Kinjal Basu, Ibrahim Abdelaziz, Kiran Kate, Mayank Agarwal, Maxwell Crouse, Yara Rizk, Kelsey Bradford, Asim Munawar, Sadhana Kumaravel, Saurabh Goyal, Xin Wang, Luis A. Lastras, Pavan Kapanipathi. Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing. 2025.

Kinjal Basu, Ibrahim Abdelaziz, Subhajit Chaudhury, Soham Dan, Maxwell Crouse, Asim Munawar, Vernon Austel, Sadhana Kumaravel, Vinod Muthusamy, Pavan Kapanipathi, Luis Lastras. Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2024.

Maxwell Crouse, Pavan Kapanipathi, Subhajit Chaudhury, Tahira Naseem, Ramon Fernandez Astudillo, Achille Fokoue, Tim Klinger. Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2023.

Using reinforcement learning for automated theorem proving has recently received much attention. Current approaches use representations of logical statements that often rely on the names used in these statements and, as a result, the models are generally not transferable from one domain to another. The size of these representations and whether to include the whole theory or part of it are other important decisions that affect the performance of these approaches as well as their runtime efficiency. In this paper, we present NIAGRA; an ensemble Name InvAriant Graph RepresentAtion. NIAGRA addresses this problem by using 1) improved Graph Neural Networks for learning name-invariant formula representations that is tailored for their unique characteristics and 2) an efficient ensemble approach for automated theorem proving. Our experimental evaluation shows state-of-the-art performance on multiple datasets from different domains with improvements up to 10% compared to the best learning-based approaches. Furthermore, transfer learning experiments show that our approach significantly outperforms other learning-based approaches by up to 28%.

Traditional automated theorem provers have relied on manually tuned heuristics to guide how they perform proof search. Recently, however, there has been a surge of interest in the design of learning mechanisms that can be integrated into theorem provers to improve their performance automatically. In this work, we describe TRAIL (Trial Reasoner for AI that Learns), a deep learning-based approach to theorem proving that characterizes core elements of saturation-based theorem proving within a neural framework. TRAIL leverages (a) an effective graph neural network for representing logical formulas, (b) a novel neural representation of the state of a saturation-based theorem prover in terms of processed clauses and available actions, and (c) a novel representation of the inference selection process as an attention-based action policy. We show through a systematic analysis that these components allow TRAIL to significantly outperform previous reinforcement learning-based theorem provers on two standard benchmark datasets (up to 36% more theorems proved). In addition, to the best of our knowledge, TRAIL is the first reinforcement learning-based approach to exceed the performance of a state-of-the-art traditional theorem prover on a standard theorem proving benchmark (solving up to 17% more theorems).

Subhajit Chaudhury, Sarathkrishna Swaminathan, Chulaka Gunasekara, Maxwell Crouse, Srinivas Ravishankar, Daiki Kimura, Keerthiram Murugesan, Ramón Fernandez Astudillo, Tahira Naseem, Pavan Kapanipathi, Alexander Gray. Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing. 2022.

Automated theorem provers have traditionally relied on manually tuned heuristics to guide how they perform proof search. Deep reinforcement learning has been proposed as a way to obviate the need for such heuristics, however, its deployment in automated theorem proving remains a challenge. In this paper we introduce TRAIL, a system that applies deep reinforcement learning to saturation-based theorem proving. TRAIL leverages (a) a novel neural representation of the state of a theorem prover and (b) a novel characterization of the inference selection process in terms of an attention-based action policy. We show through systematic analysis that these mechanisms allow TRAIL to significantly outperform previous reinforcement-learning-based theorem provers on two benchmark datasets for first-order logic automated theorem proving (proving around 15% more theorems).

Analogy is core to human cognition. It allows us to solve problems based on prior experience, it governs the way we conceptualize new information, and it even influences our visual perception. The importance of analogy to humans has made it an active area of research in the broader field of artificial intelligence, resulting in data-efficient models that learn and reason in human-like ways. While cognitive perspectives of analogy and deep learning have generally been studied independently of one another, the integration of the two lines of research is a promising step towards more robust and efficient learning techniques. As part of a growing body of research on such an integration, we introduce the Analogical Matching Network: a neural architecture that learns to produce analogies between structured, symbolic representations that are largely consistent with the principles of Structure-Mapping Theory.

Creating systems that can learn to answer natural language questions has been a longstanding challenge for artificial intelligence. Most prior approaches focused on producing a specialized language system for a particular domain and dataset, and they required training on a large corpus manually annotated with logical forms. This paper introduces an analogy-based approach that instead adapts an existing general purpose semantic parser to answer questions in a novel domain by jointly learning disambiguation heuristics and query construction templates from purely textual question-answer pairs. Our technique uses possible semantic interpretations of the natural language questions and answers to constrain a query-generation procedure, producing cases during training that are subsequently reused via analogical retrieval and composed to answer test questions. Bootstrapping an existing semantic parser in this way significantly reduces the number of training examples needed to accurately answer questions. We demonstrate the efficacy of our technique using the Geoquery corpus, on which it approaches state of the art performance using 10-fold cross validation, shows little decrease in performance with 2-folds, and achieves above 50% accuracy with as few as 10 examples.