mlsanityData to 7 Oct 2026

Belief Propagation Neural Networks

arXiv 2007.00295 ↗First posted 1 Jul 2020cs.LG stat.MLcited by 31

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Abstract (arXiv)

Learned neural solvers have successfully been used to solve combinatorial optimization and decision problems. More general counting variants of these problems, however, are still largely solved with hand-crafted solvers. To bridge this gap, we introduce belief propagation neural networks (BPNNs), a class of parameterized operators that operate on factor graphs and generalize Belief Propagation (BP). In its strictest form, a BPNN layer (BPNN-D) is a learned iterative operator that provably maintains many of the desirable properties of BP for any choice of the parameters. Empirically, we show that by training BPNN-D learns to perform the task better than the original BP: it converges 1.7x faster on Ising models while providing tighter bounds. On challenging model counting problems, BPNNs compute estimates 100's of times faster than state-of-the-art handcrafted methods, while returning an estimate of comparable quality.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Jul 2020.

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Citing papers per year: 2021: 10; 2022: 6; 2023: 3; 2024: 5; 2025: 5; 2026: 2.

31 papers.

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  1. 2022Understanding Non-linearity in Graph Neural Networks from the Bayesian-Inference Perspectivecited by 19
  2. 2022NSNet: A General Neural Probabilistic Framework for Satisfiability Problemscited by 18
  3. 2021A visual introduction to Gaussian Belief Propagationcited by 12
  4. 2021Deep learning via message passing algorithms based on belief propagationcited by 12
  5. 2023Joint Entity and Relation Extraction with Span Pruning and Hypergraph Neural Networkscited by 11
  6. 2021Partition Function Estimation: A Quantitative Studycited by 8
  7. 2021Neural Belief Propagation for Scene Graph Generationcited by 6
  8. 2021Relational Reasoning Networkscited by 4
  9. 2024Learning to Solve the Constrained Most Probable Explanation Task in Probabilistic Graphical Modelscited by 3
  10. 2024Understanding GNNs for Boolean Satisfiability through Approximation Algorithmscited by 3
  11. 2021Graph Belief Propagation Networkscited by 2
  12. 2025Mitigating Attention Localization in Small Scale: Self-Attention Refinement via One-step Belief Propagationcited by 2
19 more
  1. 2025Vejde: A Framework for Inductive Deep Reinforcement Learning Based on Factor Graph Color Refinementcited by 2
  2. 2021Equivariant Neural Network for Factor Graphscited by 1
  3. 2021Robust Deep Learning from Crowds with Belief Propagationcited by 1
  4. 2021Adversarial Neural Networks for Error Correcting Codescited by 1
  5. 2022IBIA: Bayesian Inference via Incremental Build-Infer-Approximate operations on Clique Treescited by 1
  6. 2022Graph Neural Networks for Propositional Model Countingcited by 1
  7. 2022Deep Attentive Belief Propagation: Integrating Reasoning and Learning for Solving Constraint Optimization Problemscited by 1
  8. 2025Physics Informed Constrained Learning of Dynamics from Static Datacited by 1
  9. 2025Transformer-Based Decoding in Concatenated Coding Schemes Under Synchronization Errorscited by 1
  10. 2021Unifying AI Algorithms with Probabilistic Programming using Implicitly Defined Representationscited by 0
  11. 2022Neural Bayesian Network Understudycited by 0
  12. 2023Local Message Passing on Frustrated Systemscited by 0
  13. 2023Classification-Aided Robust Multiple Target Tracking Using Neural Enhanced Message Passingcited by 0
  14. 2024Circular Belief Propagation for Approximate Probabilistic Inferencecited by 0
  15. 2024ReMAP: Neural Reparameterization for Scalable MAP Inference in Arbitrary-Order Markov Random Fieldscited by 0
  16. 2024The Role of Recurrency in Image Segmentation for Noisy and Limited Sample Settingscited by 0
  17. 2025Attn-JGNN: Attention Enhanced Join-Graph Neural Networkscited by 0
  18. 2026In-Context Graphical Inferencecited by 0
  19. 2026Graph neural networks and the energetic cavity method for combinatorial optimizationcited by 0