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(Nk)) 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(logN)) 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.
Figures & tables
Figure 1: Bounded Composition. The concentric circles around i∗ represent similarity thresholds that define the bounded space M .
Model
Accuracy
Frontier Models
GPT-4o-mini
41.99%
Claude-Sonnet-4.6
45.02%
DeepSeek-R1
45.11%
GPT-4o
48.37%
Gemini-3-Flash
51.44%
Table 1: Inspiration retrieval results.
Model
Total
Mot
Mec
Met
Length
Frontier Models
GPT-4o-mini
5.18
2.26
1.64
1.28
175.29
GPT-4o
5.99
2.43
1.95
1.60
264.93
DeepSeek-R1
6.42
2.54
2.10
1.77
264.46
Gemini-3-Flash
6.42
2.48
2.16
1.79
351.79
Gemini-3-Pro
6.70
2.59
2.26
1.85
300.86
Table 2: Hypothesis composition performance given the ground-truth inspiration i∗ , judged by GPT-4o under the M3 rubric . “Total” aggregates the scores for Motivation (Mot), Mechanism (Mec), and Methodology (Met). “w/ n× bounded” indicates the model was trained with n additional copies of bounded composition data.
Easy (E)
Medium (M)
Hard (H)
Model
Total
Mot
Mec
Met
Total
Mot
Mec
Met
Total
Mot
Mec
Met
R1-Distilled-Qwen-7B
2.72
1.50
0.70
0.51
2.27
1.35
0.55
0.38
2.00
1.24
0.46
0.31
MS-HC-7B
3.10
1.63
0.81
0.66
2.59
1.46
0.61
0.53
2.39
1.38
0.54
0.48
w/ 1× bounded
3.09
1.61
0.81
0.67
2.72
1.48
0.66
0.57
2.42
1.39
0.55
0.47
w/ 2× bounded
3.18
1.67
0.83
0.68
2.74
1.51
0.66
0.57
2.56
1.45
0.58
0.53
MS-7B
3.37
1.72
0.90
0.75
2.86
1.55
0.69
0.62
2.78
1.52
0.66
0.60
Table 3: Hypothesis composition performance under inspiration noise, judged by GPT-4o under the M3 rubric . The tiers Easy (E), Medium (M), and Hard (H) correspond to the semantic similarity of the retrieved proxy inspiration to the ground truth. “w/ n× bounded” indicates the model was trained with n additional copies of bounded composition data.
Search Method
IR inference calls
Proposed Rank
Tournament Search
218.00
987.76
Hierarchical Search
67.78
813.40
w/ motivation (simple)
63.80
767.64
w/ motivation (detailed)
63.05
742.50
Table 4: Efficiency and accuracy of hierarchical search variants compared to a tournament baseline. IR inference calls : Average number of IR model queries required to identify the ground-truth inspiration. Proposed Rank : The average position of the ground-truth inspiration in the retrieved list (lower is better).
k
BF
HC
IR
1
9.46% (1,674 / 17,692)
18.88% (51,564 / (273,175 ×1 ))
27.84% (91,634 / (329,178 ×1 ))
2
1.17% (393 / 33,558)
22.53% (208,723 / (463,230 ×2 ))
25.48% (295,455 / (579,769 ×2 ))
3
0.23% (20 / 8,683)
25.75% (90,900 / (117,663 ×3 ))
24.22% (109,224 / (150,351 ×3 ))
Total
3.48% (2,087 / 59,933)
22.62% (351,187 / 1,552,624)
25.59% (496,313 / 1,939,769)
Table 5: Per-attempt pass rates of brute-force end-to-end (BF) vs. decomposed subtasks (HC, IR), all generated by R1-Distilled-Qwen-32B . BF and HC are evaluated with the same model under the M3 rubric ( ≥8/12 ); IR is judged by retrieval correctness.
Figure 2: Scaling laws of MOOSE-Star: (a) IR and (b) HC.
