Qiyue Gao

Valeria de Paiva, Qiyue Gao, Pavel Kovalev et al.

We extract mathematical concepts from mathematical text using generative large language models (LLMs) like ChatGPT, contributing to the field of automatic term extraction (ATE) and mathematical text processing, and also to the study of LLMs themselves. Our work builds on that of others in that we aim for automatic extraction of terms (keywords) in one mathematical field, category theory, using as a corpus the 755 abstracts from a snapshot of the online journal "Theory and Applications of Categories", circa 2020. Where our study diverges from previous work is in (1) providing a more thorough analysis of what makes mathematical term extraction a difficult problem to begin with; (2) paying close attention to inter-annotator disagreements; (3) providing a set of guidelines which both human and machine annotators could use to standardize the extraction process; (4) introducing a new annotation tool to help humans with ATE, applicable to any mathematical field and even beyond mathematics; (5) using prompts to ChatGPT as part of the extraction process, and proposing best practices for such prompts; and (6) raising the question of whether ChatGPT could be used as an annotator on the same level as human experts. Our overall findings are that the matter of mathematical ATE is an interesting field which can benefit from participation by LLMs, but LLMs themselves cannot at this time surpass human performance on it.

Shibo Hao, Yi Gu, Haotian Luo et al.

Generating accurate step-by-step reasoning is essential for Large Language Models (LLMs) to address complex problems and enhance robustness and interpretability. Despite the flux of research on developing advanced reasoning approaches, systematically analyzing the diverse LLMs and reasoning strategies in generating reasoning chains remains a significant challenge. The difficulties stem from the lack of two key elements: (1) an automatic method for evaluating the generated reasoning chains on different tasks, and (2) a unified formalism and implementation of the diverse reasoning approaches for systematic comparison. This paper aims to close the gap: (1) We introduce AutoRace for fully automated reasoning chain evaluation. Existing metrics rely on expensive human annotations or pre-defined LLM prompts not adaptable to different tasks. In contrast, AutoRace automatically creates detailed evaluation criteria tailored for each task, and uses GPT-4 for accurate evaluation following the criteria. (2) We develop LLM Reasoners, a library for standardized modular implementation of existing and new reasoning algorithms, under a unified formulation of the search, reward, and world model components. With the new evaluation and library, (3) we conduct extensive study of different reasoning approaches (e.g., CoT, ToT, RAP). The analysis reveals interesting findings about different factors contributing to reasoning, including the reward-guidance, breadth-vs-depth in search, world model, and prompt formats, etc.

Valeria de Paiva, Qiyue Gao, Hai Hu et al.

We ask whether contemporary LLMs are able to perform natural language inference (NLI) tasks on mathematical texts. We call this the Math NLI problem. We construct a corpus of Math NLI pairs whose premises are from extant mathematical text and whose hypotheses and gold labels were provided by people with experience in both research-level mathematics and also in the NLI field. We also investigate the quality of corpora using the same premises but whose hypotheses are provided by LLMs themselves. We not only investigate the performance but also the inter-group consistency of the diverse group of LLMs. We have both positive and negative findings. Among our positive findings: in some settings, using a majority vote of LLMs is approximately equivalent to using human-labeled data in the Math NLI area. On the negative side: LLMs still struggle with mathematical language. They occasionally fail at even basic inferences. Current models are not as prone to hypothesis-only "inference" in our data the way the previous generation had been. In addition to our findings, we also provide our corpora as data to support future work on Math NLI.

Zeming Chen, Qiyue Gao, Lawrence S. Moss

Deep learning (DL) based language models achieve high performance on various benchmarks for Natural Language Inference (NLI). And at this time, symbolic approaches to NLI are receiving less attention. Both approaches (symbolic and DL) have their advantages and weaknesses. However, currently, no method combines them in a system to solve the task of NLI. To merge symbolic and deep learning methods, we propose an inference framework called NeuralLog, which utilizes both a monotonicity-based logical inference engine and a neural network language model for phrase alignment. Our framework models the NLI task as a classic search problem and uses the beam search algorithm to search for optimal inference paths. Experiments show that our joint logic and neural inference system improves accuracy on the NLI task and can achieve state-of-art accuracy on the SICK and MED datasets.

Zeming Chen, Qiyue Gao

Dependency parsing is a tool widely used in the field of Natural language processing and computational linguistics. However, there is hardly any work that connects dependency parsing to monotonicity, which is an essential part of logic and linguistic semantics. In this paper, we present a system that automatically annotates monotonicity information based on Universal Dependency parse trees. Our system utilizes surface-level monotonicity facts about quantifiers, lexical items, and token-level polarity information. We compared our system's performance with existing systems in the literature, including NatLog and ccg2mono, on a small evaluation dataset. Results show that our system outperforms NatLog and ccg2mono.