# DeepFlow: Two Convergent Differentiable Approaches for Pairwise Conditional Random Fields

arXiv: https://arxiv.org/abs/2610.16546 · HTML: https://mlsanity.com/paper/2610.16546/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 19 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Builds on (most cited first, 8 of 8)

- [Generalised Dice overlap as a deep learning loss function for highly unbalanced segmentations](https://mlsanity.com/paper/1707.03237/) (2017)
- [A survey of loss functions for semantic segmentation](https://mlsanity.com/paper/2006.14822/) (2020)
- [Conditional Random Fields as Recurrent Neural Networks](https://mlsanity.com/paper/1502.03240/) (2015)
- [Neural Enhanced Belief Propagation on Factor Graphs](https://mlsanity.com/paper/2003.01998/) (2020)
- [Neural Markov Random Field for Stereo Matching](https://mlsanity.com/paper/2403.11193/) (2024)
- [Belief Propagation Neural Networks](https://mlsanity.com/paper/2007.00295/) (2020)
- [Higher Order Conditional Random Fields in Deep Neural Networks](https://mlsanity.com/paper/1511.08119/) (2015)
- [gcDLSeg: Integrating Graph-cut into Deep Learning for Binary Semantic Segmentation](https://mlsanity.com/paper/2312.04713/) (2023)

## Abstract (arXiv)

Basic probabilistic models form the basis of modern deep learning largely by defining the final activation layer of a network and allowing the networks outputs to be interpreted through a probabilistic lens. By increasing the complexity of these final activation layers to include features such as spatial regularisation, allow for these models to improve in performance without requiring significantly more data. The challenge however is to ensure that these more complex probabilistic graphical models adapt well to being used in tandem with deep learning, that is, ensuring they converge and have meaningful derivatives. The goal of this paper is to show two algorithms with provable convergence properties to allow this type of regularisation for image and signal classification models. Through both rigorous mathematical analysis and in silico experiments, we can show the differing performance between these solution types.