Homology-constrained vector quantization entropy regularizer

Abstract: This paper describes an entropy regularization term for vector quantization (VQ) based on the analysis of persistent homology of the VQ embeddings. Higher embedding entropy positively correlates with higher codebook utilization, mitigating overfit towards the identity and codebook collapse in VQ-based autoencoders [1]. We show that homology-constrained regularization is an effective way to increase entropy of the VQ process (approximated to input entropy) while preserving the approximated topology in the quantized latent space, averaged over mini batches. This work further explores some patterns of persistent homology diagrams of latents formed by vector quantization. We implement and test the proposed algorithm as a module integrated into a sample VQ-VAE. Linked code repository provides a functioning implementation of the proposed architecture, referred to as homology-constrained vector quantization (HC-VQ) further in this work.