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Olaf Teschke

Publications and source records attributed to Olaf Teschke.

15 recordsLinked to original sources

Aspect-Aware Content-Based Recommendations for Mathematical Research Papers

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.

cs.IR

LLM-supported document separation for printed reviews from zbMATH Open

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.

cs.DL

An Overview of zbMATH Open Digital Library

Mathematical research thrives on the effective dissemination and discovery of knowledge. zbMATH Open has emerged as a pivotal platform in this landscape, offering a comprehensive repository of mathematical literature. Beyond indexing and abstracting, it serves as a unified quality-assured infrastructure for finding, evaluating, and connecting mathematical information that advances mathematical research as well as interdisciplinary exploration. zbMATH Open enables scientific quality control by post-publication reviews and promotes connections between researchers, institutions, and research outputs. This paper represents the functionalities of the most significant features of this open-access service, highlighting its role in shaping the future of mathematical information retrieval.

cs.DL

Reducing the climate impact of data portals: a case study

The carbon footprint share of the information and communication technology (ICT) sector has steadily increased in the past decade and is predicted to make up as much as 23 \% of global emissions in 2030. This shows a pressing need for developers, including the information retrieval community, to make their code more energy-efficient. In this project proposal, we discuss techniques to reduce the energy footprint of the MaRDI (Mathematical Research Data Initiative) Portal, a MediaWiki-based knowledge base. In future work, we plan to implement these changes and provide concrete measurements on the gain in energy efficiency. Researchers developing similar knowledge bases can adapt our measures to reduce their environmental footprint. In this way, we are working on mitigating the climate impact of Information Retrieval research.

cs.IR

Taxonomy of Mathematical Plagiarism

Plagiarism is a pressing concern, even more so with the availability of large language models. Existing plagiarism detection systems reliably find copied and moderately reworded text but fail for idea plagiarism, especially in mathematical science, which heavily uses formal mathematical notation. We make two contributions. First, we establish a taxonomy of mathematical content reuse by annotating potentially plagiarised 122 scientific document pairs. Second, we analyze the best-performing approaches to detect plagiarism and mathematical content similarity on the newly established taxonomy. We found that the best-performing methods for plagiarism and math content similarity achieve an overall detection score (PlagDet) of 0.06 and 0.16, respectively. The best-performing methods failed to detect most cases from all seven newly established math similarity types. Outlined contributions will benefit research in plagiarism detection systems, recommender systems, question-answering systems, and search engines. We make our experiment's code and annotated dataset available to the community: https://github.com/gipplab/Taxonomy-of-Mathematical-Plagiarism

cs.IR

Can LLMs Master Math? Investigating Large Language Models on Math Stack Exchange

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}

cs.CL

The extension of zbMATH Open by arXiv preprints

zbMATH Open has started a new feature -- relevant preprints posted at arXiv will also be displayed in the database. In this article we introduce this new feature and the underlying editorial policy. We also describe some of the technical issues involved and discuss the challenges this presents for future developments.

cs.DL

Bravo MaRDI: A Wikibase Powered Knowledge Graph on Mathematics

Mathematical world knowledge is a fundamental component of Wikidata. However, to date, no expertly curated knowledge graph has focused specifically on contemporary mathematics. Addressing this gap, the Mathematical Research Data Initiative (MaRDI) has developed a comprehensive knowledge graph that links multimodal research data in mathematics. This encompasses traditional research data items like datasets, software, and publications and includes semantically advanced objects such as mathematical formulas and hypotheses. This paper details the abilities of the MaRDI knowledge graph, which is based on Wikibase, leading up to its inaugural public release, codenamed Bravo, available on https://portal.mardi4nfdi.de.

cs.DL

TEIMMA: The First Content Reuse Annotator for Text, Images, and Math

This demo paper presents the first tool to annotate the reuse of text, images, and mathematical formulae in a document pair -- TEIMMA. Annotating content reuse is particularly useful to develop plagiarism detection algorithms. Real-world content reuse is often obfuscated, which makes it challenging to identify such cases. TEIMMA allows entering the obfuscation type to enable novel classifications for confirmed cases of plagiarism. It enables recording different reuse types for text, images, and mathematical formulae in HTML and supports users by visualizing the content reuse in a document pair using similarity detection methods for text and math.

