模型能建模却难绑定，用结构化数据提升优化问题求解准确率
Models Can Model, But Can't Bind: Structured Grounding in Text-to-Optimization
- 将数值数据外置到结构文件，让模型程序化绑定而非口头转述
- 外置数据后准确率提升12至27个百分点，验证绑定是关键瓶颈
- 专用绑定模型仅1.5B参数就媲美7B端到端模型，适合部署应用
文本到优化任务包含两个独立能力：建模（选择正确的优化结构）和绑定（将每个系数、索引和参数与具体问题数据对齐）。我们通过Text2Opt-Bench基准评估这一能力，该基准涵盖12类可扩展的求解器验证优化问题，从教科书线性规划到含上千变量的随机与多目标公式。在10余种模型上，我们发现当实例数据规模增大时，即使公式简单，准确率也急剧下降，称此为有效绑定极限。我们提出一系列技术（BIND），将数值数据外置于结构化文件，使模型能程序化绑定而非从提示中转录。使用理想外置方案时，准确率提升12至27点，证实绑定是可恢复的关键失败模式。在无理想外置访问的可部署场景中，通过仅对绑定任务微调模型，其在三个结构不同的优化类别中超越端到端SFT与强化学习方法，1.5B绑定专用模型性能媲美7B端到端基线。
原文摘要 · Abstract (English)
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 study it with a family of techniques, BIND, that externalize numeric data to structured files so the model binds data programmatically rather than transcribing from the prompt. When using an oracle for externalizing data, we recover between 12 and 27 accuracy points, confirming binding as a key -- but recoverable -- failure mode. In a deployable setting without oracle access, 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.
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