# MOOSE-Star: Unlocking Tractable Training for Scientific Discovery by Breaking the Complexity Barrier

arXiv: https://arxiv.org/abs/2603.03756 · HTML: https://mlsanity.com/paper/2603.03756/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 23 of its 39 references that are in the map.
- First posted on arXiv 4 Mar 2026.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 23 of 23)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [MinerU: An Open-Source Solution for Precise Document Content Extraction](https://mlsanity.com/paper/2409.18839/) (2024)
- [SciMON: Scientific Inspiration Machines Optimized for Novelty](https://mlsanity.com/paper/2305.14259/) (2023)
- [CycleResearcher: Improving Automated Research via Automated Review](https://mlsanity.com/paper/2411.00816/) (2024)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [SciRepEval: A Multi-Format Benchmark for Scientific Document Representations](https://mlsanity.com/paper/2211.13308/) (2022)
- [The Semantic Scholar Open Data Platform](https://mlsanity.com/paper/2301.10140/) (2023)
- [Large Language Models for Automated Open-domain Scientific Hypotheses Discovery](https://mlsanity.com/paper/2309.02726/) (2023)
- [LLM4SR: A Survey on Large Language Models for Scientific Research](https://mlsanity.com/paper/2501.04306/) (2025)
- [MOOSE-Chem: Large Language Models for Rediscovering Unseen Chemistry Scientific Hypotheses](https://mlsanity.com/paper/2410.07076/) (2024)
- [ResearchBench: Benchmarking LLMs in Scientific Discovery via Inspiration-Based Task Decomposition](https://mlsanity.com/paper/2503.21248/) (2025)
- [A Simple Model of Inference Scaling Laws](https://mlsanity.com/paper/2410.16377/) (2024)
- [Reverse-Engineered Reasoning for Open-Ended Generation](https://mlsanity.com/paper/2509.06160/) (2025)
- [Training AI Co-Scientists Using Rubric Rewards](https://mlsanity.com/paper/2512.23707/) (2025)
- [PiFlow: Principle-Aware Scientific Discovery with Multi-Agent Collaboration](https://mlsanity.com/paper/2505.15047/) (2025)
- [Sparks of Science: Hypothesis Generation Using Structured Paper Data](https://mlsanity.com/paper/2504.12976/) (2025)
- [Can Large Language Models Unlock Novel Scientific Research Ideas?](https://mlsanity.com/paper/2409.06185/) (2024)
- [MOOSE-Chem2: Exploring LLM Limits in Fine-Grained Scientific Hypothesis Discovery via Hierarchical Search](https://mlsanity.com/paper/2505.19209/) (2025)
- [MIR: Methodology Inspiration Retrieval for Scientific Research Problems](https://mlsanity.com/paper/2506.00249/) (2025)
- [MOOSE-Chem3: Toward Experiment-Guided Hypothesis Ranking via Simulated Experimental Feedback](https://mlsanity.com/paper/2505.17873/) (2025)

## Built on by (most cited first, 4 of 4)

- [MOOSE-Copilot: A Web-Based Interactive Assistant for Unified Exploratory and Fine-Grained Scientific Hypothesis Discovery](https://mlsanity.com/paper/2605.29475/) (2026)
- [IdeaTrail: Full-Process Agent Trajectories for Scientific Ideation](https://mlsanity.com/paper/2607.10144/) (2026)
- [SGHA: Evidence-Grounded Research Problem Discovery with Local Language Models](https://mlsanity.com/paper/2608.17501/) (2026)
- [Priced Guidance: Can Language Models Generate Future Research Ideas?](https://mlsanity.com/paper/2610.04976/) (2026)

## Abstract (arXiv)

While large language models (LLMs) show promise in scientific discovery, existing research focuses on inference or feedback-driven training, leaving the direct modeling of the generative reasoning process, P(hypothesis|background) (P(h|b)), unexplored. We demonstrate that directly training P(h|b) is mathematically intractable due to the combinatorial complexity (O(Nk)) inherent in retrieving and composing inspirations from a vast knowledge base. To break this barrier, we introduce MOOSE-Star, a unified framework that enables tractable and scalable training of P(h|b), while supporting more scalable inference. In the best case, MOOSE-Star reduces complexity from exponential to logarithmic (O(log N)) by (1) training on decomposed subtasks derived from the probabilistic equation of discovery, (2) employing motivation-guided hierarchical search to enable logarithmic retrieval and prune irrelevant subspaces, and (3) utilizing bounded composition for robustness against retrieval noise. To facilitate this, we release TOMATO-Star, a dataset of 108,717 decomposed papers (38,400 GPU hours) for training. Empirically, MOOSE-Star scales continuously with training data and inference budget, whereas direct brute-force sampling hits a complexity wall.