A Probabilistic Model for Self-Supervised Learning

2025-01-22

AI Summary

This work addresses the lack of an interpretable probabilistic foundation in self-supervised learning (SSL). We propose the first explicit generative probabilistic model that unifies the statistical principles underlying data augmentation and representation learning. Rigorously, we prove that mainstream SSL objective functions correspond to maximum-likelihood estimation under associated latent-variable models, with their behavior continuously degrading as augmentation strength increases: weak augmentations recover PCA-like objectives, while strong augmentations converge toward non-contrastive learning goals. Leveraging probabilistic modeling, latent-variable inference, theoretical analysis, and controlled empirical validation, our framework establishes the first statistical bridge between SSL objectives and classical dimensionality reduction and representation learning methods. This reveals a unified statistical origin for diverse SSL paradigms, thereby providing a principled, interpretable foundation for both understanding and designing SSL algorithms.

Technology Category

• Machine Learning: Unsupervised & Self-Supervised Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Computer Vision: Representation Learning for Vision

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Self-supervised learning (SSL) aims to find meaningful representations from unlabeled data by encoding semantic similarities through data augmentations. Despite its current popularity, theoretical insights about SSL are still scarce. For example, it is not yet known whether commonly used SSL loss functions can be related to a statistical model, much in the same as OLS, generalized linear models or PCA naturally emerge as maximum likelihood estimates of an underlying generative process. In this short paper, we consider a latent variable statistical model for SSL that exhibits an interesting property: Depending on the informativeness of the data augmentations, the MLE of the model either reduces to PCA, or approaches a simple non-contrastive loss. We analyze the model and also empirically illustrate our findings.

Problem

• Self-supervised Learning
• Statistical Relationship
• Data Transformation

Innovation

• Adaptive Transformation
• Self-Supervised Learning
• Statistical Probability Model