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13:00-14:30 Session 14: Teaching and Geometric Reasoning + Search and Classification (I)

Regular papers

Automated Generation of Exam Sheets for Automated Deduction

ABSTRACT. Amid the COVID-19 pandemic, distance teaching became default in higher education, urging teachers and researchers to revise course materials into an accessible online content for a diverse audience. Probably one of the hardest challenges came with online assessments of course performance, for example by organizing online written exams. In this teaching-related project paper we survey the setting we organized for our master's level course ``Automated Deduction'' in logic and computation at TU Wien. The algorithmic and rigorous reasoning developed within our course called for individual exam sheets focused on problem solving and deductive proofs; as such exam sheets using test grids were not a viable solution for written exams within our course. We believe the toolchain of automated reasoning tools we have developed for holding online written exams could be beneficial not only for other distance learning platforms, but also to researchers in automated reasoning, by providing our community with a large set of randomly generated benchmarks in SAT/SMT solving and first-order theorem proving.

Learning to solve geometric construction problems from images

ABSTRACT. We describe a purely image-based method for finding geometric constructions with a ruler and compass in the Euclidea geometric game. The method is based on adapting the Mask R-CNN state-of-the-art visual recognition neural architecture and adding a tree-based search procedure to it. In a supervised setting, the method learns to solve all 68 kinds of geometric construction problems from the first six level packs of Euclidea with an average 92% accuracy. When evaluated on new kinds of problems, the method can solve 31 of the 68 kinds of Euclidea problems. We believe that this is the first time that a purely image-based learning has been trained to solve geometric construction problems of this difficulty.

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

ABSTRACT. 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.

WebMIaS on Docker: Deploying Math-Aware Search in a Single Line of Code
PRESENTER: Dávid Lupták

ABSTRACT. Math informational retrieval (MIR) search engines are absent in the wide-spread production use, even though documents in the STEM fields contain many mathematical formulae, which are sometimes more important than text for understanding. We have developed and open-sourced the WebMIaS MIR search engine that has been successfully deployed in the European Digital Mathematics Library (EuDML). However, its deployment is difficult to automate due to the complexity of this task. Moreover, the solutions developed so far to tackle this challenge are imperfect in terms of speed, maintenance, and robustness. In this paper, we will describe the virtualization of WebMIaS using Docker that solves all three problems and allows anyone to deploy containerized WebMIaS in a single line of code. The publicly available Docker image will also help the community push the development of math-aware search engines in the ARQMath workshop series.

14:30-15:00Coffee Break
15:00-16:00 Session 15: Invited Talk (IV)

Invited speaker

Referential Semantics -- a Concept for Bridging between Representations of mathematical/technical Documents and Knowledge
16:00-16:30Coffee Break
16:30-17:00 Session 16: Search and Classification (II)

Regular papers

Searching for mathematical formulas based on graph representation learning

ABSTRACT. Significant advances have been witnessed in the area of representation learning. Recently, there have been some attempts of applying representation learning methods on mathematical formula retrieval. We introduce a new formula embedding model based on a kind of graph representation generated from hierarchical representation for mathematical formula. Such a representation characterizes structural features in a compact form by merging the same part of a mathematical formula. Following the approach of graph self-supervised learning, we pre-train Graph Neural Networks at the level of individual nodes to learn local representations and then produce a global representation for an entire graph. In this way, formulas can be embedded into a low-dimensional vector space, which allows efficient nearest neighbor search using cosine similarity. We use 579,628 formulas extracted from Wikipedia Corpus provided by NTCIR-12 Wikipedia Formula Browsing Task to train our model, leading to state-of-the-art results for full relevance on the task. Experiments with a preliminary implementation of the embedding model illustrate the feasibility and capability of graph representation learning in capturing structural similarities of mathematical formulas.