Multiple Invertible and Partial-Equivariant Function for Latent Vector Transformation to Enhance Disentanglement in VAEs

Disentanglement learning is a core issue for understanding and re-using trained information in Variational AutoEncoder (VAE), and effective inductive bias has been reported as a key factor. However, the actual implementation of such bias is still vague. In this paper, we propose a novel method, called Multiple Invertible and partial-equivariant transformation (MIPE-transformation), to inject inductive bias by 1) guaranteeing the invertibility of latent-to-latent vector transformation while preserving a certain portion of equivariance of input-to-latent vector transformation, called Invertible and partial-equivariant transformation (IPE-transformation), 2) extending the form of prior and posterior in VAE frameworks to an unrestricted form through a learnable conversion to an approximated exponential family, called Exponential Family conversion (EF-conversion), and 3) integrating multiple units of IPE-transformation and EF-conversion, and their training. In experiments on 3D Cars, 3D Shapes, and dSprites datasets, MIPE-transformation improves the disentanglement performance of state-of-the-art VAEs.