# Learning Branching Heuristics from Graph Neural Networks

arXiv: https://arxiv.org/abs/2211.14405 · HTML: https://mlsanity.com/paper/2211.14405/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 17 references that are in the map.
- First posted on arXiv 26 Nov 2022.

## Builds on (most cited first, 9 of 9)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Learning a SAT Solver from Single-Bit Supervision](https://mlsanity.com/paper/1802.03685/) (2018)
- [Combinatorial Optimization with Graph Convolutional Networks and Guided Tree Search](https://mlsanity.com/paper/1810.10659/) (2018)
- [Erdos Goes Neural: an Unsupervised Learning Framework for Combinatorial Optimization on Graphs](https://mlsanity.com/paper/2006.10643/) (2020)
- [What's Wrong with Deep Learning in Tree Search for Combinatorial Optimization](https://mlsanity.com/paper/2201.10494/) (2022)

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

- [FourierCSP: Differentiable Constraint Satisfaction Problem Solving by Walsh-Fourier Expansion](https://mlsanity.com/paper/2510.04480/) (2025)

## Abstract (arXiv)

Backtracking has been widely used for solving problems in artificial intelligence (AI), including constraint satisfaction problems and combinatorial optimization problems. Good branching heuristics can efficiently improve the performance of backtracking by helping prune the search space and leading the search to the most promising direction. In this paper, we first propose a new graph neural network (GNN) model designed using the probabilistic method. From the GNN model, we introduce an approach to learn a branching heuristic for combinatorial optimization problems. In particular, our GNN model learns appropriate probability distributions on vertices in given graphs from which the branching heuristic is extracted and used in a backtracking search. Our experimental results for the (minimum) dominating-clique problem show that this learned branching heuristic performs better than the minimum-remaining-values heuristic in terms of the number of branches of the whole search tree. Our approach introduces a new way of applying GNNs towards enhancing the classical backtracking algorithm used in AI.