Quasi-Monte Carlo Methods Enable Extremely Low-Dimensional Deep Generative Models

ICLR 2026 Conference Submission5292 Authors

Keywords: representation learning, quasi monte-carlo integration, generative modeling, variational autoencoder

TL;DR: We introduce a new latent variable model that allows easy exploration of scientific datasets

Abstract:

This paper introduces *quasi-Monte Carlo latent variable models* (QLVMs): a class of deep generative models that are specialized for finding extremely low-dimensional and interpretable embeddings of high-dimensional datasets.
Unlike standard approaches, which rely on a learned encoder and variational lower bounds, QLVMs directly approximate the marginal likelihood by randomized quasi-Monte Carlo integration.
While this brute force approach has drawbacks in higher-dimensional spaces, we find that it excels in fitting one, two, and three dimensional deep latent variable models.
Empirical results on a range of datasets show that QLVMs consistently outperform conventional variational autoencoders (VAEs) and importance weighted autoencoders (IWAEs) with matched latent dimensionality.
The resulting embeddings enable transparent visualization and *post hoc* analyses such as nonparametric density estimation, clustering, and geodesic path computation, which are nontrivial to validate in higher-dimensional spaces.
While our approach is compute-intensive and struggles to generate fine-scale details in complex datasets, it offers a compelling solution for applications prioritizing interpretability and latent space analysis.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Submission Number: 5292