研究用 Claude Opus 5.5 写论文：LLM 直接写网络权重加速 MILP 求解
Can a Language Model Write the Weights? An Empirical Study of LLM-Written Scoring Networks for Column Generation and MILP Branching, with a Bus-Driver Scheduling Application
一篇由 Claude Opus 5.5 写的运筹学论文，让 LLM 不训练直接写网络权重来加速 SCIP 求解，结论很诚实：便宜但没惊喜。
论文主体由 Claude Opus 5.5 在作者指导下生成，测试 LLM 无梯度训练、直接写小神经网络权重的权重空间编程方法。在列生成中选择弧、标签和 ng-邻域的四个实验均无实质收益。分支定界方面，LLM 写的网络在独立集合成实例上耗时为 SCIP 默认规则的 0.37 倍（18 组配对实例，Wilcoxon p<10^-5），但在 39 个 MIPLIB 2017 实例上解出 19 个，低于 SCIP 的 24 个。基于亚特兰大 MARTA 公交时刻表的班组调度模型中，LLM 写的规则耗时为默认的 0.63 倍（32 个留出实例，p<10^-4），但收益来自计算便宜，而非 LLM 写的权重本身。
Can a Language Model Write the Weights? An Empirical Study of LLM-Written Scoring Networks for Column Generation and MILP Branching, with a Bus-Driver Scheduling Application
This paper was generated by an AI model (Claude Opus 5.5, Anthropic) under the author's direction; all results come from computations run on the author's machine, and every reference was checked. Weight-space programming (WSP) is the idea that a large language model (LLM) can write the weights of a small neural network directly, guided only by reading forward-pass outputs, with no gradient training. We test whether WSP can improve exact operations research algorithms where they rely on cheap scoring rules. In four studies, an LLM wrote small multilayer perceptrons that (i) select arcs, labels and ng-neighbourhoods inside column generation for the vehicle routing problem with time windows, and (ii) choose branching variables in SCIP's branch-and-bound. The algorithms stay exact whatever the weights; a bad network only costs time. In column generation, no lever gave a material gain. In branching on synthetic classes, a hand-written network solved independent-set instances in 0.37x the time of SCIP's default rule (18 paired instances, Wilcoxon $p<10^{-5}$) and matched or beat networks trained by imitation of strong branching, but on 39 MIPLIB 2017 instances it solved 19 versus 24. In an application built from the real GTFS feed of Atlanta's transit agency (MARTA), a crew scheduling set-partitioning model solved by a native C plugin with SCIP's factory settings, the LLM-written rules took 0.63x the default's time on 32 held-out instances ($p<10^{-4}$), but SCIP's plain pseudocost rule did exactly as well (ratio 0.99, $p=0.19$). In these settings, the gains came from being cheap, not from what the LLM wrote. All code, logs and the numbers behind every figure are released.
