International Journal of Engineering and Manufacturing (IJEM)
IJEM Vol. 16, No. 4, 8 Aug. 2026
Cover page and Table of Contents: PDF (size: 940KB)
Context-Aware Semantic Fusion for Mathematical Formula Equivalence Detection
PDF (940KB), PP.81-96
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Author(s)
Andrii Dyriv
1,*
Olga Lozynska
1
Victoria Vysotska
1
Dmytro Uhryn
2
Yuriy Ushenko
2
Index Terms
Mathematical formulas, semantic analysis, equivalence of formulas, publication context, vector representation (Embeddings), transformer models (SciBERT, MathBERT), machine learning, clustering, natural language processing (NLP)
Abstract
The paper investigates the problem of automatically detecting equivalent mathematical formulas in scientific texts. The authors propose a novel hybrid approach that combines structural analysis of formulas (normalisation, Abstract Syntax Tree (AST) construction, and vectorisation) with deep semantic analysis of the surrounding publication text using transformer models such as SciBERT and Sentence Transformers. During the study, a software implementation was developed that uses cosine similarity to assess context proximity and a Siamese neural network for equivalence classification. Evaluated on a custom dataset of 12,500 formula-context pairs from academic papers, the proposed hybrid model achieved an F1-score of 0.88, significantly outperforming baseline models that rely solely on structural (F1: 0.71) or textual (F1: 0.59) features. The experimental results were further visualised using heat maps, dendrograms, and UMAP projections, confirming the model's ability to identify equivalent expressions even when their syntactic notation differs significantly. The proposed framework is promising for use in anti-plagiarism systems, intelligent search services, and digital scientific libraries.
Cite This Paper
Andrii Dyriv, Olga Lozynska, Victoria Vysotska, Dmytro Uhryn, Yuriy Ushenko, "Context-Aware Semantic Fusion for Mathematical Formula Equivalence Detection", International Journal of Engineering and Manufacturing (IJEM), Vol.16, No.4, pp.81-96, 2026. DOI:10.5815/ijem.2026.04.06
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