LM4OPT: Unveiling the potential of Large Language Models in formulating mathematical optimization problems
Bibliographic record
Abstract
In the fast-paced domain of natural language processing, converting linguistic descriptions into mathematical optimization problems is a complex task, requiring profound comprehension and processing skills from Large Language Models (LLMs). In this study, various LLMs were evaluated, including GPT-3.5, GPT-4, and smaller variants with seven billion parameters: Llama-2, Falcon, Mistral, and Zephyr. This research investigated their performance in both zero-shot and one-shot settings for this task, revealing that GPT-4 outperformed others, particularly in the one-shot scenario. A core contribution of this study is the development of LM4OPT, a progressive fine-tuning framework specifically designed for smaller LLMs. This framework leverages noisy embeddings and specialized datasets to enhance the performance of the models. Regardless of the inherent limitations of smaller models in processing complex and lengthy input contexts, our experimental results indicate a significant reduction in the performance disparity between smaller and larger models when the former are fine-tuned using LM4OPT. Our empirical study, utilizing the NL4Opt dataset, unveils that GPT-4 surpasses the baseline performance established by previous research, achieving an accuracy of 63.30%, solely based on the problem description in natural language, and without relying on any additional named entity information. GPT-3.5 follows closely, both outperforming the progressively fine-tuned smaller models.
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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 | 0.002 | 0.011 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".