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, $P(\text{hypothesis}|\text{background})$ ($P(h|b)$), 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."

Scientific discovery often requires combining ideas from very different fields—much as the chain rule from calculus inspired the backpropagation algorithm in neural networks. Recent large language models (LLMs) show promise in helping researchers make such cross-disciplinary leaps, but directly teaching an LLM to do so turns out to be mathematically infeasible: the model would have to consider an astronomical number of possible combinations of ideas drawn from the entire scientific literature. This paper introduces MOOSE-Star, a training framework that sidesteps this difficulty by breaking the discovery process into smaller, manageable steps. Instead of asking the model to invent a complete hypothesis in one shot, MOOSE-Star teaches it to (1) plan a research direction, (2) locate a relevant prior idea in the literature, and (3) combine that idea with the research question to form one increment of a hypothesis. Repeating these steps builds up a full discovery. We also release TOMATO-Star, a dataset of over 108,000 scientific papers processed into this structured form, and show that the resulting trained models keep improving as we add more training data or computing budget—whereas the standard end-to-end approach quickly hits a wall it cannot scale past.