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Moritz Schubotz

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11 published item(s)

preprint2026arXiv

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.

preprint2022arXiv

Comparative Verification of the Digital Library of Mathematical Functions and Computer Algebra Systems

Digital mathematical libraries assemble the knowledge of years of mathematical research. Numerous disciplines (e.g., physics, engineering, pure and applied mathematics) rely heavily on compendia gathered findings. Likewise, modern research applications rely more and more on computational solutions, which are often calculated and verified by computer algebra systems. Hence, the correctness, accuracy, and reliability of both digital mathematical libraries and computer algebra systems is a crucial attribute for modern research. In this paper, we present a novel approach to verify a digital mathematical library and two computer algebra systems with one another by converting mathematical expressions from one system to the other. We use our previously eveloped conversion tool (referred to as LaCASt) to translate formulae from the NIST Digital Library of Mathematical Functions to the computer algebra systems Maple and Mathematica. The contributions of our presented work are as follows: (1) we present the most comprehensive verification of computer algebra systems and digital mathematical libraries with one another; (2) we significantly enhance the performance of the underlying translator in terms of coverage and accuracy; and (3) we provide open access to translations for Maple and Mathematica of the formulae in the NIST Digital Library of Mathematical Functions.

preprint2022arXiv

Design and Evaluation of IPFS: A Storage Layer for the Decentralized Web

Recent years have witnessed growing consolidation of web operations. For example, the majority of web traffic now originates from a few organizations, and even micro-websites often choose to host on large pre-existing cloud infrastructures. In response to this, the "Decentralized Web" attempts to distribute ownership and operation of web services more evenly. This paper describes the design and implementation of the largest and most widely used Decentralized Web platform - the InterPlanetary File System (IPFS) - an open-source, content-addressable peer-to-peer network that provides distributed data storage and delivery. IPFS has millions of daily content retrievals and already underpins dozens of third-party applications. This paper evaluates the performance of IPFS by introducing a set of measurement methodologies that allow us to uncover the characteristics of peers in the IPFS network. We reveal presence in more than 2700 Autonomous Systems and 152 countries, the majority of which operate outside large central cloud providers like Amazon or Azure. We further evaluate IPFS performance, showing that both publication and retrieval delays are acceptable for a wide range of use cases. Finally, we share our datasets, experiences and lessons learned.

preprint2020arXiv

A First Step Towards Content Protecting Plagiarism Detection

Plagiarism detection systems are essential tools for safeguarding academic and educational integrity. However, today's systems require disclosing the full content of the input documents and the document collection to which the input documents are compared. Moreover, the systems are centralized and under the control of individual, typically commercial providers. This situation raises procedural and legal concerns regarding the confidentiality of sensitive data, which can limit or prohibit the use of plagiarism detection services. To eliminate these weaknesses of current systems, we seek to devise a plagiarism detection approach that does not require a centralized provider nor exposing any content as cleartext. This paper presents the initial results of our research. Specifically, we employ Private Set Intersection to devise a content-protecting variant of the citation-based similarity measure Bibliographic Coupling implemented in our plagiarism detection system HyPlag. Our evaluation shows that the content-protecting method achieves the same detection effectiveness as the original method while making common attacks to disclose the protected content practically infeasible. Our future work will extend this successful proof-of-concept by devising plagiarism detection methods that can analyze the entire content of documents without disclosing it as cleartext.

preprint2020arXiv

Classification and Clustering of arXiv Documents, Sections, and Abstracts, Comparing Encodings of Natural and Mathematical Language

In this paper, we show how selecting and combining encodings of natural and mathematical language affect classification and clustering of documents with mathematical content. We demonstrate this by using sets of documents, sections, and abstracts from the arXiv preprint server that are labeled by their subject class (mathematics, computer science, physics, etc.) to compare different encodings of text and formulae and evaluate the performance and runtimes of selected classification and clustering algorithms. Our encodings achieve classification accuracies up to $82.8\%$ and cluster purities up to $69.4\%$ (number of clusters equals number of classes), and $99.9\%$ (unspecified number of clusters) respectively. We observe a relatively low correlation between text and math similarity, which indicates the independence of text and formulae and motivates treating them as separate features of a document. The classification and clustering can be employed, e.g., for document search and recommendation. Furthermore, we show that the computer outperforms a human expert when classifying documents. Finally, we evaluate and discuss multi-label classification and formula semantification.

