  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
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 codebook 2) Learning a composite symmetry to express unknown factors
change between two random samples by learning factor-aligned symmetries within
the codebook 3) Inducing 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.
