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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 cannotcapture context-specific independence (CSI). Existing methods require carefullydeveloped theories and purpose-built inference methods, which limit theirapplications to only small-scale problems. In this paper, we propose the MarkovAttention Model (MAM), a family of discrete MRFs that incorporates an attentionmechanism. The attention mechanism allows variables to dynamically attend tosome other variables while ignoring the rest, and enables capturing of CSIs inMRFs. A MAM is formulated as an MRF, allowing it to benefit from the rich setof existing MRF inference methods and scale to large models and datasets. Todemonstrate MAM's capabilities to capture CSIs at scale, we apply MAMs tocapture an important type of CSI that is present in a symbolic approach torecurrent computations in perceptual grouping. Experiments on two recentlyproposed synthetic perceptual grouping tasks and on realistic imagesdemonstrate the advantages of MAMs in sample-efficiency, interpretability andgeneralizability when compared with strong recurrent neural network baselines,and validate MAM's capabilities to efficiently capture CSIs at scale.

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