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This paper introduces a method for unsupervised discovery of symmetry group structure by an embodied agent interacting with its environment, enabling symmetry-based disentangled representation learning without prior knowledge of the group. They prove identifiability of the true symmetry group decomposition under minimal assumptions and derive two algorithms for group discovery and Linear Symmetry-Based Disentangled (LSBD) representation learning. Experiments across three environments demonstrate that the proposed approach outperforms existing LSBD methods.
Unlocking disentangled representations just got easier: now agents can autonomously discover environmental symmetries without needing pre-defined group structures.
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.
