# Belief Propagation Reloaded: Learning BP-Layers for Labeling Problems

arXiv: https://arxiv.org/abs/2003.06258 · HTML: https://mlsanity.com/paper/2003.06258/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2020.

## Built on by (most cited first, 9 of 9)

- [IterMVS: Iterative Probability Estimation for Efficient Multi-View Stereo](https://mlsanity.com/paper/2112.05126/) (2021)
- [Neural Markov Random Field for Stereo Matching](https://mlsanity.com/paper/2403.11193/) (2024)
- [Learning-based Multi-View Stereo: A Survey](https://mlsanity.com/paper/2408.15235/) (2024)
- [Deep learning via message passing algorithms based on belief propagation](https://mlsanity.com/paper/2110.14583/) (2021)
- [Combinatorial Optimization for Panoptic Segmentation: A Fully Differentiable Approach](https://mlsanity.com/paper/2106.03188/) (2021)
- [Diffusion at Absolute Zero: Langevin Sampling Using Successive Moreau Envelopes [conference paper]](https://mlsanity.com/paper/2502.01358/) (2025)
- [A Positive/Unlabeled Approach for the Segmentation of Medical Sequences using Point-Wise Supervision](https://mlsanity.com/paper/2107.08394/) (2021)
- [A Novel Factor Graph-Based Optimization Technique for Stereo Correspondence Estimation](https://mlsanity.com/paper/2109.11077/) (2021)
- [FCDSN-DC: An Accurate and Lightweight Convolutional Neural Network for Stereo Estimation with Depth Completion](https://mlsanity.com/paper/2209.06525/) (2022)

## Abstract (arXiv)

It has been proposed by many researchers that combining deep neural networks with graphical models can create more efficient and better regularized composite models. The main difficulties in implementing this in practice are associated with a discrepancy in suitable learning objectives as well as with the necessity of approximations for the inference. In this work we take one of the simplest inference methods, a truncated max-product Belief Propagation, and add what is necessary to make it a proper component of a deep learning model: We connect it to learning formulations with losses on marginals and compute the backprop operation. This BP-Layer can be used as the final or an intermediate block in convolutional neural networks (CNNs), allowing us to design a hierarchical model composing BP inference and CNNs at different scale levels. The model is applicable to a range of dense prediction problems, is well-trainable and provides parameter-efficient and robust solutions in stereo, optical flow and semantic segmentation.