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1. Neural-Symbolic Inference for Robust Autoregressive Graph Parsing via Compositional Uncertainty Quantification

   Lin, Zi; Liu, Jeremiah; Shang, Jingbo (January 2022, Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing)

   Pre-trained seq2seq models excel at graph semantic parsing with rich annotated data, but generalize worse to out-of-distribution (OOD) and long-tail examples. In comparison, symbolic parsers under-perform on population-level metrics, but exhibit unique strength in OOD and tail generalization. In this work, we study compositionality-aware approach to neural-symbolic inference informed by model confidence, performing fine-grained neural-symbolic reasoning at subgraph level (i.e., nodes and edges) and precisely targeting subgraph components with high uncertainty in the neural parser. As a result, the method combines the distinct strength of the neural and symbolic approaches in capturing different aspects of the graph prediction, leading to well-rounded generalization performance both across domains and in the tail. We empirically investigate the approach in the English Resource Grammar (ERG) parsing problem on a diverse suite of standard in-domain and seven OOD corpora. Our approach leads to 35.26% and 35.60% error reduction in aggregated SMATCH score over neural and symbolic approaches respectively, and 14% absolute accuracy gain in key tail linguistic categories over the neural model, outperforming prior state-of-art methods that do not account for compositionality or uncertainty. 

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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. LLM+AL: Bridging Large Language Models and Action Languages for Complex Reasoning about Actions

   Isay, Adam; Lee, Joohyung (February 2025, AAAI Press)

   Large Language Models (LLMs) have made significant strides in various intelligent tasks but still struggle with complex action reasoning tasks that require systematic search. To address this limitation, we introduce a method that bridges the natural language understanding capability of LLMs with the symbolic reasoning capability of action languages---formal languages for reasoning about actions. Our approach, termed {\sf LLM+AL}, leverages the LLM's strengths in semantic parsing and commonsense knowledge generation alongside the action language's expertise in automated reasoning based on encoded knowledge. We compare {\sf LLM+AL} against state-of-the-art LLMs, including {\sc ChatGPT-4}, {\sc Claude 3 Opus}, {\sc Gemini Ultra 1.0}, and {\sc o1-preview}, using benchmarks for complex reasoning about actions. Our findings indicate that while all methods exhibit various errors, {\sf LLM+AL}, with relatively simple human corrections, consistently leads to correct answers, whereas using LLMs alone does not yield improvements even after human intervention. {\sf LLM+AL} also contributes to automated generation of action languages. 

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4. 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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5. 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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