自监督编码器趋向正态分布,源于信息瓶颈原理。
Why Self-Supervised Encoders Want to Be Normal

- 将信息瓶颈重构为预测流形上的率失真问题,解释正态分布偏好。
- 发现潜在表示对应输入的软聚类,组织成自然单纯形结构。
- 提供可落地的损失函数,适用于主流自监督基准测试。
自监督学习在无标签情况下学习鲁棒表征方面取得了显著进展,尤其体现在联合嵌入预测架构(JEPA)中。然而,一个根本性问题仍待解答:驱动编码器趋向特定分布状态的分析原理是什么?本文证明,自监督编码器对正态分布的偏好是信息瓶颈(IB)原理的直接结果。通过将IB目标重新表述为预测流形上的率失真问题,我们为最优、目标无关的潜在表示趋于各向同性高斯状态提供了理论依据。在此框架下,潜在表示对应于具有相似预测分布的输入的软聚类,并在自然单纯形结构中组织。这一视角统一了多种现有监督与弱监督目标,并为常用正则化方案提供了原则性解释。此外,我们推导出近似该结构的实用损失目标,并在标准基准上验证其有效性。最终,我们的框架为理解表征坍缩提供了几何视角,并建立了一个数学系统,用于设计正则化策略,以确保现代自监督模型产生高熵、信息丰富的嵌入。
原文摘要 · Abstract (English)
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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