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1. Injecting Logical Constraints into Neural Networks via Straight-Through Estimators

   Yang, Zhun ; Lee, Joohyung ; Park, Chiyoun. ( July 2022 , International Conference on Machine Learning)

   Injecting discrete logical constraints into neural network learning is one of the main challenges in neuro-symbolic AI. We find that a straight-through-estimator, a method introduced to train binary neural networks, could effectively be applied to incorporate logical constraints into neural network learning. More specifically, we design a systematic way to represent discrete logical constraints as a loss function; minimizing this loss using gradient descent via a straight-through-estimator updates the neural network's weights in the direction that the binarized outputs satisfy the logical constraints. The experimental results show that by leveraging GPUs and batch training, this method scales significantly better than existing neuro-symbolic methods that require heavy symbolic computation for computing gradients. Also, we demonstrate that our method applies to different types of neural networks, such as MLP, CNN, and GNN, making them learn with no or fewer labeled data by learning directly from known constraints. 

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2. A Semantic Loss Function for Deep Learning with Symbolic Knowledge

   Xu, Jingyi ; Zhang, Zilu ; Friedman, Tal ; Liang, Yitao ; Van den Broeck, Guy ( July 2018 , Proceedings of the 35th International Conference on Machine Learning (ICML))

   This paper develops a novel methodology for using symbolic knowledge in deep learning. From first principles, we derive 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 it 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, such as rankings and paths. These discrete concepts are tremendously difficult to learn, and benefit from a tight integration of deep learning and symbolic reasoning methods. 

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3. Pylon: A PyTorch Framework for Learning with Constraints

   https://doi.org/10.1609/aaai.v36i11.21711  

   Ahmed, Kareem ; Li, Tao ; Ton, Thy ; Guo, Quan ; Chang, Kai-Wei ; Kordjamshidi, Parisa ; Srikumar, Vivek ; Van den Broeck, Guy ; Singh, Sameer ( January 2022 , Proceedings of the NeurIPS 2021 Competitions and Demonstrations Track)

   Kiela, Douwe ; Ciccone, Marco ; Caputo, Barbara (Ed.)

   Deep learning excels at learning low-level task information from large amounts of data, but struggles with learning high-level domain knowledge, which can often be directly and succinctly expressed. In this work, we introduce Pylon, a neuro-symbolic training framework that builds on PyTorch to augment procedurally trained neural networks with declaratively specified knowledge. Pylon allows users to programmatically specify constraints as PyTorch functions, and compiles them into a differentiable loss, thus training predictive models that fit the data whilst satisfying the specified constraints. Pylon includes both exact as well as approximate compilers to efficiently compute the loss, employing fuzzy logic, sampling methods, and circuits, ensuring scalability even to complex models and constraints. A guiding principle in designing Pylon has been the ease with which any existing deep learning codebase can be extended to learn from constraints using only a few lines: a function expressing the constraint and a single line of code to compile it into a loss. We include case studies from natural language processing, computer vision, logical games, and knowledge graphs, that can be interactively trained, and highlights Pylon’s usage. 

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4. NeuPSL: Neural Probabilistic Soft Logic

   Pryor, Connor ; Dickens, Charles Andrew ; Augustine, Eriq ; Albalak ; Alon ; Wang ; William Yang ; Getoor, Lise ( June 2022 , ArXivorg)

   We present Neural Probabilistic Soft Logic (NeuPSL), a novel neuro-symbolic (NeSy) framework that unites state-of-the-art symbolic reasoning with the low-level perception of deep neural networks. To explicitly model the boundary between neural and symbolic representations, we introduce NeSy Energy-Based Models, a general family of energy-based models that combine neural and symbolic reasoning. Using this framework, we show how to seamlessly integrate neural and symbolic parameter learning and inference. We perform an extensive empirical evaluation and show that NeuPSL outperforms existing methods on joint inference and has significantly lower variance in almost all settings. 

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5. ECIR 23 Tutorial: Neuro-Symbolic Approaches for Information Retrieval

   https://doi.org/10.1007/978-3-031-28241-6_33  

   Dietz, Laura ; Bast, Hannah ; Chatterjee, Shubham ; Dalton, Jeff ; Meij, Edgar Meij ; de Vries, Arjen ( April 2023 , Springer)

   This tutorial will provide an overview of recent advances on neuro-symbolic approaches for information retrieval. A decade ago, knowledge graphs and semantic annotations technology led to active re- search on how to best leverage symbolic knowledge. At the same time, neural methods have demonstrated to be versatile and highly effective. From a neural network perspective, the same representation approach can service document ranking or knowledge graph reasoning. End-to-end training allows to optimize complex methods for downstream tasks. We are at the point where both the symbolic and the neural research advances are coalescing into neuro-symbolic approaches. The underlying research questions are how to best combine symbolic and neural ap- proaches, what kind of symbolic/neural approaches are most suitable for which use case, and how to best integrate both ideas to advance the state of the art in information retrieval. 

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