Understanding Self-Supervised Learning via Latent Distribution Matching

2026-07-22 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

The paper introduces Latent Distribution Matching (LDM) as a unifying theoretical framework for self-supervised learning (SSL). LDM conceptualizes SSL as matching a data distribution in latent space to an assumed latent model, while maximizing latent entropy to prevent representational collapse. This framework unifies diverse SSL methods, including contrastive (SimCLR), non-contrastive (VICReg), and predictive approaches, clarifying their underlying assumptions. The research demonstrates that mutual information (MI) maximization contributes minimally to representation quality beyond entropy maximization within LDM. Leveraging LDM, the authors derive new SSL objectives, such as a nonlinear, sampling-free Bayesian filtering model with a Kalman-based predictor for high-dimensional timeseries, enabling principled uncertainty quantification. Furthermore, LDM provides identifiability guarantees for predictive SSL, proving that learned latent representations can recover true underlying variables up to affine transformations under mild assumptions.

Key takeaway

For AI Scientists designing or evaluating self-supervised learning models, this LDM framework provides a robust theoretical foundation to guide development. You should prioritize specifying appropriate latent models and effective entropy estimators, as these factors significantly impact representation quality and identifiability, rather than solely focusing on mutual information maximization. Consider LDM-derived objectives, like Kalman-based predictive models, for high-dimensional timeseries to achieve principled uncertainty quantification and affine identifiability.

Key insights

Latent Distribution Matching unifies SSL methods by aligning latent data distributions with assumed models and maximizing entropy.

Principles

• SSL can be framed as latent distribution matching.
• Entropy maximization prevents representational collapse.
• MI maximization's role is secondary to entropy.

Method

LDM involves matching a data distribution to an assumed latent model (alignment) and maximizing latent entropy (uniformity). This framework allows deriving new SSL objectives, like Kalman-based predictive models.

In practice

• Apply Kalman-based SSL for timeseries data.
• Use LDM to design identifiable SSL algorithms.
• Evaluate SSL methods based on latent space and entropy estimator.

Topics

• Self-Supervised Learning
• Latent Distribution Matching
• Representation Learning
• Identifiability
• Bayesian Filtering
• Kalman Filter
• Nonlinear ICA

Code references

• fmi-basel/latent_distribution_matching

Best for: Research Scientist, AI Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.