Perturbation theory approach to study the latent space degeneracy of Variational Autoencoders

TL;DR

This paper introduces a novel perturbation theory approach, inspired by physics, to analyze and correct latent space degeneracy in Variational Autoencoders, enhancing interpretability and modeling capabilities.

Contribution

It applies perturbation theory to VAE latent spaces, providing a new framework for understanding and addressing degeneracy through energy spectrum analysis.

Findings

The approach reveals the energy landscape of latent spaces.

Perturbation-based correction improves latent space structure.

The method offers insights into the generative process of VAEs.

Abstract

The use of Variational Autoencoders in different Machine Learning tasks has drastically increased in the last years. They have been developed as denoising, clustering and generative tools, highlighting a large potential in a wide range of fields. Their embeddings are able to extract relevant information from highly dimensional inputs, but the converged models can differ significantly and lead to degeneracy on the latent space. We leverage the relation between theoretical physics and machine learning to explain this behaviour, and introduce a new approach to correct for degeneration by using perturbation theory. The re-formulation of the embedding as multi-dimensional generative distribution, allows mapping to a new set of functions and their corresponding energy spectrum. We optimise for a perturbed Hamiltonian, with an additional energy potential that is related to the unobserved topology of the data. Our results show the potential of a new theoretical approach that can be used to interpret the latent space and generative nature of unsupervised learning, while the energy landscapes defined by the perturbations can be further used for modelling and dynamical purposes.