Information theoretic underpinning of self-supervised learning by clustering

Most self-supervised image clustering models, actually almost all deep learning approaches, are based on gradient descent: In order to calculate the loss, every optimization step requires a clearly defined target, whether a contrastive split, a masked patch or entity, an EMA-teacher output, a pseudo-label, or a differentiable information-theoretic functional. We propose a self-supervised framework that drops this requirement for image clustering. Without any prior knowledge, we have to assume that each pixel is i.i.d. according to the Principle of Maximum Entropy. Taking this as our null hypothesis H0, we define a "surprise score" that measures how unlikely the model's output representation would be under H0. Maximizing the surprise score forces the deep learning model to reject H0 - equivalently, to discover non-random feature from data. Also, here is our fundamental assumption: a surprise score cannot, in general, be reduced to a per-step loss. Hence, we propose the "converge-to-surprise" scheme to optimize our model: an evolution-strategy (ES) outer loop, which directly maximizes the surprise score without needing its gradient, paired with a periodic gradient-descent inner loop, which uses the surprising clusters already discovered by ES as surrogate targets. On standard image benchmarks, our framework achieves new state-of-the-art results in non-parametric self-supervised image clustering - the strictest deep-clustering setting, in which the number of ground-truth classes is not given to the model.

Self-supervised learning (SSL) excels at finding general-purpose latent representations from complex data, yet lacks a unifying theoretical framework that explains the diverse existing methods and guides the design of new ones. We cast SSL as latent distribution matching (LDM): learning representations that maximize their log-probability under an assumed latent model (alignment), while maximizing latent entropy to prevent collapse (uniformity). This view unifies independent component analysis with contrastive, non-contrastive, and predictive SSL methods, including stop gradient approaches. Leveraging LDM, we derive a nonlinear, sampling-free Bayesian filtering model with a Kalman-based predictor for high-dimensional timeseries. We further prove that predictive LDM yields identifiable latent representations under mild assumptions, even with nonlinear predictors. Overall, LDM clarifies the assumptions behind established SSL methods and provides principled guidance for developing new approaches.

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.