用词典筛选取代大模型进化，显著提升科学方程发现效率
Dictionaries, Not Darwin: Set-Level Selection Beats LLM Evolution in Scientific Equation Discovery
- 将大模型生成的候选项归纳为问题专属词典，通过集合级稀疏选择优化
- 单轮生成+集合筛选在717个测试单元中解决165-169个，远超传统方法
- 适合需要高效、低成本科学发现的科研人员，尤其擅长非线性复杂系统
大型语言模型被用于作为科学方程发现的进化引擎：生成候选解，选择优胜者，回传为父代并重复迭代。我们评估该循环是否真能推动科学发现——在有限样本导致结构不确定、插值易行的场景下。在相同的大模型调用预算下，基于父代条件的演化与独立采样无差异：外推误差中位数为0.045对比0.049；多父代交叉指导反而更差；最终成功仅由初始提案质量决定，多种迭代策略未能增加已解问题数。实际操作中，该循环退化为所生成的候选项词典。据此提出PTB-Search，一种单代组件化发现方法：仅调用一次大模型生成候选，提取可复用项形成问题词典，再以仅训练集的集合级稀疏选择与最小二乘系数求解。核心理念是：在数据不足时，应识别项集的联合行为，而非逐项赋信。在相同词典且零额外调用下，集合级选择解决165–169/717个单元，而单项缩减仅解决74–78个。在官方239题的LLM-SRBench基准上，使用Llama-3.1-8B达73.2% Acc0.1，DeepSeek-V4单种子锚点达77.0%，优于最佳基线49.2%，且仅需其十分之一的调用预算。程序域压力测试显示：生成次数仍不可靠，但保留外部状态在更难的非线性空间中有帮助。综合结果表明，大模型宜视为材料供应商，真正的发现依赖于外部集合级选择对可复用组件的组合。
原文摘要 · Abstract (English)
Large language models are increasingly used as evolutionary engines for scientific discovery: generate candidates, select winners, feed them back as parents, and repeat. We audit whether this loop actually compounds discovery in scientific equation discovery, a setting where finite samples make structure underdetermined and interpolation easy. Under matched LLM-call budgets, parent-conditioned evolution is indistinguishable from fresh independent sampling: median OOD NMSE is 0.045 vs. 0.049, instructed multi-parent crossover is worse, final success is predicted by initial proposal quality, and multiple iteration schemes fail to add solved problems. Operationally, the loop reduces to what it produces: a dictionary of candidate terms. We turn that diagnosis into PTB-Search, a one-generation method for componentized scientific discovery. PTB-Search samples independent LLM proposals once, extracts reusable terms into a per-problem dictionary, and performs train-only set-level sparse selection with least-squares coefficients. Its central principle is that underdetermined data identifies the joint behavior of term sets, not reliable per-term credit. On identical dictionaries and zero additional LLM calls, set-level selectors solve 165--169 of 717 cells, while single-term reductions solve only 74--78. On the official 239-problem LLM-SRBench split, PTB-Search reaches 73.2% Acc0.1 with Llama-3.1-8B and 77.0% with a single-seed DeepSeek-V4 anchor, versus 49.2% for the best reported baseline, using one tenth of the standardized call budget. A program-domain stress test gives a scoped boundary: generation count remains unreliable, while retained external state can help in harder non-linear spaces. Across these results, LLMs are best understood as material suppliers; discovery is carried by external set-level selection over reusable components.
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