Exploration of Formalization Techniques for Geometric Entities in Planar Geometry Proposition Texts
Bibliographic record
Abstract
This paper explores the formalization technology of geometric entities in planar geometry proposition texts and proposes a formal definition of planar geometric entities. The study investigates the formalization of planar geometry proposition texts using NER technology and the latest large language models. The research utilizes the classic NER model BiLSTM-CRF for sequence labeling and training to achieve geometric entity recognition, followed by dictionary-based formalization. Additionally, the study employs the PROMPT approach based on Baidu's ERNIE-Bot and iFlytek's Spark large language models for geometric entity recognition and subsequent formalization. The results show that the BiLSTM-CRF model achieves an accuracy of 98% in geometric entity recognition, demonstrating stable performance but limited flexibility. ERNIE-Bot performs exceptionally well, with a recognition accuracy of 99%, although it struggles with certain special geometric entities. The Spark large model performs slightly worse, with issues primarily related to repeated or missed entity recognition. While the classic deep learning model exhibits high stability for recognizing common expressions in planar geometry proposition texts, it has limited adaptability to new and complex expressions not present in the training set. Large language models excel in simple tasks due to their strong language processing and contextual understanding capabilities; however, their accuracy depends heavily on the precision of PROMPT design, and their commercial use entails significant costs. This paper provides technical insights into the formalization of geometric entities in planar geometry proposition texts and offers a valuable reference for applications in intelligent education, particularly in geometry teaching and automated proof generation.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.011 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".