Commutator-Induced Uncertainty in VAEs
Variational autoencoders (VAEs) often struggle to represent non-commutative structure in learned latent spaces. Symmetry-aware VAEs commonly address this issue by enforcing commutativity through algebraic regularization, which is appropriate for commutative transformation groups but can suppress meaningful non-commutative structure when it is intrinsic to the data. We argue that non-commutativity should instead be explicitly diagnosed and reflected in reconstruction behavior. We introduce a Lie Group VAE framework that combines geometric and algebraic perspectives on uncertainty while separating discrete generative factors from continuous geometric transformations. In a first phase, the m...
| Authors | Tahereh Dehdarirad, Michael Felsberg, Gabriel Eilertsen et al. |
|---|---|
| Primary category | cs.LG |
| Published | 22 May 2026 |
| Last updated at source | 22 May 2026 |
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