarks. Ultimately, our framework offers a geometric lens to understanding representation collapse and it establishes a mathematical system for regularization strategies to be used to ensure high-entropy, informative embeddings in modern self-supervised models.

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