Figure 3: Test-time scaling behavior of MOOSE-Star ( MS-7B ) versus brute-force sampling ( R1-Distilled-Qwen-7B ).
Appendix figures & tables7 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 4: MOOSE-Star Concept Figure
Model
Original
All Random
All Hard
Decoy Cluster
Frontier Models
GPT-4o-mini
41.99
77.43
41.00
77.43
Claude-Sonnet-4.6
45.02
91.44
58.69
92.38
DeepSeek-R1
45.11
75.29
43.84
75.64
GPT-4o
48.37
82.18
49.43
82.02
Gemini-3-Flash
51.44
78.86
48.05
80.84
Appendix
Table 6: IR ablation study: accuracy (%) under modified negative construction.
BF
HC
k
Mot
Mec
Met
Total
Mot
Mec
Met
Total
1
2.05
0.91
0.90
3.86
2.48
1.83
1.47
5.77
2
1.49
0.74
0.70
2.93
2.28
1.72
1.52
5.52
3
1.27
0.78
0.66
2.71
2.25
1.76
1.55
5.56
Appendix
Table 7: Per-dimension M3 scores by inspiration depth k . BF scores drop sharply from single-step to multi-step cases, while HC remains comparatively stable.
Step j
n
Pass%
Mot
Mec
Met
Total
0
854,067
20.22%
2.44
1.76
1.46
5.66
1
580,894
24.71%
2.13
1.72
1.58
5.43
2
117,663
29.67%
2.19
1.80
1.65
5.64
Appendix
Table 8: HC per-attempt scores by step index j across PMIDs with k≤3 . Later steps condition on hj−1 ; the mild pass-rate increase is mainly associated with methodology, while total scores remain similar.
Condition
n
Pass%
Mot
Mec
Met
Total
With background survey context
HC step 0 baseline
1998
33.7%
2.95
2.00
1.62
6.57
HC step 1 without hj−1
1996
29.2%
2.64
1.96
1.56
6.16
HC step 1 with hj−1
1998
37.9%
2.68
2.14
1.79
6.62
HC step 2 without hj−1
1996
32.8%
2.64
2.04
1.56
6.24
HC step 2 with hj−1
1999
44.2%
2.75
2.22
1.83
6.80
Appendix
Table 9: Controlled ablation on the roles of the background survey context and the previous hypothesis state hj−1 , evaluated on the same 500k=3 PMIDs. The research question is retained in all conditions. All samples in this diagnostic are regenerated by R1-Distilled-Qwen-32B and scored by Gemini-3-Flash using the Total ≥8/12 threshold. For BF, each generation is scored separately against every Δhj∗ for the per-delta average, while joint pass requires all three comparisons to pass.
Rank
HC Score
MS-HC-7B
MS-7B
GPT-4o
GPT-5.4
DeepSeek-R1
Claude-Sonnet-4.6
Gemini-3-Pro
≤25
≥4
14.0%
17.0%
19.0%
19.0%
18.5%
18.5%
18.5%
≥5
10.0%
14.0%
18.0%
18.5%
17.0%
18.5%
18.0%
≥6
8.0%
10.0%
14.5%
16.5%
14.0%
16.0%
16.0%
≥7
2.0%
4.5%
10.5%
16.0%
13.0%
16.0%
14.5%
≥8
0.0%
0.5%
5.5%
12.5%
7.5%
11.0%
8.5%
≥9
0.0%
0.0%
2.0%
8.0%
3.0%
4.0%
4.0%
Appendix
Table 10: ”Retrieval success” denotes the fraction of all 200 test cases whose ground-truth inspiration is retrieved within Rank ≤K . Other entries report the fraction of all 200 test cases for which this retrieval condition holds and the HC module, when conditioned on the ground-truth inspiration, reaches the corresponding score threshold.
