Ankit Satpute

Moritz Schubotz, Ankit Satpute, Andre Greiner-Petter et al.

Small to medium-scale data science experiments often rely on research software developed ad-hoc by individual scientists or small teams. Often there is no time to make the research software fast, reusable, and open access. The consequence is twofold. First, subsequent researchers must spend significant work hours building upon the proposed hypotheses or experimental framework. In the worst case, others cannot reproduce the experiment and reuse the findings for subsequent research. Second, suppose the ad-hoc research software fails during often long-running computationally expensive experiments. In that case, the overall effort to iteratively improve the software and rerun the experiments creates significant time pressure on the researchers. We suggest making caching an integral part of the research software development process, even before the first line of code is written. This article outlines caching recommendations for developing research software in data science projects. Our recommendations provide a perspective to circumvent common problems such as propriety dependence, speed, etc. At the same time, caching contributes to the reproducibility of experiments in the open science workflow. Concerning the four guiding principles, i.e., Findability, Accessibility, Interoperability, and Reusability (FAIR), we foresee that including the proposed recommendation in a research software development will make the data related to that software FAIRer for both machines and humans. We exhibit the usefulness of some of the proposed recommendations on our recently completed research software project in mathematical information retrieval.

Ivan Pluzhnikov, Ankit Satpute, Moritz Schubotz et al.

This paper presents a specialized methodology for digitizing and segmenting mathematical documents from zbMATH Open, a comprehensive database of mathematical literature, to enhance machine processing capabilities. Currently, approximately 831,000 documents exist only in scanned volumes, which makes them not machine-processable. Furthermore, these scans often span multiple pages or share pages with other documents and incorporate diverse typesetting techniques, posing challenges for automated processing. To address these issues, we evaluate various Optical Character Recognition (OCR) tools and document separation techniques, proposing an optimized pipeline that outperforms existing approaches. Our study identifies Mathpix as the most effective OCR tool for LaTeX conversion, demonstrating superior performance based on BLEU and Edit Distance metrics. For document separation, we fine-tune generative Large Language Models (LLMs) and integrate them into a Majority Voting framework, achieving 97.5% accuracy when providing the text of the document. Additionally, our method identifies the start and end indexes for 90.6% of the test dataset, with an accuracy of 98.4% on applicable cases, resulting in an overall accuracy of 89.1% on the entire dataset. This approach surpasses traditional baselines, including regular expressions, ChatGPT-4o, and computer vision-based techniques. As a practical outcome, we process 810,977 mathematical documents into machine-readable text and extract precise document boundaries for 721,288 documents in LaTeX format. These contributions significantly improve accessibility for mathematical information retrieval systems, machine learning models, and related applications.

Ankit Satpute, Noah Giessing, Andre Greiner-Petter et al.

Large Language Models (LLMs) have demonstrated exceptional capabilities in various natural language tasks, often achieving performances that surpass those of humans. Despite these advancements, the domain of mathematics presents a distinctive challenge, primarily due to its specialized structure and the precision it demands. In this study, we adopted a two-step approach for investigating the proficiency of LLMs in answering mathematical questions. First, we employ the most effective LLMs, as identified by their performance on math question-answer benchmarks, to generate answers to 78 questions from the Math Stack Exchange (MSE). Second, a case analysis is conducted on the LLM that showed the highest performance, focusing on the quality and accuracy of its answers through manual evaluation. We found that GPT-4 performs best (nDCG of 0.48 and P@10 of 0.37) amongst existing LLMs fine-tuned for answering mathematics questions and outperforms the current best approach on ArqMATH3 Task1, considering P@10. Our Case analysis indicates that while the GPT-4 can generate relevant responses in certain instances, it does not consistently answer all questions accurately. This paper explores the current limitations of LLMs in navigating complex mathematical problem-solving. Through case analysis, we shed light on the gaps in LLM capabilities within mathematics, thereby setting the stage for future research and advancements in AI-driven mathematical reasoning. We make our code and findings publicly available for research: \url{https://github.com/gipplab/LLM-Investig-MathStackExchange}

Ankit Satpute, André Greiner-Petter, Noah Gießing et al.

Content-based research paper recommendation (CbRPR) has seen advances in computer science and biomedicine, but remains unexplored for mathematics, where paper relatedness is more conceptual than explicit textual or citation-based similarity. Mathematics papers may be connected through shared proof techniques, logical implications, or natural generalizations, yet exhibit minimal textual or citation overlap, rendering existing CbRPR ineffective. To address this gap, we first conduct an expert-driven study characterizing mathematical recommendations, revealing that relevance is inherently \textit{aspect}-driven. Grounded in this insight, we introduce GoldRiM (small, expert-annotated) and SilverRiM (large, automatically derived), the first datasets for \textit{aspect}-aware CbRPR in mathematics. Recognizing that LLM embeddings of mathematical content alone yield suboptimal representation, we propose AchGNN, an \textit{aspect}-conditioned heterogeneous GNN that jointly models textual semantics, citation structure, and author lineage. Across GoldRiM and SilverRiM, AchGNN consistently outperforms prior \textit{aspect}-based CbRPR methods, achieving substantial gains across all evaluated \textit{aspects}. We conduct ablation studies to analyze the contributions of individual \textit{aspect} supervision, authorship lineage, and graph-structural signals to AchGNN's performance. To assess domain generality, we further evaluate AchGNN on the \textit{Papers with Code} dataset of machine learning publications, demonstrating that our \textit{aspect}-aware approach effectively transfers beyond mathematics. We deploy our system on the MaRDI platform to help mathematicians with recommendations and release datasets and code publicly for reproducibility.