Graphical Models with Attention for Context-Specific Independence and an Application to Perceptual Grouping

TL;DR

This paper introduces the Markov Attention Model (MAM), a novel discrete MRF that incorporates attention mechanisms to dynamically capture context-specific independence, enabling scalable and interpretable probabilistic modeling in perceptual grouping tasks.

Contribution

The paper proposes MAM, a new class of discrete MRFs with attention, allowing scalable capture of CSIs and application to perceptual grouping, overcoming limitations of traditional MRFs.

Findings

MAM effectively captures CSIs in large models.

MAM outperforms recurrent neural networks in sample-efficiency.

MAM demonstrates improved interpretability and generalizability.

Abstract

Discrete undirected graphical models, also known as Markov Random Fields (MRFs), can flexibly encode probabilistic interactions of multiple variables, and have enjoyed successful applications to a wide range of problems. However, a well-known yet little studied limitation of discrete MRFs is that they cannot capture context-specific independence (CSI). Existing methods require carefully developed theories and purpose-built inference methods, which limit their applications to only small-scale problems. In this paper, we propose the Markov Attention Model (MAM), a family of discrete MRFs that incorporates an attention mechanism. The attention mechanism allows variables to dynamically attend to some other variables while ignoring the rest, and enables capturing of CSIs in MRFs. A MAM is formulated as an MRF, allowing it to benefit from the rich set of existing MRF inference methods and scale to large models and datasets. To demonstrate MAM's capabilities to capture CSIs at scale, we apply MAMs to capture an important type of CSI that is present in a symbolic approach to recurrent computations in perceptual grouping. Experiments on two recently proposed synthetic perceptual grouping tasks and on realistic images demonstrate the advantages of MAMs in sample-efficiency, interpretability and generalizability when compared with strong recurrent neural network baselines, and validate MAM's capabilities to efficiently capture CSIs at scale.