The Impact of Enforcing Representational Consistency of Identical Transformations for Disentangled Representation

Abstract: Recent symmetry-based approaches in Variational Autoencoders (VAEs) have advanced disentanglement learning and compositional generalization. However, existing methods can encode identical semantic transformations differently depending on the specific sample pairs, which reduce the representational consistency of identical transformations. In this paper, we analyze how three commonly used symmetry parameterization families in prior work, namely (1) matrix-exponential parameterizations over the general linear group GL(n), (2) vector-additive actions in latent space, and (3) surjective mappings from latent vectors to the unit circle, can make it difficult to represent identical transformations consistently in dimension-wise disentangled latent spaces. To address this issue, we propose a framework that maps latent vectors to a bijective cyclic representation on the unit circle via the Cayley transform, together with a fixed-grid codebook regularization. We study this problem in a controlled setting and develop practical weakly supervised and supervised variants. Experiments on disentanglement benchmarks and compositional generalization tasks show that the proposed framework yields improved disentanglement performance and strong compositional generalization under supervised settings, with the stronger-supervision variants providing empirical reference points for the representational capacity of the framework. Overall, our results suggest that consistent representation of identical transformations is a useful design principle for improving disentanglement and generalization performance in the considered setting.

Submission Type: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Vincent_Fortuin1

Submission Number: 8440