Low-Rank Constraints for Fast Inference in Structured Models

TL;DR

This paper introduces a low-rank constraint approach to reduce the computational complexity of structured probabilistic models, enabling faster inference without sacrificing accuracy in large state spaces.

Contribution

It proposes a simple low-rank constraint method that accelerates inference in structured models by trading off model expressivity and speed, applicable across various domains.

Findings

Achieves significant speedups in inference.

Maintains accuracy comparable to standard models.

Applicable to language, music, grammar induction, and video modeling.

Abstract

Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory complexity with respect to the size of the latent representations. Common models such as Hidden Markov Models (HMMs) and Probabilistic Context-Free Grammars (PCFGs) require time and space quadratic and cubic in the number of hidden states respectively. This work demonstrates a simple approach to reduce the computational and memory complexity of a large class of structured models. We show that by viewing the central inference step as a matrix-vector product and using a low-rank constraint, we can trade off model expressivity and speed via the rank. Experiments with neural parameterized structured models for language modeling, polyphonic music modeling, unsupervised grammar induction, and video modeling show that our approach matches the accuracy of standard models at large state spaces while providing practical speedups.