cs.IR

10 Years Later: The Mathematics Subject Classification and Linked Open Data

Ten years ago, the Mathematics Subject Classification MSC 2010 was released, and a corresponding machine-readable Linked Open Data collection was published using the Simple Knowledge Organization System (SKOS). Now, the new MSC 2020 is out. This paper recaps the last ten years of working on machine-readable MSC data and presents the new machine-readable MSC 2020. We describe the processing required to convert the version of record, as agreed by the editors of zbMATH and Mathematical Reviews, into the Linked Open Data form we call MSC2020-SKOS. The new form includes explicit marking of the changes from 2010 to 2020, some translations of English code descriptions into Chinese, Italian, and Russian, and extra material relating MSC to other mathematics classification efforts. We also outline future potential uses for MSC2020-SKOS in semantic indexing and sketch its embedding in a larger vision of scientific research data.

cs.DL

zbMATH Open: API Solutions and Research Challenges

We present zbMATH Open, the most comprehensive collection of reviews and bibliographic metadata of scholarly literature in mathematics. Besides our website https://zbMATH.org which is openly accessible since the beginning of this year, we provide API endpoints to offer our data. The API improves interoperability with others, i.e., digital libraries, and allows using our data for research purposes. In this article, we (1) illustrate the current and future overview of the services offered by zbMATH; (2) present the initial version of the zbMATH links API; (3) analyze potentials and limitations of the links API based on the example of the NIST Digital Library of Mathematical Functions; (4) and finally, present the zbMATH Open dataset as a research resource and discuss connected open research problems.

cs.DL

ARQMath Lab: An Incubator for Semantic Formula Search in zbMATH Open?

The zbMATH database contains more than 4 million bibliographic entries. We aim to provide easy access to these entries. Therefore, we maintain different index structures, including a formula index. To optimize the findability of the entries in our database, we continuously investigate new approaches to satisfy the information needs of our users. We believe that the findings from the ARQMath evaluation will generate new insights into which index structures are most suitable to satisfy mathematical information needs. Search engines, recommender systems, plagiarism checking software, and many other added-value services acting on databases such as the arXiv and zbMATH need to combine natural and formula language. One initial approach to address this challenge is to enrich the mostly unstructured document data via Entity Linking. The ARQMath Task at CLEF 2020 aims to tackle the problem of linking newly posted questions from Math Stack Exchange (MSE) to existing ones that were already answered by the community. To deeply understand MSE information needs, answer-, and formula types, we performed manual runs for tasks 1 and 2. Furthermore, we explored several formula retrieval methods: For task 2, such as fuzzy string search, k-nearest neighbors, and our recently introduced approach to retrieve Mathematical Objects of Interest (MOI) with textual search queries. The task results show that neither our automated methods nor our manual runs archived good scores in the competition. However, the perceived quality of the hits returned by the MOI search particularly motivates us to conduct further research about MOI.

cs.DL

AutoMSC: Automatic Assignment of Mathematics Subject Classification Labels

Authors of research papers in the fields of mathematics, and other math-heavy disciplines commonly employ the Mathematics Subject Classification (MSC) scheme to search for relevant literature. The MSC is a hierarchical alphanumerical classification scheme that allows librarians to specify one or multiple codes for publications. Digital Libraries in Mathematics, as well as reviewing services, such as zbMATH and Mathematical Reviews (MR) rely on these MSC labels in their workflows to organize the abstracting and reviewing process. Especially, the coarse-grained classification determines the subject editor who is responsible for the actual reviewing process. In this paper, we investigate the feasibility of automatically assigning a coarse-grained primary classification using the MSC scheme, by regarding the problem as a multi-class classification machine learning task. We find that our method achieves an (F_1)-score of over 77%, which is remarkably close to the agreement of zbMATH and MR ((F_1)-score of 81%). Moreover, we find that the method's confidence score allows for reducing the effort by 86% compared to the manual coarse-grained classification effort while maintaining a precision of 81% for automatically classified articles.

cs.DL

Mathematical Formulae in Wikimedia Projects 2020

This poster summarizes our contributions to Wikimedia's processing pipeline for mathematical formulae. We describe how we have supported the transition from rendering formulae as course-grained PNG images in 2001 to providing modern semantically enriched language-independent MathML formulae in 2020. Additionally, we describe our plans to improve the accessibility and discoverability of mathematical knowledge in Wikimedia projects further.

cs.DL

Forms of Plagiarism in Digital Mathematical Libraries

We report on an exploratory analysis of the forms of plagiarism observable in mathematical publications, which we identified by investigating editorial notes from zbMATH. While most cases we encountered were simple copies of earlier work, we also identified several forms of disguised plagiarism. We investigated 11 cases in detail and evaluate how current plagiarism detection systems perform in identifying these cases. Moreover, we describe the steps required to discover these and potentially undiscovered cases in the future.

cs.DL