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

arXiv: https://arxiv.org/abs/2112.03371 · HTML: https://mlsanity.com/paper/2112.03371/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 5 references that are in the map.
- First posted on arXiv 6 Dec 2021.

## Builds on (most cited first, 5 of 5)

- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Multi-view Self-supervised Deep Learning for 6D Pose Estimation in the Amazon Picking Challenge](https://mlsanity.com/paper/1609.09475/) (2016)
- [Context-Specific Independence in Bayesian Networks](https://mlsanity.com/paper/1302.3562/) (2013)
- [Hierarchical compositional feature learning](https://mlsanity.com/paper/1611.02252/) (2016)
- [Scene Grammars, Factor Graphs, and Belief Propagation](https://mlsanity.com/paper/1606.01307/) (2016)

## Built on by (most cited first, 3 of 3)

- [PGMax: Factor Graphs for Discrete Probabilistic Graphical Models and Loopy Belief Propagation in JAX](https://mlsanity.com/paper/2202.04110/) (2022)
- [Learning noisy-OR Bayesian Networks with Max-Product Belief Propagation](https://mlsanity.com/paper/2302.00099/) (2023)
- [Neural expectation-maximization and meta-models](https://mlsanity.com/paper/2610.12741/) (2026)

## Abstract (arXiv)

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.