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This paper unifies diverse self-supervised learning methods under a latent distribution matching framework, offering theoretical clarity on alignment and uniformity principles. By deriving a nonlinear Bayesian filtering model for high-dimensional time series, it provides a principled path toward developing more robust representation learning algorithms without relying on sampling. The work significantly advances the foundational understanding of how SSL achieves general-purpose representations from complex data.
Understanding Self-Supervised Learning via Latent Distribution Matching
arXiv:2605.03517v4 Announce Type: replace Abstract: 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.
Abstract: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.
Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2605.03517 [cs.LG]
(or arXiv:2605.03517v4 [cs.LG] for this version)
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