GeoCoder: Solving Geometry Problems by Generating Modular Code through Vision-Language Models
Why this work is in the frame
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Bibliographic record
Abstract
Geometry problem-solving demands advanced reasoning abilities to process multimodal inputs and employ mathematical knowledge effectively.Vision-language models (VLMs) have made significant progress in various multimodal tasks.Yet, they still struggle with geometry problems and are significantly limited by their inability to perform mathematical operations not seen during pre-training, such as calculating the cosine of an arbitrary angle, and by difficulties in correctly applying relevant geometry formulas.To overcome these challenges, we present GeoCoder, which leverages modular code-finetuning to generate and execute code using a predefined geometry function library.By executing the code, we achieve accurate and deterministic calculations, contrasting the stochastic nature of autoregressive token prediction, while the function library minimizes errors in formula usage.We also propose a multimodal retrieval-augmented variant of GeoCoder, named RAG-GeoCoder, which incorporates a non-parametric memory module for retrieving functions from the geometry library, thereby reducing reliance on parametric memory.Our modular code-finetuning approach enhances the geometric reasoning capabilities of VLMs, yielding an average improvement of over 16% across various question complexities on the GeomVerse dataset compared to other fine-tuning methods.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it