An Empirically Grounded Identifiability Theory Will Accelerate Self-Supervised Learning Research

2025-04-17

AI Summary

Current self-supervised learning (SSL) methods achieve empirical success without a unified theoretical foundation—particularly lacking explanation for why diverse approaches converge to similar ideal representations. Existing identifiability theory (IT) fails to characterize the full SSL pipeline, including data assumptions, training dynamics, and inductive biases. To address this gap, we propose **Singular Identifiability Theory (SITh)**, the first framework extending IT to the entire SSL workflow and providing formal grounding for the Platonic representation hypothesis. SITh unifies representation learning, statistical learning theory, and training dynamics analysis to reveal three key mechanisms: finite-sample effects, architectural bias, and optimization trajectory constraints. By rigorously modeling how these factors jointly shape learned representations, SITh bridges the theory–practice divide in SSL. It establishes an interpretable, generalizable paradigm for representation learning and furnishes principled guidelines for theory-driven SSL algorithm design.

Technology Category

• Machine Learning: Representation Learning
• Computer Vision: Representation Learning for Vision
• Search and Optimization: Learning to Search

Application Category

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

Abstract

Self-Supervised Learning (SSL) powers many current AI systems. As research interest and investment grow, the SSL design space continues to expand. The Platonic view of SSL, following the Platonic Representation Hypothesis (PRH), suggests that despite different methods and engineering approaches, all representations converge to the same Platonic ideal. However, this phenomenon lacks precise theoretical explanation. By synthesizing evidence from Identifiability Theory (IT), we show that the PRH can emerge in SSL. However, current IT cannot explain SSL's empirical success. To bridge the gap between theory and practice, we propose expanding IT into what we term Singular Identifiability Theory (SITh), a broader theoretical framework encompassing the entire SSL pipeline. SITh would allow deeper insights into the implicit data assumptions in SSL and advance the field towards learning more interpretable and generalizable representations. We highlight three critical directions for future research: 1) training dynamics and convergence properties of SSL; 2) the impact of finite samples, batch size, and data diversity; and 3) the role of inductive biases in architecture, augmentations, initialization schemes, and optimizers.

Problem

• Bridging theory-practice gap in Self-Supervised Learning identifiability
• Explaining empirical success of SSL via Singular Identifiability Theory
• Advancing interpretable SSL representations through expanded theoretical framework

Innovation

• Expanding Identifiability Theory into SITh
• Analyzing SSL training dynamics and convergence
• Studying inductive biases in SSL architectures