preprint2020arXiv

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.

preprint2020arXiv

Pairwise Multi-Class Document Classification for Semantic Relations between Wikipedia Articles

Many digital libraries recommend literature to their users considering the similarity between a query document and their repository. However, they often fail to distinguish what is the relationship that makes two documents alike. In this paper, we model the problem of finding the relationship between two documents as a pairwise document classification task. To find the semantic relation between documents, we apply a series of techniques, such as GloVe, Paragraph-Vectors, BERT, and XLNet under different configurations (e.g., sequence length, vector concatenation scheme), including a Siamese architecture for the Transformer-based systems. We perform our experiments on a newly proposed dataset of 32,168 Wikipedia article pairs and Wikidata properties that define the semantic document relations. Our results show vanilla BERT as the best performing system with an F1-score of 0.93, which we manually examine to better understand its applicability to other domains. Our findings suggest that classifying semantic relations between documents is a solvable task and motivates the development of recommender systems based on the evaluated techniques. The discussions in this paper serve as first steps in the exploration of documents through SPARQL-like queries such that one could find documents that are similar in one aspect but dissimilar in another.

preprint2015arXiv

Growing the Digital Repository of Mathematical Formulae with Generic LaTeX Sources

One initial goal for the DRMF is to seed our digital compendium with fundamental orthogonal polynomial formulae. We had used the data from the NIST Digital Library of Mathematical Functions (DLMF) as initial seed for our DRMF project. The DLMF input LaTeX source already contains some semantic information encoded using a highly customized set of semantic LaTeX macros. Those macros could be converted to content MathML using LaTeXML. During that conversion the semantics were translated to an implicit DLMF content dictionary. This year, we have developed a semantic enrichment process whose goal is to infer semantic information from generic LaTeX sources. The generated context-free semantic information is used to build DRMF formula home pages for each individual formula. We demonstrate this process using selected chapters from the book "Hypergeometric Orthogonal Polynomials and their $q$-Analogues" (2010) by Koekoek, Lesky and Swarttouw (KLS) as well as an actively maintained addendum to this book by Koornwinder (KLSadd). The generic input KLS and KLSadd LaTeX sources describe the printed representation of the formulae, but does not contain explicit semantic information. See http://drmf.wmflabs.org.

preprint2014arXiv

Digital Repository of Mathematical Formulae

The purpose of the NIST Digital Repository of Mathematical Formulae (DRMF) is to create a digital compendium of mathematical formulae for orthogonal polynomials and special functions (OPSF) and of associated mathematical data. The DRMF addresses needs of working mathematicians, physicists and engineers: providing a platform for publication and interaction with OPSF formulae on the web. Using MediaWiki extensions and other existing technology (such as software and macro collections developed for the NIST Digital Library of Mathematical Functions), the DRMF acts as an interactive web domain for OPSF formulae. Whereas Wikipedia and other web authoring tools manifest notions or descriptions as first class objects, the DRMF does that with mathematical formulae. See http://gw32.iu.xsede.org/index.php/Main_Page.

preprint2014arXiv

Mathoid: Robust, Scalable, Fast and Accessible Math Rendering for Wikipedia

Wikipedia is the first address for scientists who want to recap basic mathematical and physical laws and concepts. Today, formulae in those pages are displayed as Portable Network Graphics images. Those images do not integrate well into the text, can not be edited after copying, are inaccessible to screen readers for people with special needs, do not support line breaks for small screens and do not scale for high resolution devices. Mathoid improves this situation and converts formulae specified by Wikipedia editors in a TeX-like input format to MathML, with Scalable Vector Graphics images as a fallback solution.

preprint2013arXiv

Making Math Searchable in Wikipedia

Wikipedia, the world largest encyclopedia contains a lot of knowledge that is expressed as formulae exclusively. Unfortunately, this knowledge is currently not fully accessible by intelligent information retrieval systems. This immense body of knowledge is hidden form value-added services, such as search. In this paper, we present our MathSearch implementation for Wikipedia that enables users to perform a combined text and fully unlock the potential benefits.