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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.21751 |
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| _version_ | 1866913151157534720 |
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| author | Gao, Zhiqi Ge, Albert Berenbeim, Alexander Bastian, Nathaniel D. Sala, Frederic |
| author_facet | Gao, Zhiqi Ge, Albert Berenbeim, Alexander Bastian, Nathaniel D. Sala, Frederic |
| contents | Text-to-optimization requires two separable capabilities: modeling -- choosing the right optimization structure -- and binding -- grounding every coefficient, index, and parameter in the concrete problem data. We study this via Text2Opt-Bench, a scalable benchmark of solver-verified optimization problems spanning 12 categories, from textbook linear programs to stochastic and multi-objective formulations with up to thousands of variables. Across 10+ models, we find that accuracy collapses as instance data grows, even when the formulation itself is simple. We call this the effective binding limit. We address this via a simple inference-time approach, BIND, which externalizes numeric data to structured files so the model binds data programmatically rather than transcribing from the prompt. BIND improves GPT-5-Nano from 59.1% to 82.4% accuracy, matching pass@5 (82.0%) at lower token cost than pass@1, and GPT-5 from 86.2% to 95.8%. Furthermore, we validate our hypothesis by finetuning a model exclusively on binding and show that it outperforms end-to-end SFT and RL across three structurally distinct optimization categories, with a 1.5B binding specialist alone matching a 7B end-to-end baseline. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21751 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Models Can Model, But Can't Bind: Structured Grounding in Text-to-Optimization Gao, Zhiqi Ge, Albert Berenbeim, Alexander Bastian, Nathaniel D. Sala, Frederic Machine Learning Text-to-optimization requires two separable capabilities: modeling -- choosing the right optimization structure -- and binding -- grounding every coefficient, index, and parameter in the concrete problem data. We study this via Text2Opt-Bench, a scalable benchmark of solver-verified optimization problems spanning 12 categories, from textbook linear programs to stochastic and multi-objective formulations with up to thousands of variables. Across 10+ models, we find that accuracy collapses as instance data grows, even when the formulation itself is simple. We call this the effective binding limit. We address this via a simple inference-time approach, BIND, which externalizes numeric data to structured files so the model binds data programmatically rather than transcribing from the prompt. BIND improves GPT-5-Nano from 59.1% to 82.4% accuracy, matching pass@5 (82.0%) at lower token cost than pass@1, and GPT-5 from 86.2% to 95.8%. Furthermore, we validate our hypothesis by finetuning a model exclusively on binding and show that it outperforms end-to-end SFT and RL across three structurally distinct optimization categories, with a 1.5B binding specialist alone matching a 7B end-to-end baseline. |
| title | Models Can Model, But Can't Bind: Structured Grounding in Text-to-Optimization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.21751 |