Coupled Harness--Model Evolution for Scientific Equation Discovery

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.

What happens when you teach an LLM-based agent the scientific method? Motivation: Scientific discovery emerges from cycles of hypothesis, implementation, empirical testing, and feedback. Can this process be automated? We approach automated algorithm design through the lens of the scientific method, where an LLM-based agent goes through each step of the process in an ordered, iterative fashion. Results: We present The Little Scientist, a framework in which a "Scientist agent" works inside an evaluation environment that benchmarks its code and returns structured per-instance diagnostics. When the Scientist plateaus at a local optimum, a "Kuhn agent" injects a paradigm-shifting conjecture paired with a cross-disciplinary inspiration, forcing exploration of a different region of the LLM's latent space. We demonstrate the framework on two problems that require fundamentally different modes of discovery. For protein fitness prediction, the Scientist discovered Delta V, an ensemble calibration strategy that ranks first on the ProteinGym DMS Substitutions Zero-Shot leaderboard across all five official evaluation metrics, exceeding the #2 model (VenusREM) by +0.033 mean Spearman correlation across 217 DMS assays. For DNA motif discovery, the Scientist wrote an algorithm from scratch--DALE (Dual-seed Algorithm for Latent Enumeration)--that outperforms STREME (the default in the MEME Suite) across 132 ENCODE transcription factors (mean AUROC 0.842 vs. 0.803, Wilcoxon p < 10^{-6}) while running 11x faster. This demonstrates that the framework can produce genuinely novel algorithms, not just optimize existing components. Together, these results show that an LLM agent stepping through the scientific method can discover both new algorithms and new ensemble strategies that outperform prior solutions. The entire research program consumed 704M tokens on a single virtual machine with no GPUs

Evolutionary coding agents such as AlphaEvolve are one of the notable successes in using Large Language Models (LLMs) to build AI Scientists. These agents tackle open-ended scientific problems by iteratively improving and evolving programs, leveraging the prior knowledge and reasoning capabilities of LLMs. Despite their success, mutations over programs are mostly low-level upon surface heuristics, without a persistent unit of control. In contrast, science compounds through ideas. In this work, we propose ExpEvolve, which injects idea-level extraction and control into evolution: it discovers and leverages the high-level factors from programs that explain scoring differences among different programs. We characterize theoretical conditions on when discovery with idea factors improves sample efficiency. We also build a practical framework to show that the extracted high-level idea factors are helpful for guiding exploitation from experience and exploration when discovery comes to a plateau. Across 11 open-ended mathematical tasks, ExpEvolve significantly improves the final performance and sample efficiency up to 5.0x. The improvements also transfer to 4 other LLMs and to 6 machine learning tasks from MLS-Bench. Analysis shows that ExpEvolve can discover idea-level factors to provide better exploration and exploitation for evolutionary discovery.