# Belief Propagation Neural Networks

@article{Kuck2020BeliefPN, title={Belief Propagation Neural Networks}, author={Jonathan Kuck and Shuvam Chakraborty and Hao Tang and Rachel Luo and Jiaming Song and Ashish Sabharwal and Stefano Ermon}, journal={ArXiv}, year={2020}, volume={abs/2007.00295} }

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…

## 21 Citations

### Deep Attentive Belief Propagation: Integrating Reasoning and Learning for Solving Constraint Optimization Problems

- Computer Science
- 2022

This work proposes a novel self-supervised learning algorithm for DABP with a smoothed solution cost, which does not require expensive training labels and also avoids the common out-of-distribution issue through efﬁcient online learning.

### Deep learning via message passing algorithms based on belief propagation

- Computer ScienceMach. Learn. Sci. Technol.
- 2022

This paper presents and adapt to mini-batch training on GPUs a family of BP-based message-passing algorithms with a reinforcement term that biases distributions towards locally entropic solutions, capable of training multi-layer neural networks with performance comparable to SGD heuristics in a diverse set of experiments on natural datasets.

### Variational message passing neural network for Maximum-A-Posteriori (MAP) inference

- Computer ScienceUAI
- 2022

A variational message passing neural network (V-MPNN), where both the power of neural networks in modeling complex functions and the well-established algorithmic theories on variational belief propagation are leveraged.

### NSNet: A General Neural Probabilistic Framework for Satisfiability Problems

- Computer Science
- 2022

A general neural framework for solving satisﬁability problems as probabilistic inference that outperforms BP and other neural baselines and achieves competitive results compared with the state-of-the-art solvers.

### Graph Neural Networks for Propositional Model Counting

- Computer ScienceESANN 2022 proceedings
- 2022

This work presents an architecture based on the GNN framework for belief propagation of [15], extended with self-attentive GNN and trained to approximately solve the #SAT problem, showing that this model is able to scale effectively to much larger problem sizes, with comparable or better performances of state of the art approximate solvers.

### A visual introduction to Gaussian Belief Propagation

- Computer ScienceArXiv
- 2021

This article presents a visual introduction to Gaussian Belief Propagation, an approximate probabilistic inference algorithm that operates by passing messages between the nodes of arbitrarily structured factor graphs that has the right computational properties to act as a scalable distributed probabilism inference framework for future machine learning systems.

### Robust Deep Learning from Crowds with Belief Propagation

- Computer ScienceAISTATS
- 2022

A neural-powered Bayesian framework is established, from which deepMF and deepBP are devise with diﬀerent choice of variational approximation methods, mean ﬁeld (MF) and belief propagation (BP), respectively, which provides a uniﬁed view of existing methods, which are special cases of deepMF with di-erent priors.

### Learning Feasibility of Factored Nonlinear Programs in Robotic Manipulation Planning

- Computer ScienceArXiv
- 2022

The model is trained with a dataset of labeled subgraphs of Factored- NLPs, and importantly, can make useful predictions on larger factored nonlinear programs than the ones seen during training, which is important for robotic manipulation planning.

### Neural Belief Propagation for Scene Graph Generation

- Computer ScienceArXiv
- 2021

A novel neural belief propagation method that employs a structural Bethe approximation rather than the mean field approximation to infer the associated marginals and achieves the state-of-the-art performance on various popular scene graph generation benchmarks.

### Equivariant Neural Network for Factor Graphs

- Computer ScienceArXiv
- 2021

This paper precisely characterize these isomorphic properties of factor graphs and proposes two inference models: FactorEquivariant Neural Belief Propagation (FE-NBP and FE-GNN), a neural network that generalizes BP and respects each of the above properties.

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