Disentangled Representation Learning through Unsupervised Symmetry Group Discovery

2026-03-12

AI Summary

This work proposes an unsupervised approach to disentangled representation learning that circumvents the need for strong priors on symmetry group structures or restrictive assumptions about subgroup properties commonly required by existing methods. By leveraging agent–environment interactions, the method autonomously discovers symmetry groups within the action space and subsequently learns disentangled representations grounded in these symmetries. Under minimal assumptions, the authors theoretically establish the identifiability of symmetry group decomposition and integrate a group-theoretic decomposition algorithm with the Linear Symmetry-Based Disentanglement (LSBD) framework to enable end-to-end learning. Empirical evaluations demonstrate that the proposed method significantly outperforms current LSBD approaches across three distinct environments featuring different group structures, thereby confirming its effectiveness and broad applicability.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Symmetry-based disentangled representation learning leverages the group structure of environment transformations to uncover the latent factors of variation. Prior approaches to symmetry-based disentanglement have required strong prior knowledge of the symmetry group's structure, or restrictive assumptions about the subgroup properties. In this work, we remove these constraints by proposing a method whereby an embodied agent autonomously discovers the group structure of its action space through unsupervised interaction with the environment. We prove the identifiability of the true symmetry group decomposition under minimal assumptions, and derive two algorithms: one for discovering the group decomposition from interaction data, and another for learning Linear Symmetry-Based Disentangled (LSBD) representations without assuming specific subgroup properties. Our method is validated on three environments exhibiting different group decompositions, where it outperforms existing LSBD approaches.

Problem

• disentangled representation learning
• symmetry group
• unsupervised learning
• group discovery
• embodied agent

Innovation

• disentangled representation learning
• symmetry group discovery
• unsupervised learning
• embodied agent
• group decomposition