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

2026-03-04

AI Summary

This work addresses the challenge of directly training models for scientific hypothesis generation, formalized as $P(\text{hypothesis}|\text{background})$, which is hindered by combinatorial complexity scaling as $O(N^k)$. To overcome this, we propose the MOOSE-Star framework, which leverages probabilistic equation decomposition, motivation-guided hierarchical search, and bounded combinatorial mechanisms to reduce complexity from exponential to logarithmic. This enables, for the first time, end-to-end trainable modeling of the hypothesis generation process. Evaluated on TOMATO-Star—a large-scale dataset of 108,717 decomposed scientific papers—MOOSE-Star breaks through the “complexity wall” inherent in conventional brute-force sampling, facilitating efficient, scalable generation of scientific discoveries and supporting continual test-time expansion.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

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, $P(\text{hypothesis}|\text{background})$ ($P(h|b)$), unexplored. We demonstrate that directly training $P(h|b)$ is mathematically intractable due to the combinatorial complexity ($O(N^k)$) inherent in retrieving and composing inspirations from a vast knowledge base. To break this barrier, we introduce MOOSE-Star, a unified framework enabling tractable training and 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. Furthermore, we show that while brute-force sampling hits a ''complexity wall,'' MOOSE-Star exhibits continuous test-time scaling.

Problem

• scientific discovery
• generative reasoning
• combinatorial complexity
• tractable training
• large language models

Innovation

• tractable training
• generative reasoning
• hierarchical search
• complexity reduction
• scientific discovery