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This research proposes a novel framework for equivariant representation learning by decomposing latent spaces into invariant class factors and symmetry groups. By leveraging group theory to enforce lossless disentanglement between object identity and pose, the method offers improved interpretability over existing models on datasets with complex geometric symmetries.

Sursă care acoperăarXiv

Equivariant Representation Learning via Class-Pose Decomposition

arXiv15 iunie 20261 min de cititArticolul și perspectiva sunt în engleză.

arXiv:2207.03116v4 Announce Type: replace Abstract: We introduce a general method for learning representations that are equivariant to symmetries of data. Our central idea is to decompose the latent space into an invariant factor and the symmetry group itself. The components semantically correspond to intrinsic data classes and poses respectively. The learner is trained on a loss encouraging equivariance based on supervision from relative symmetry information. The approach is motivated by theoretical results from group theory and guarantees representations that are lossless, interpretable and disentangled. We provide an empirical investigation via experiments involving datasets with a variety of symmetries. Results show that our representations capture the geometry of data and outperform other equivariant representation learning frameworks.

Abstract:We introduce a general method for learning representations that are equivariant to symmetries of data. Our central idea is to decompose the latent space into an invariant factor and the symmetry group itself. The components semantically correspond to intrinsic data classes and poses respectively. The learner is trained on a loss encouraging equivariance based on supervision from relative symmetry information. The approach is motivated by theoretical results from group theory and guarantees representations that are lossless, interpretable and disentangled. We provide an empirical investigation via experiments involving datasets with a variety of symmetries. Results show that our representations capture the geometry of data and outperform other equivariant representation learning frameworks.

Machine Learning (cs.LG); Group Theory (math.GR)

arXiv:2207.03116 [cs.LG]

(or arXiv:2207.03116v4 [cs.LG] for this version)

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