This paper develops a novel methodology for using symbolic knowledge in deep learning. We define a semantic loss function that bridges between neural output vectors and logical constraints. This loss function captures how close the neural network is to satisfying the constraints on its output. An experimental evaluation shows that our semantic loss function effectively guides the learner to achieve (near-)state-of-the-art results on semi-supervised multi-class classification. Moreover, it significantly increases the ability of the neural network to predict structured objects under weak supervision, such as rankings and shortest paths.

@inproceedings{XuLLD17,
  author    = {Xu, Jingyi and Zhang, Zilu and Friedman, Tal and Liang, Yitao and Van den Broeck, Guy},
  title     = {A Semantic Loss Function for Deep Learning Under Weak Supervision},
  booktitle = {NIPS 2017 Workshop on Learning with Limited Labeled Data: Weak Supervision and Beyond},
  month     = Dec,
  year      = {2017},
  url       = "https://starai.cs.ucla.edu/papers/XuLLD17.pdf",
  code = "https://github.com/UCLA-StarAI/Semantic-Loss",
  annotation = "(LLD best paper award runner up)",
  keywords  = {workshop}
}