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.

翻译：尽管大语言模型在科学发现中展现出潜力，但现有研究集中于推理或反馈驱动训练，未探索生成推理过程 $P(\text{假设}|\text{背景})$（$P(h|b)$）的直接建模。我们证明，由于从庞大知识库中检索并组合灵感的组合复杂度（$O(N^k)$），直接训练 $P(h|b)$ 在数学上难以实现。为突破这一瓶颈，我们提出统一框架MOOSE-Star，实现可驾驭训练与可扩展推理。最佳情况下，MOOSE-Star通过以下方式将复杂度从指数级降至对数级（$O(\log N)$）：（1）基于科学发现的概率方程，对子任务进行分解训练；（2）采用动机引导的分层搜索实现对数级检索并剪枝无关子空间；（3）利用有界组合机制应对检索噪声。为此，我们发布数据集TOMATO-Star（含108,717篇分解论文，消耗38,400 GPU小时）用于训练。此外，我们证明蛮力采样会遭遇"复杂度墙"，而MOOSE-Star则展现出持续的测试时缩放能力。