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

Zonglin Yang; Lidong Bing

cs.LGMar 4, 2026

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

Authors: Zonglin Yang, Lidong Bing

Organizations: MiroMind AI

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.

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\times

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/ $1\times$ 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/ $2\times$ 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\times

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).

$\bm{k}$	BF	HC	IR
1	9.46% (1,674 / 17,692)	18.88% (51,564 / (273,175 $\,\bm{\times 1}$ ))	27.84% (91,634 / (329,178 $\,\bm{\times 1}$ ))
2	1.17% (393 / 33,558)	22.53% (208,723 / (463,230 $\,\bm{\times 2}$ ))	25.48% (295,455 / (579,769 $\,\bm{\times 2}$ ))
3	0.23% (20 / 8,683)	25.75% (90,900 / (117,663 $\,\bm{\times 3}$ ))	24.22% (109,224 / (150,351 $\,\bm{\times 3}$ ))
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 (

\geq 8/12

); IR is judged by retrieval correctness.

Panel of Figure 2 — Figure 2: Scaling laws of MOOSE-Star: (a) IR and (b) HC.

Panel of Figure 3 — 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

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
$\bm{k}$	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\leq 3

. Later steps condition on

h_{j-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 $h_{j-1}$	1996	29.2%	2.64	1.96	1.56	6.16
HC step $1$ with $h_{j-1}$	1998	37.9%	2.68	2.14	1.79	6.62
HC step $2$ without $h_{j-1}$	1996	32.8%	2.64	2.04	1.56	6.24
HC step $2$ with $h_{j-1}$	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

h_{j-1}

, evaluated on the same

500

k{=}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

\geq 8/12

threshold. For BF, each generation is scored separately against every

\Delta h_{j}^{*}

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
$\leq 25$	$\geq 4$	14.0%	17.0%	19.0%	19.0%	18.5%	18.5%	18.5%
	$\geq 5$	10.0%	14.0%	18.0%	18.5%	17.0%	18.5%	18.0%
	$\geq 6$	8.0%	10.0%	14.5%	16.5%	14.0%	16.0%	16.0%
	$\geq 7$	2.0%	4.5%	10.5%	16.0%	13.0%	16.0%	14.5%
	$\geq 8$	0.0%	0.5%	5.5%	12.5%	7.5%	11.0%	8.5%
	$\geq 9$	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

\leq 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.

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