Scaling Up Probabilistic Circuits by Latent Variable Distillation

TL;DR

This paper introduces latent variable distillation, a method that enhances probabilistic circuits by leveraging deep generative models to improve their scalability and performance on large, high-dimensional datasets.

Contribution

It proposes a novel latent variable distillation technique that uses Transformer-based generative models to guide the training of probabilistic circuits, enabling better scalability and performance.

Findings

Latent variable distillation significantly improves PC performance on image and language benchmarks.

Large PCs with distillation achieve competitive results against deep generative models.

The method enables tractable probabilistic modeling for complex, high-dimensional data.

Abstract

Probabilistic Circuits (PCs) are a unified framework for tractable probabilistic models that support efficient computation of various probabilistic queries (e.g., marginal probabilities). One key challenge is to scale PCs to model large and high-dimensional real-world datasets: we observe that as the number of parameters in PCs increases, their performance immediately plateaus. This phenomenon suggests that the existing optimizers fail to exploit the full expressive power of large PCs. We propose to overcome such bottleneck by latent variable distillation: we leverage the less tractable but more expressive deep generative models to provide extra supervision over the latent variables of PCs. Specifically, we extract information from Transformer-based generative models to assign values to latent variables of PCs, providing guidance to PC optimizers. Experiments on both image and language modeling benchmarks (e.g., ImageNet and WikiText-2) show that latent variable distillation substantially boosts the performance of large PCs compared to their counterparts without latent variable distillation. In particular, on the image modeling benchmarks, PCs achieve competitive performance against some of the widely-used deep generative models, including variational autoencoders and flow-based models, opening up new avenues for tractable generative modeling. Our code can be found at https://github.com/UCLA-StarAI/LVD.