# Structured Scaling of AI Discovery Across Diverse Scientific Domains

arXiv: https://arxiv.org/abs/2604.19341 · HTML: https://mlsanity.com/paper/2604.19341/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 56 of its 178 references that are in the map.
- First posted on arXiv 21 Apr 2026.

## Builds on (most cited first, 30 of 56)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning](https://mlsanity.com/paper/2507.19457/) (2025)
- [MLE-bench: Evaluating Machine Learning Agents on Machine Learning Engineering](https://mlsanity.com/paper/2410.07095/) (2024)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [PaperBench: Evaluating AI's Ability to Replicate AI Research](https://mlsanity.com/paper/2504.01848/) (2025)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training](https://mlsanity.com/paper/2309.17179/) (2023)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [KernelBench: Can LLMs Write Efficient GPU Kernels?](https://mlsanity.com/paper/2502.10517/) (2025)
- [MedXpertQA: Benchmarking Expert-Level Medical Reasoning and Understanding](https://mlsanity.com/paper/2501.18362/) (2025)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [Data Mixing Laws: Optimizing Data Mixtures by Predicting Language Modeling Performance](https://mlsanity.com/paper/2403.16952/) (2024)
- [ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolution](https://mlsanity.com/paper/2509.19349/) (2025)
- [A Survey of Self-Evolving Agents: What, When, How, and Where to Evolve on the Path to Artificial Super Intelligence](https://mlsanity.com/paper/2507.21046/) (2025)
- [Towards a Science of Scaling Agent Systems](https://mlsanity.com/paper/2512.08296/) (2025)
- [Emergent autonomous scientific research capabilities of large language models](https://mlsanity.com/paper/2304.05332/) (2023)
- [Learning to Discover at Test Time](https://mlsanity.com/paper/2601.16175/) (2026)
- [Self-Adapting Language Models](https://mlsanity.com/paper/2506.10943/) (2025)
- [Planning In Natural Language Improves LLM Search For Code Generation](https://mlsanity.com/paper/2409.03733/) (2024)
- [A Self-Improving Coding Agent](https://mlsanity.com/paper/2504.15228/) (2025)
- [Mathematical exploration and discovery at scale](https://mlsanity.com/paper/2511.02864/) (2025)

## Built on by (most cited first, 21 of 21)

- [MLEvolve: A Self-Evolving Framework for Automated Machine Learning Algorithm Discovery](https://mlsanity.com/paper/2606.06473/) (2026)
- [MLS-Bench: A Holistic and Rigorous Assessment of AI Systems on Building Better AI](https://mlsanity.com/paper/2605.08678/) (2026)
- [Harnessing Agentic Evolution](https://mlsanity.com/paper/2605.13821/) (2026)
- [Escher-Loop: Mutual Evolution by Closed-Loop Self-Referential Optimization](https://mlsanity.com/paper/2604.23472/) (2026)
- [Frontis-MA1: Training an AI4AI Model towards Recursive Self-Improvement in Machine Learning Engineering](https://mlsanity.com/paper/2607.28568/) (2026)
- [Evolution Fine-Tuning: Learning to Discover Across 371 Optimization Tasks](https://mlsanity.com/paper/2606.29082/) (2026)
- [SwarmResearch: Orchestrating Coding Agents for Open-Ended Discovery](https://mlsanity.com/paper/2607.02807/) (2026)
- [Physics of Agents: Statistical Mechanics Predicts Collective Behavior of AI Agents](https://mlsanity.com/paper/2608.16578/) (2026)
- [What Do Evolutionary Coding Agents Evolve?](https://mlsanity.com/paper/2605.20086/) (2026)
- [AI-Assisted Discovery of Convex Relaxations via Dual Agents](https://mlsanity.com/paper/2606.31182/) (2026)
- [SciResearcher: Scaling Deep Research Agents for Frontier Scientific Reasoning](https://mlsanity.com/paper/2605.01489/) (2026)
- [Autonomous Mathematical Discovery in an Open-World Multi-Agent Environment](https://mlsanity.com/paper/2608.23691/) (2026)
- [Closing the Prior-Posterior Loop: Self-Reflective Molecular Design with Analysis-Driven LLM Iteration](https://mlsanity.com/paper/2606.09520/) (2026)
- [A Vocabulary for Multi-Agent Automated Research Systems](https://mlsanity.com/paper/2607.22682/) (2026)
- [Budget-Aware LLM Discovery via Cost-Calibrated Frontier Utility](https://mlsanity.com/paper/2607.26828/) (2026)
- [Hill Sampling for Test-Time Scaling: A Simple and Better Alternative to Repeated Sampling, Evolution, and Training](https://mlsanity.com/paper/2609.25510/) (2026)
- [iCoder-27B: Recursive AI-Led Development of Frontier Industrial Coding Model](https://mlsanity.com/paper/2609.29626/) (2026)
- [EvoDuet: Bilevel Co-Evolution of Web Searching and Task Solving for Scientific Discovery](https://mlsanity.com/paper/2609.40340/) (2026)
- [CURIO: Curiosity-Driven Test-Time Learning for Open-Ended Discovery](https://mlsanity.com/paper/2610.04851/) (2026)
- [Evolving in Thought Space: Training a Small Model at Test Time Unlocks Better Discoveries](https://mlsanity.com/paper/2610.06269/) (2026)
- [One-Sided Verification Under Limited Expert Review](https://mlsanity.com/paper/2610.18089/) (2026)

## Abstract (arXiv)

Scientific discovery often requires many cycles of proposing, testing, and refining candidate solutions. Language models can increasingly participate in these loops, but simply generating more attempts does not ensure progress: parallel searches may duplicate one another and iterative refinement may become trapped in poor directions. The central challenge is therefore not only to scale AI-driven discovery, but to structure that scaling so that evaluation signals compound over time. Here we introduce SimpleTES (Simple Test-time Evaluation-driven Scaling), a framework that focuses on the structured scaling of AI discovery loops, organizing evaluator queries across independent trajectories, iterative refinement, local candidate selection, and the selective reuse of evaluated histories. Drawing on structural features of scientific communities, SimpleTES uses a single open-source GPT-OSS model to establish new state-of-the-art solutions across 28 open-ended problems in diverse scientific domains ranging from quantum physics and astronomy to biology, AI, and mathematics. These include a 24.5% reduction in quantum circuit compilation overhead, up to 23% lower propulsive cost for deep-space trajectories, a 2.17x faster lasso-path solver, an 8.5% lower-error whole-brain neural-activity predictor, the fastest reported TriMul kernel, and new mathematical constructions beyond prior human or AI records. We further post-train the model for long-horizon discovery by assigning each attempt the final outcome of the trajectory it helped produce. This improves performance on both training and held-out mathematics problems, further advancing the frontier. Together, these results establish structured scaling as a general mechanism for advancing AI scientific discovery.