MOOSE-Star: Scalable Scientific Discovery

• MOOSE-Star is a unified framework that decomposes hypothesis generation into tractable subtasks, enabling efficient training and inference in scientific discovery.
• It employs motivation-guided hierarchical search to restrict the inspiration space, reducing the combinatorial complexity from O(N^k) to O(kN) and enhancing retrieval efficiency.
• Robust composition via bounded tolerance sets mitigates retrieval noise, yielding scalable performance validated on the large-scale TOMATO-Star dataset.

MOOSE-Star denotes a unified framework for enabling tractable training and scalable inference in scientific discovery tasks, specifically addressing the problem of directly modeling the generative reasoning process $P(\text{hypothesis}|\text{background})$, abbreviated $P(h|b)$. Traditional approaches to $P(h|b)$ confront mathematical intractability due to the combinatorial complexity of retrieving and composing sequences of “inspirations” from large scientific corpora. MOOSE-Star overcomes this by introducing: (i) principled decomposition into tractable subtasks, (ii) motivation-guided hierarchical search over the inspiration space, and (iii) bounded composition for robustness to retrieval noise. The framework is supported by the large-scale TOMATO-Star dataset of decomposed scientific papers and demonstrates superior scaling and robustness compared to brute-force or traditional sampling baselines (Yang et al., 4 Mar 2026).

1. Motivation and Mathematical Intractability

The scientific discovery process, when modeled as conditional generation ($P(h|b)$), is inherently combinatorial: given a background $b$ and a hypothesis $h$, generating $h$ requires assembling a sequence of $k$ inspirations $(i_1, ..., i_k)$ from a corpus of size $N$. The end-to-end space of retrievals is $P(h|b)$0, leading to $P(h|b)$1 even for small $P(h|b)$2. For $P(h|b)$3, $P(h|b)$4, the search space quickly reaches $P(h|b)$5, making direct end-to-end training mathematically ill-posed and computationally infeasible. This exponential barrier manifests as a "complexity wall" in brute-force sampling, where success rates saturate far below 100% and scale poorly with $P(h|b)$6 (Yang et al., 4 Mar 2026).

2. Decomposition via the Probabilistic Equation of Discovery

MOOSE-Star circumvents intractable global search using the probabilistic equation of discovery, which factorizes $P(h|b)$7 under a Markov assumption:

$P(h|b)$8

where $P(h|b)$9 and $P(h|b)$0. Each step involves (1) retrieving the next inspiration $P(h|b)$1 given current context $P(h|b)$2 and (2) composing the delta-hypothesis $P(h|b)$3. The overall complexity reduces from $P(h|b)$4 to $P(h|b)$5, making sequential retrieval and local composition feasible at scale.

3. Motivation-Guided Hierarchical Search

Prior to inspiration retrieval, the model produces a lightweight “motivation” $P(h|b)$6 that encodes high-level intent (e.g., “seek a catalyst mechanism”). This narrows search to a subset $P(h|b)$7. Motivated retrieval is performed over a pre-indexed semantic search tree: SPECTER2 embeddings for every paper are clustered into a balanced $P(h|b)$8-ary (typically $P(h|b)$9) tree via recursive $P(h|b)$0-means. Best-first traversal uses a priority queue, scoring each candidate node $P(h|b)$1 via normalized local probabilities and path scores derived from log-probabilities in the IR model. Search complexity per step is $P(h|b)$2 (motivation) + $P(h|b)$3 (tree traversal) + $P(h|b)$4 (bounded composition), yielding total per-instance cost $P(h|b)$5 in the ideal (balanced) regime.

4. Bounded Composition and Robustness to Retrieval Noise

Exact-match training for hypothesis composition (HC) modules is brittle to retrieval noise. MOOSE-Star addresses this by defining a tolerance set $P(h|b)$6 containing $P(h|b)$7 papers with cosine similarity $P(h|b)$8 to the ground-truth inspiration $P(h|b)$9. During training and inference, any $b$0 suffices, dropping IR cost from $b$1 to $b$2 and shifting composition cost from $b$3 to $b$4. Robustness is empirically validated by training on proxy inspirations of increasing difficulty (varied similarity bands), with rejection-sampling fine-tuning to expand the semantic radius for successful composition.

5. TOMATO-Star Dataset Construction and Workflow

MOOSE-Star is trained using TOMATO-Star, a dataset comprising 108,717 open-access biomedical, chemistry, and cognitive science papers (Jan 2020–Oct 2025), decomposed into (background, hypothesis, inspirations) tuples. Pipeline stages:

• Markdown conversion (MinerU)
• Automated chain-of-thought (CoT) decomposition to extract background $b$5, delta-hypotheses $b$6, and inspiration sets from citations (using DeepSeek-R1 and R1-distilled-Qwen-32B)
• Annotation of each hypothesis with structured fields: Motivation, Mechanism, Methodology
• Strict quality controls for necessity, sufficiency, and non-redundancy Distribution: 152K IR training and 97K HC training examples; average step count $b$7.

6. Experimental Results and Performance

Inspiration Retrieval (IR)

• Baseline R1-distilled-Qwen-7B (zero-shot): 28.4% accuracy
• MS-IR-7B (CoT fine-tuned): 54.4% (Table 1)

Hypothesis Composition (HC)

• Baseline: M3 score 4.34/12
• MS-HC-7B (rejection sampling, bounded proxies): 5.08/12; further improved with tolerance-augmented data (Tables 2–3)

Search Efficiency and Scaling

• Hierarchical search: average 67.8 retrieval calls/instance with best-first, 63.05 calls with detailed motivation (vs. 218 for tournament/baseline; see Table 4)
• Log-linear scaling with training size ($b$8–$b$9 examples); both IR and HC tasks remain tractable as data scales

Robustness and Scaling at Test Time

• MOOSE-Star test-time performance: 100% success at ~6K inference calls (109 test cases)
• Brute-force sampling plateaus at 41.3% overall, dropping rapidly for $h$0 (36%) and $h$1 (8%) (Figure 1)

7. Broader Implications, Limitations, and Extensions

By decomposing hypothesis generation into motivation planning, hierarchical retrieval, and local robust composition, MOOSE-Star operationalizes the generative process of scientific reasoning at tractable computational cost, facilitating scalable and robust scientific discovery automation. The motivation layer interfaces with human-in-the-loop workflows, allowing domain experts to guide search via high-level goals. Limitations include dependence on embedding quality/tree balance—errors at high-level nodes can irrevocably exclude correct inspirations—and the fixed size $h$2 for tolerance sets, with dynamic adaptation yet unexplored. Planned extensions involve adaptive tree structures, integration of experimental data, multi-modal inspirations, and ontology-driven augmentation (Yang et al., 4 Mar 2026).