Soft-Constrained Optimization of Latent Space in Variational Autoencoders

2026-07-26

AI Summary

This work addresses the challenge in variational autoencoders (VAEs) of simultaneously achieving high representational capacity and disentangled, low-dimensional latent representations. The authors formulate VAE training as a soft-constrained optimization problem, introducing an entropy-based soft constraint mechanism to regulate the information content of individual latent variables. Coupled with weight filtering, this approach enables automatic pruning of low-entropy dimensions. The proposed method enhances representation efficiency while preserving disentanglement. Experiments demonstrate significant improvements: on dSprites, activation scores increase by 43–62%, FactorVAE score reaches 0.891, and reconstruction error decreases by 38%; on MNIST, over 90% classification accuracy is achieved using only two latent dimensions—reducing input dimensionality by 80% compared to baselines—and training convergence accelerates by 37%.

Abstract

The usefulness of a variational autoencoder (VAE) depends on two properties of its latent space that are hard to obtain together: high encoding capacity in the individual latent variables, and a low-dimensional, disentangled organization of those variables. Weakening the Kullback-Leibler regularization raises capacity but degrades disentanglement, while strengthening it prunes latent variables away entirely. We formulate VAE training as a soft-constrained optimization problem that addresses both. First, we impose an entropy-based constraint (EC) on individual latent variables, showing that the entropy of a latent code upper-bounds the mutual information it carries about the generative factors of the data. Second, we propose a weight-filter method that exploits the slack of the soft constraint to prune low-entropy dimensions during downstream training. On dSprites, the EC raises the aggregate latent-variable activation score by 43-62% over a vanilla VAE, attains the highest FactorVAE score among the \b{eta} \b{eta}-VAE variants (0.891 vs 0.847), and lowers reconstruction error by up to 38%. On MNIST, the weight filter reduces the latent dimensionality supplied to a downstream classifier from ten to two while holding accuracy above 90%, converging in 37% fewer epochs than the same procedure without the EC. We also find that low-entropy discrete factors tend to merge into a single latent variable, whereas high-entropy continuous factors are distributed across several.

Problem

• variational autoencoder
• latent space
• disentanglement
• encoding capacity
• soft-constrained optimization

Innovation

• soft-constrained optimization
• entropy-based constraint
• latent space disentanglement
• weight filter
• variational autoencoder