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Volume 1, Issue 1, Frontiers in Educational Innovation and Research
Volume 1, Issue 1, 2024
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Frontiers in Educational Innovation and Research, Volume 1, Issue 1, 2024: 10-21

Open Access | Research Article | 20 May 2025
Enhanced Dynamic Label Allocation for Mathematical Formula Named Entity Recognition in Learning Path Recommendations
1 National Engineering Research Centre for Agri-Product Quality Traceability, Beijing Technology and Business University, Beijing 100048, China
* Corresponding Author: Qingchuan Zhang, [email protected]
Received: 13 December 2024, Accepted: 14 April 2025, Published: 20 May 2025  
Abstract
In the field of natural language processing, Named entity recognition (NER) is a essential task. Mathematical formulas usually contain a large number of terminologies, units of measure and other proprietary knowledge, and the integration of this information into the knowledge graph can significantly enhance the semantic expression ability of the graph. By identifying the named entities in data formulas, the key concepts, entities and relationships between them in the knowledge graph can be extracted, establishing basis for the construction of the knowledge graph and making it easier to interpret and analyse in practical applications. Furthermore, the structured knowledge derived from this process can facilitate personalized learning path recommendations by mapping identified entities to educational resources and prerequisite relationships. Aiming at the problem of insufficient recognition ability of existing models for mathematical formula entities, a mathematical formula named entity recognition method combining enhanced dynamic allocation of labels is proposed. A mathematical formula entity recognition model consisted of BERT(Bidirectional Encoder Representation from Transformer), BiLSTM(Bidirectional Long Short-term Memory) and Transformer was constructed, namely BERT-formula. The feature representation of deep semantic information is enhanced by adding extra sequences to the original vector representation for splicing at the model input; and the entity label prediction problem is regarded as a one-to-many linear allocation problem, and an auction algorithm is introduced to acquire the optimal allocation result with the smallest cost. Experiments demonstrate that the accuracy of the model prediction on the mathematical formula set is 98.8%, and the F1 value is 98.8%, which is improved by 1.51 and 1.05 percentage points compared with BERT-BiLSTM-CRF. It is evident that the approach performs well on the objective of identifying mathematical formula entities.

Graphical Abstract
Enhanced Dynamic Label Allocation for Mathematical Formula Named Entity Recognition in Learning Path Recommendations

Keywords
named entity recognition (NER)
mathematics
bidirectional encoder representations from transformer (BERT)
deep learning
auction algorithm

Data Availability Statement
The source code is available at https://github.com/Ctrius/formula.

Funding
This work was supported in part by the Project of Construction and Support for high-level Innovative Teams of Beijing Municipal Institutions under Grant BPHR20220104; in part by the Beijing Scholars Program under Grant 099; in part by the IFLYTEK University Intelligent Teaching Innovation Research Special Project under Grant 2022XF055.

Conflicts of Interest
The authors declare no conflicts of interest.

Ethical Approval and Consent to Participate
Not applicable.

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APA Style
Liu, H., & Zhang, Q. (2025). Enhanced Dynamic Label Allocation for Mathematical Formula Named Entity Recognition in Learning Path Recommendations. Frontiers in Educational Innovation and Research, 1(1), 10–21. https://doi.org/10.62762/FEIR.2024.416675

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