CFASL: Composite Factor-Aligned Symmetry Learning for Disentanglement in Variational AutoEncoder

Symmetries of input and latent vectors have provided valuable insights for disentanglement learning in VAEs. However, only a few works were proposed as an unsupervised method, and even these works require known factor information in the training data. We propose a novel method, Composite Factor-Aligned Symmetry Learning (CFASL), which is integrated into VAEs for learning symmetry-based disentanglement in unsupervised learning without any knowledge of the dataset factor information. CFASL incorporates three novel features for learning symmetry-based disentanglement: 1) Injecting inductive bias to align latent vector dimensions to factor-aligned symmetries within an explicit learnable symmetry code-book 2) Learning a composite symmetry to express unknown factors change between two random samples by learning factor-aligned symmetries within the codebook 3) Inducing a group equivariant encoder and decoder in training VAEs with the two conditions. In addition, we propose an extended evaluation metric for multi-factor changes in comparison to disentanglement evaluation in VAEs. In quantitative and in-depth qualitative analysis, CFASL demonstrates a significant improvement of disentanglement in single-factor change, and multi-factor change conditions compared to state-of-the-art methods.