Models Can Model, But Can't Bind: Structured Grounding in Text-to-Optimization

TL;DR

This paper investigates the limitations of models in grounding optimization problem data within text-to-optimization tasks and proposes a simple externalization method, BIND, to significantly improve accuracy.

Contribution

The paper introduces BIND, an inference-time approach that externalizes data to improve model binding accuracy in text-to-optimization tasks.

Findings

BIND improves GPT-5-Nano accuracy from 59.1% to 82.4%.

BIND enhances GPT-5 accuracy from 86.2% to 95.8%.

Finetuning on binding data outperforms end-to-end methods, with a 1.5B binding specialist matching a 7B baseline.

Abstract

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.