Andre Greiner-Petter

Sunisth Kumar, Xanh Ho, Tim Schopf et al.

Multimodal LLMs are increasingly used to assist scientific peer review, where a core requirement is verifying whether claims in a paper are supported by its evidence. Prior work has shown that models perform substantially better at this task when the evidence is a table than when it is a chart of the same underlying data. This raises the question of whether models fail to extract information from charts, or do they extract it but fail to use it when forming their prediction? We study this question through layer-wise linear probing and attention analysis on three open-weight VLMs over table and chart evidence, representing the same underlying data. We find consistent evidence for the latter. Chart information is encoded in the models' intermediate representations but does not reach the prediction position, a gap that is absent for tables and holds across all conditions tested. Attention analysis further reveals that this disconnect takes two architecturally distinct forms across model families. These findings reframe the table-chart gap as a failure of how encoded visual information is routed at prediction time, rather than a failure of encoding itself.

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.

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}

Tomas Horych, Christoph Mandl, Terry Ruas et al.

High annotation costs from hiring or crowdsourcing complicate the creation of large, high-quality datasets needed for training reliable text classifiers. Recent research suggests using Large Language Models (LLMs) to automate the annotation process, reducing these costs while maintaining data quality. LLMs have shown promising results in annotating downstream tasks like hate speech detection and political framing. Building on the success in these areas, this study investigates whether LLMs are viable for annotating the complex task of media bias detection and whether a downstream media bias classifier can be trained on such data. We create annolexical, the first large-scale dataset for media bias classification with over 48000 synthetically annotated examples. Our classifier, fine-tuned on this dataset, surpasses all of the annotator LLMs by 5-9 percent in Matthews Correlation Coefficient (MCC) and performs close to or outperforms the model trained on human-labeled data when evaluated on two media bias benchmark datasets (BABE and BASIL). This study demonstrates how our approach significantly reduces the cost of dataset creation in the media bias domain and, by extension, the development of classifiers, while our subsequent behavioral stress-testing reveals some of its current limitations and trade-offs.

Felix Petersen, Moritz Schubotz, Andre Greiner-Petter et al.

We tackle the problem of neural machine translation of mathematical formulae between ambiguous presentation languages and unambiguous content languages. Compared to neural machine translation on natural language, mathematical formulae have a much smaller vocabulary and much longer sequences of symbols, while their translation requires extreme precision to satisfy mathematical information needs. In this work, we perform the tasks of translating from LaTeX to Mathematica as well as from LaTeX to semantic LaTeX. While recurrent, recursive, and transformer networks struggle with preserving all contained information, we find that convolutional sequence-to-sequence networks achieve 95.1% and 90.7% exact matches, respectively.

Andre Greiner-Petter, Moritz Schubotz, Fabian Mueller et al.

Mathematical notation, i.e., the writing system used to communicate concepts in mathematics, encodes valuable information for a variety of information search and retrieval systems. Yet, mathematical notations remain mostly unutilized by today's systems. In this paper, we present the first in-depth study on the distributions of mathematical notation in two large scientific corpora: the open access arXiv (2.5B mathematical objects) and the mathematical reviewing service for pure and applied mathematics zbMATH (61M mathematical objects). Our study lays a foundation for future research projects on mathematical information retrieval for large scientific corpora. Further, we demonstrate the relevance of our results to a variety of use-cases. For example, to assist semantic extraction systems, to improve scientific search engines, and to facilitate specialized math recommendation systems. The contributions of our presented research are as follows: (1) we present the first distributional analysis of mathematical formulae on arXiv and zbMATH; (2) we retrieve relevant mathematical objects for given textual search queries (e.g., linking $P_{n}^{(α, β)}\!\left(x\right)$ with `Jacobi polynomial'); (3) we extend zbMATH's search engine by providing relevant mathematical formulae; and (4) we exemplify the applicability of the results by presenting auto-completion for math inputs as the first contribution to math recommendation systems. To expedite future research projects, we have made available our source code and data.

Moritz Schubotz, Andre Greiner-Petter, Philipp Scharpf et al.

Mathematical formulae represent complex semantic information in a concise form. Especially in Science, Technology, Engineering, and Mathematics, mathematical formulae are crucial to communicate information, e.g., in scientific papers, and to perform computations using computer algebra systems. Enabling computers to access the information encoded in mathematical formulae requires machine-readable formats that can represent both the presentation and content, i.e., the semantics, of formulae. Exchanging such information between systems additionally requires conversion methods for mathematical representation formats. We analyze how the semantic enrichment of formulae improves the format conversion process and show that considering the textual context of formulae reduces the error rate of such conversions. Our main contributions are: (1) providing an openly available benchmark dataset for the mathematical format conversion task consisting of a newly created test collection, an extensive, manually curated gold standard and task-specific evaluation metrics; (2) performing a quantitative evaluation of state-of-the-art tools for mathematical format conversions; (3) presenting a new approach that considers the textual context of formulae to reduce the error rate for mathematical format conversions. Our benchmark dataset facilitates future research on mathematical format conversions as well as research on many problems in mathematical information retrieval. Because we annotated and linked all components of formulae, e.g., identifiers, operators and other entities, to Wikidata entries, the gold standard can, for instance, be used to train methods for formula concept discovery and recognition. Such methods can then be applied to improve mathematical information retrieval systems, e.g., for semantic formula search, recommendation of mathematical content, or detection of mathematical plagiarism.