Step
Ground-Truth Inspiration
DOI
Retrieval Rank
0
Underlying Mechanism of Lysosomal Membrane Permeabilization in CNS Injury: A Literature Review ( Molecular Neurobiology , 2024)
10.1007/s12035-024-04290-6
12 / 3035
1
TFEB links autophagy to lysosomal biogenesis (Settembre et al., Science , 2011)
10.1126/science.1204592
1 / 3035
Appendix
Table 11: Retrieved ground-truth inspirations for the temporally held-out TREM2 case. For this k=2 example, MOOSE-Star ranks the two ground-truth inspirations at 12/3035 and 1/3035, respectively.
Scientific ideation aims to propose novel solutions within a given scientific context. Existing LLM-based agentic approaches emulate human research workflows, yet inadequately model scientific reasoning, resulting in surface-level conceptual recombinations that lack technical depth and scientific grounding. To address this issue, we propose MoRI (Motivation-grounded Reasoning for Scientific Ideation), a framework that enables LLMs to explicitly learn the reasoning process from research motivations to methodologies. The base LLM is initialized via supervised fine-tuning to generate a research motivation from a given context, and is subsequently trained under a composite reinforcement learning reward that approximates scientific rigor: (1) entropy-aware information gain encourages the model to uncover and elaborate high-complexity technical details grounded in ground-truth methodologies, and (2) contrastive semantic gain constrains the reasoning trajectory to remain conceptually aligned with scientifically valid solutions. Empirical results show that MoRI consistently outperforms strong commercial LLMs and complex agentic baselines across multiple dimensions, including novelty, technical rigor, and feasibility. The code is available on GitHub.
Chenyang Gu, Jiahao Cheng, Meicong Zhang +3
School of Economics and Management, East China Normal University
Open-ended scientific discovery with large language models (LLMs) increasingly operates as a long-horizon loop of hypothesis search and verification, where a reward signal guides which hypotheses to test next. A notable recent example is AutoDiscovery, which uses "Bayesian surprise" - the belief shift an LLM undergoes after observing evidence for a hypothesis - as both a discovery metric and a reward for search. We first observe that AutoDiscovery treats surprisal as a static quantity, while surprisal in human reasoning is non-stationary - it is defined relative to beliefs that evolve with experience, a prerequisite for continual scientific discovery. We address this mismatch with evidence-informed LLM beliefs: priors updated with evidence from previous hypotheses to compute non-stationary surprisal for new hypotheses. We compare in-context belief-updating mechanisms and find that embedding-based retrieval-augmented generation over prior discoveries best anticipates eventual posteriors, identifying 37.5% of static surprisals as spurious. We then modify search to avoid these spurious rewards and prioritize hypotheses that remain surprising under non-stationary beliefs. Concretely, we introduce two complementary changes to the original search procedure: belief-update filtering and diversity maximization. Across five discovery domains, our method increases accumulated non-stationary surprisal by 30.62% on average compared to the original search procedure, demonstrating that continual scientific discovery with LLMs requires not only better belief measurement but also search procedures that avoid redundancy and encourage diversity.
Dhruv Agarwal, Reece Adamson, Andrew McCallum +3
University of Massachusetts Amherst · Allen Institute for AI
Large Language Models (LLMs) trained on extensive scientific research are increasingly integrated as assistants for scientific discovery. However, most research papers omit the fine-grained cognitive process of examining constraints, failed alternatives, and iterative decisions required to achieve the desired goal. Such cognitive processes are vital for real-world scientists working toward specific goals under constraints. In this paper, we show that LLMs, when trained to produce such cognitive traces, perform better as scientific discovery assistants than when trained solely on scientific literature. We propose COGTRL, a trajectory-level reinforcement learning framework that trains LLMs to emulate cognitively grounded reasoning by jointly optimizing cognitive traces and the scientific steps produced in an interleaved manner. Across two 3B-parameter models and two scientific domains (AI and Materials Science), COGTRL improves method quality by an average of 7.85 points over comparable 3B model baselines and achieves competitive performance relative to 70B parameter models. Moreover, analysis by domain experts shows a preference for methods generated by COGTRL over the baselines.