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

TL;DR

MOOSE-Star introduces a scalable framework for scientific discovery modeling that reduces complexity from exponential to logarithmic, enabling efficient training and inference in large knowledge bases.

Contribution

It presents a novel approach that makes training $P(h|b)$ tractable and scalable by decomposing tasks, hierarchical search, and bounded composition, supported by a large dataset.

Findings

MOOSE-Star scales with training data and inference budget.

Direct brute-force sampling faces a complexity wall.

The framework achieves logarithmic complexity in retrieval.

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 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.