# Deeply Learning the Messages in Message Passing Inference

arXiv: https://arxiv.org/abs/1506.02108 · HTML: https://mlsanity.com/paper/1506.02108/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2015.

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- [Dynamic Graph Message Passing Networks for Visual Recognition](https://mlsanity.com/paper/2209.09760/) (2022)
- [CRF Loss is How Networks Should Learn Boundaries in Weakly Supervised Segmentation](https://mlsanity.com/paper/2609.34183/) (2026)

## Abstract (arXiv)

Deep structured output learning shows great promise in tasks like semantic image segmentation. We proffer a new, efficient deep structured model learning scheme, in which we show how deep Convolutional Neural Networks (CNNs) can be used to estimate the messages in message passing inference for structured prediction with Conditional Random Fields (CRFs). With such CNN message estimators, we obviate the need to learn or evaluate potential functions for message calculation. This confers significant efficiency for learning, since otherwise when performing structured learning for a CRF with CNN potentials it is necessary to undertake expensive inference for every stochastic gradient iteration. The network output dimension for message estimation is the same as the number of classes, in contrast to the network output for general CNN potential functions in CRFs, which is exponential in the order of the potentials. Hence CNN message learning has fewer network parameters and is more scalable for cases that a large number of classes are involved. We apply our method to semantic image segmentation on the PASCAL VOC 2012 dataset. We achieve an intersection-over-union score of 73.4 on its test set, which is the best reported result for methods using the VOC training images alone. This impressive performance demonstrates the effectiveness and usefulness of our CNN message learning method.