Restructuring Tractable Probabilistic Circuits

TL;DR

This paper introduces a method to restructure probabilistic circuits to conform to different vtrees, enabling more flexible and efficient inference in probabilistic models, which broadens their practical applicability.

Contribution

It proposes a generic restructuring approach for PCs, resulting in polynomial-time algorithms for multiplying circuits with different vtrees and a depth-reduction method that maintains structured decomposability.

Findings

Enables multiplication of PCs with different vtrees efficiently.

Provides a depth-reduction algorithm preserving structured decomposability.

Facilitates training with less restrictive PC structures.

Abstract

Probabilistic circuits (PCs) are a unifying representation for probabilistic models that support tractable inference. Numerous applications of PCs like controllable text generation depend on the ability to efficiently multiply two circuits. Existing multiplication algorithms require that the circuits respect the same structure, i.e. variable scopes decomposes according to the same vtree. In this work, we propose and study the task of restructuring structured(-decomposable) PCs, that is, transforming a structured PC such that it conforms to a target vtree. We propose a generic approach for this problem and show that it leads to novel polynomial-time algorithms for multiplying circuits respecting different vtrees, as well as a practical depth-reduction algorithm that preserves structured decomposibility. Our work opens up new avenues for tractable PC inference, suggesting the possibility of training with less restrictive PC structures while enabling efficient inference by changing their structures at inference time.