Dictionaries, Not Darwin: Set-Level Selection Beats LLM Evolution in Scientific Equation Discovery

• URL: http://arxiv.org/abs/2607.04108v1
• Date: Sun, 05 Jul 2026 04:10:34 GMT
• Title: Dictionaries, Not Darwin: Set-Level Selection Beats LLM Evolution in Scientific Equation Discovery
• Abstract summary: PTB-Search is a one-generation method for componentized scientific discovery.<n>It samples independent proposals once, extracts reusable terms into a per-problem dictionary, and performs train-only set-level sparse selection.<n>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.
• Score: 9.173232861966595
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• NovGauge: A Fine-Grained Benchmark for Diagnosing LLMs' Capability in Paper Novelty Assessment [54.4265627247104]
  Large language models (LLMs) are increasingly used in peer review at major AI conferences.<n>Existing benchmarks assess novelty as a single holistic score.<n>We present NovGauge, a human-anchored benchmark for fine-grained novelty assessment diagnosis.
  arXiv  Detail & Related papers  (2026-09-10T08:34:56Z)
• Select, Don't Train: The Benefits of Modular Entity Disambiguation with LLM-Based Selection [15.630318972190702]
  We present a systematic comparison of retrieval strategies for candidate generation under a shared LLM-based selection stage.<n>We show that a fully training-free BM25 retriever paired with an LLM selector reaches a new state of the art on the ZELDA benchmark.
  arXiv  Detail & Related papers  (2026-08-17T16:52:05Z)
• Evolutionary Algorithm-Guided LLMs for Physics-Informed Neural Network Design [10.706452586705375]
  Physics-informed neural networks (PINNs) are sensitive to interacting choices of architecture, activation, loss weighting, collocation, optimization, and constraint enforcement.<n>Large language models (LLMs) can propose these choices, but independent recommendations do not accumulate experience from previously trained PINNs.<n>We propose a closed-loop evolutionary algorithm that guides an LLM to generate complete, executable PINN configurations across generations.
  arXiv  Detail & Related papers  (2026-07-17T02:03:11Z)
• Beyond Inference-Time Search: Reinforcement Learning Synthesizes Reusable Solvers [0.0]
  Large language models (LLMs) typically approach optimization as an inference-time procedure, solving each instance separately.<n>We study this question on Synergistic Dependency Selection (SDS), a controlled variant of constrained Quadratic Knapsack.<n>We fine-tune Qwen2.5-Coder-14B-Instruct with Group Relative Policy Optimization using a feasibility-gated reward and light structural scaffolding.
  arXiv  Detail & Related papers  (2026-05-18T13:21:40Z)
• OpenDeepThink: Parallel Reasoning via Bradley-Terry Aggregation [53.88666485159289]
  We introduce OpenDeepThink, a population-based test-time compute framework that selects via pairwise Bradley-Terry comparison.<n>OpenDeepThink raises Gemini 3.1 Pro's effective Codeforces Elo by +405 points in eight sequential LLM-call rounds.<n>We release CF-73, a curated set of 73 expert-rated Codeforces problems with International Grandmaster annotation and 99% local-evaluation agreement against the official verdict.
  arXiv  Detail & Related papers  (2026-05-14T17:57:40Z)
• Budget-Sensitive Discovery Scoring: A Formally Verified Framework for Evaluating AI-Guided Scientific Selection [0.0]
  Budget-Sensitive Discovery Score (BSDS) penalizes false discoveries at each budget level.<n>Discovery Quality Score (DQS) provides a single summary statistic that no proposer can inflate by performing well at a cherry-picked budget.<n> framework applies to any setting where candidates are selected under budget constraints and asymmetric error costs.
  arXiv  Detail & Related papers  (2026-03-12T18:09:53Z)
• Hubble: An LLM-Driven Agentic Framework for Safe, Diverse, and Reproducible Alpha Factor Discovery [0.0]
  We present Hubble, an agentic factor mining framework that combines large language models (LLMs) with a domain-specific operator language.<n>On a U.S. equity universe of roughly 500 stocks, our main run evaluates 104 valid candidates across three rounds with zero runtime crashes.<n>We then fix the resulting top-5 factors and validate them on a held-out period from 2025-06-01 to 2026-03-13.
  arXiv  Detail & Related papers  (2026-03-09T05:21:00Z)
• Identifying Evidence-Based Nudges in Biomedical Literature with Large Language Models [2.2015514798912412]
  We present a scalable, AI-powered system that identifies and extracts evidence-based behavioral nudges from unstructured biomedical literature.<n>Nudges are subtle, non-coercive interventions that influence behavior without limiting choice, showing strong impact on health outcomes like medication adherence.
  arXiv  Detail & Related papers  (2026-02-10T22:36:07Z)
• Don't Throw Away Your Beams: Improving Consistency-based Uncertainties in LLMs via Beam Search [111.6996614063716]
  We introduce a new family of methods that employ beam search to generate candidates for consistency-based uncertainty estimates.<n>We empirically evaluate our approach on six QA datasets and find that its consistent improvements over multinomial sampling lead to state-of-the-art UQ performance.
  arXiv  Detail & Related papers  (2025-12-10T11:24:29Z)
• FR-Spec: Accelerating Large-Vocabulary Language Models via Frequency-Ranked Speculative Sampling [59.8051705468084]
  Speculative sampling has emerged as an important technique for accelerating the auto-regressive generation process of large language models.<n>We present FR-Spec, a frequency-ranked speculative sampling framework that optimize draft candidate selection through vocabulary space compression.
  arXiv  Detail & Related papers  (2025-02-20T18:58:10Z)
• Planning In Natural Language Improves LLM Search For Code Generation [5.370466208990696]
  We propose PlanSearch, a novel search algorithm for solving problems in natural language. PlanSearch shows strong results across HumanEval+, MBPP+, and LiveCodeBench. We show that, across all models, search algorithms, and benchmarks analyzed, we can accurately predict performance gains due to search.
  arXiv  Detail & Related papers  (2024-09-05T17:44:49Z)
• Self-Exploring Language Models: Active Preference Elicitation for Online Alignment [88.56809269990625]
  We propose a bilevel objective optimistically biased towards potentially high-reward responses to actively explore out-of-distribution regions. Our experimental results demonstrate that when fine-tuned on Zephyr-7B-SFT and Llama-3-8B-Instruct models, Self-Exploring Language Models (SELM) significantly boosts the performance on instruction-following benchmarks.
  arXiv  Detail & Related papers  (2024-05-29T17:59:07Z)
• Optimal Multi-Distribution Learning [88.3008613028333]
  Multi-distribution learning seeks to learn a shared model that minimizes the worst-case risk across $k$ distinct data distributions.<n>We propose a novel algorithm that yields an varepsilon-optimal randomized hypothesis with a sample complexity on the order of (d+k)/varepsilon2.
  arXiv  Detail & Related papers  (2023-12-08T16:06:29Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.