The paper introduces Discovery Loop, a lightweight system that employs a large language model (LLM) to iteratively evolve optimization algorithms for the Packomania circle‑packing benchmark. Starting from a simple seed solver, the LLM proposes algorithmic improvements guided by a scoreboard and a history of prior ideas, evaluates each candidate against an independent verifier, and retains only successful changes. Within 15 iterations and a total LLM cost of $27.72, the system broke 10 Packomania records for N between 101 and 114, improving the best known solutions by 2.4%–5.4%. The work demonstrates that a cost‑efficient, LLM‑driven approach can rapidly advance state‑of‑the‑art solutions in a complex optimization domain, suggesting broader potential for democratizing automated scientific discovery.
arXiv:2602. 10233v2 Announce Type: replace-cross Abstract: LLM-guided evolutionary computation, most notably AlphaEvolve, has been remarkably successful in discovering novel mathematical constructions by solving challenging optimization problems.
arXiv:2609.25510v1 Announce Type: new Abstract: Large language models (LLMs) can improve solutions to verifiable scientific and algorithmic problems by spending additional computation at test time. R...
arXiv:2510. 27353v2 Announce Type: replace Abstract: Recent studies have suggested that Large Language Models (LLMs) could provide interesting ideas contributing to mathematical discovery.
arXiv:2606. 29082v1 Announce Type: cross Abstract: Would experience designing faster GPU kernels also help close in on a long-standing open mathematical conjecture?
arXiv:2609.40340v1 Announce Type: new Abstract: Evolutionary search with large language models (LLMs) can stall when progress requires external knowledge the model lacks. Supplying relevant documents...
Evolutionary search with large language models (LLMs) can stall when progress requires external knowledge the model lacks. Supplying relevant documents helps, but simply adding web search tool can kee...
The paper investigates Test‑Time Scaling (TTS) for large language models (LLMs) in the context of automated scientific equation discovery, an open‑ended task where models iteratively search candidate equations using observed data for feedback. It frames equation discovery as a unified iterative search that encompasses Best‑of‑N, sequential refinement, tree search, and evolutionary methods, and studies how compute allocation—particularly search width—affects performance under fixed budgets. Experiments on the LLM‑SRBench dataset show that increasing search width with more compute improves results, while other factors like population‑branching split and controller choice have smaller impacts, indicating that controlling exploration versus exploitation is key to scaling LLM‑based equation discovery.
arXiv:2606. 26728v1 Announce Type: new Abstract: Scientific discovery is fundamentally an optimization problem, defined by a vast "state space" of theories and experiments, and an evaluation criterion based on quality, novelty, and validity.
The paper critiques the common practice of evaluating large‑language‑model (LLM) evolutionary search methods using a single seed and fixed iteration budget, arguing that this approach is insufficient. By testing three search strategies across five optimization tasks and varying both the number of seeds (width) and iterations (depth), the authors find that optimal budget allocation depends on the strategy, task, and total budget, and that strategy rankings shift with different budgets. They propose a measurement protocol that maps the seeds‑by‑iterations frontier and offers practical guidance for researchers.
arXiv:2607. 10127v1 Announce Type: cross Abstract: Evolutionary program search guided by Large Language Models (LLMs) has emerged as a powerful paradigm for automated scientific discovery.
arXiv:2604. 19341v2 Announce Type: replace-cross Abstract: Scientific discovery often requires many cycles of proposing, testing, and refining candidate solutions.
arXiv:2606. 10587v1 Announce Type: cross Abstract: Large language models (LLMs) are on the rise for accelerating scientific discovery, most recently in advanced tasks such as generating valid scientific hypotheses.