# Learning to Condition: A Neural Heuristic for Scalable MPE Inference

arXiv: https://arxiv.org/abs/2509.25217 · HTML: https://mlsanity.com/paper/2509.25217/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 51 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [The SCIP Optimization Suite 9.0](https://mlsanity.com/paper/2402.17702/) (2024)
- [Learning Primal Heuristics for Mixed Integer Programs](https://mlsanity.com/paper/2107.00866/) (2021)
- [A Theoretical and Computational Analysis of Full Strong-Branching](https://mlsanity.com/paper/2110.10754/) (2021)
- [Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks](https://mlsanity.com/paper/1703.06045/) (2017)
- [Neural Network Approximators for Marginal MAP in Probabilistic Circuits](https://mlsanity.com/paper/2402.03621/) (2024)

## Built on by (most cited first, 1 of 1)

- [Learning to Guide Local Search for MPE Inference in Probabilistic Graphical Models](https://mlsanity.com/paper/2602.01475/) (2026)

## Abstract (arXiv)

We introduce learning to condition (L2C), a scalable, data-driven framework for accelerating Most Probable Explanation (MPE) inference in Probabilistic Graphical Models (PGMs), a fundamentally intractable problem. L2C trains a neural network to score variable-value assignments based on their utility for conditioning, given observed evidence. To facilitate supervised learning, we develop a scalable data generation pipeline that extracts training signals from the search traces of existing MPE solvers. The trained network serves as a heuristic that integrates with search algorithms, acting as a conditioning strategy prior to exact inference or as a branching and node selection policy within branch-and-bound solvers. We evaluate L2C on challenging MPE queries involving high-treewidth PGMs. Experiments show that our learned heuristic significantly reduces the search space while maintaining or improving solution quality over state-of-the-art methods.