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

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(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.

• 1

  Training LLMs directly on P(hypothesis|background) is mathematically intractable due to exponential combinatorial complexity O(N^k).

• 2

  MOOSE-Star decomposes the problem into sequential retrieval and composition steps, reducing complexity from exponential to logarithmic O(log N).

• 3

  The framework uses hierarchical search, bounded composition, and motivation planning to enable scalable training on 108,717 decomposed papers.