Principia: Test-Time Hypotheses to Principle Construction for Scientific Discovery

Dongki Kim; Sangwoo Park; Jinheon Baek; Soyeong Jeong; Sung Ju Hwang

cs.LGOct 23, 2026

Principia: Test-Time Hypotheses to Principle Construction for Scientific Discovery

Authors: Dongki Kim, Sangwoo Park, Jinheon Baek, Soyeong Jeong, Sung Ju Hwang

Organizations: KAIST

Abstract

Scientific discovery requires identifying the scientific principles underlying observed phenomena to guide further investigation. As these empirical principles are often unknown in complex discovery processes, they are constructed via a hypotheses-to-principle pipeline to obtain recurring causalities from progressively accumulated observations during test-time discovery. However, constructing this knowledge requires substantial domain expertise, time, and effort, making this translation stage a bottleneck for scientific discovery. To address this limitation, we propose Principia, an LLM-based framework that constructs and continually refines scientific principles at test time. Drawing on how human researchers develop principles, Principia forms comparative causal hypotheses from related inputs and their observed outcomes, then synthesizes recurring relationships across these hypotheses into inductive principles. By applying the constructed hypotheses and inductive principles to the task, it obtains new observations, revises the hypotheses used based on these new observations, and reconstructs principles from the updated hypotheses, allowing scientific knowledge to continuously evolve throughout test-time discovery. Across benchmarks spanning molecular optimization, protein engineering, gene perturbation, and molecular property prediction, Principia outperforms baselines relying on internal knowledge, external sources, or experience summaries, while generating principles that are plausible and consistent with the scientific literature, demonstrating its effectiveness in constructing and refining task-specific hypotheses and principles at test time for scientific discovery. Our code is available at https://github.com/DongkiKim95/Principia.

Figures & tables

Figure 1: Scientific principle construction as a bottleneck in scientific discovery. As experimental observations accumulate, researchers formulate tentative explanations of individual outcomes, generalize recurring relationships across observations into scientific principles, and reassess these explanations in light of new observations. The resulting principles guide further investigation, forming an iterative discovery cycle. However, this process requires substantial domain expertise, time, labor, and financial resources, limiting the pace of scientific discovery.

Figure 2: Overview of Principia . Given scientific inputs and their observed outcomes, Principia forms comparative causal hypotheses that explain how input characteristics may contribute to the outcomes. It groups related inputs through similarity-based clustering and inductively generalizes their associated hypotheses into scientific principles. Retrieved hypotheses and principles guide subsequent prediction or candidate generation. New observations are then used to revise the hypotheses involved, and the updated hypotheses support principle reconstruction, forming a continuous cycle of scientific knowledge construction and application.

	JNK3		GSK3 $\beta$		Median1		Median2		Valsartan Smarts		Avg.
Methods	Avg@100	AUC@10	Avg@100	AUC@10	Avg@100	AUC@10	Avg@100	AUC@10	Avg@100	AUC@10	Avg@100	AUC@10
REINVENT	0.164	0.160	0.438	0.368	0.202	0.187	0.164	0.167	0.000	0.000	0.194	0.176
Memory-Aug	0.282	0.211	0.535	0.414	0.213	0.189	0.178	0.167	0.000	0.000	0.242	0.196
Graph GA	0.316	0.290	0.352	0.315	0.175	0.177	0.162	0.167	0.000	0.000	0.201	0.190
[0.5pt/1pt] MolLEO ∗	0.266	0.273	0.400	0.341	0.293	0.280	0.197	0.189	0.018	0.028	0.235	0.222
ExLLM ∗	0.245	0.227	0.438	0.363	0.293	0.281	0.198	0.190	0.096	0.188	0.254	0.250

Table 1: Comparison of Principia with ML-based and LLM-based optimization baselines on molecular optimization tasks. We report averaged values over three different runs for each metric. ∗ denotes methods reimplemented for our evaluation setting. Avg. denotes the mean of each metric across all tasks. The best results are highlighted in bold .

	Protein Sequence Engineering						Gene Perturbation
	Syn-3bfo		AAV		GB1		Scharenberg22		IFNG		Avg.
Methods	Avg@50	AUC@10	Avg@50	AUC@10	Avg@50	AUC@10	Hit Ratio	AUC@10	Hit Ratio	AUC@10	AUC@10
MolLEO ∗	-0.374	0.737	0.664	0.524	0.201	0.245	0.270	0.606	0.107	0.717	0.566
ExLLM ∗	-0.286	0.738	0.660	0.522	0.236	0.277	0.277	0.605	0.109	0.735	0.575
PiFlow ∗	-32.149	0.079	0.049	0.072	0.111	0.188	0.289	0.557	0.111	0.682	0.316
WebSearch ∗	-0.367	0.738	0.659	0.527	0.197	0.233	0.226	0.533	0.110	0.702	0.547

Table 2: Comparison of Principia with LLM-based optimization baselines on protein sequence engineering and gene perturbation tasks. We report averaged values over three different runs for each metric. ∗ denotes methods reimplemented for our evaluation setting. Avg. denotes the mean AUC@10 across all tasks. The best results are highlighted in bold .

	DILI		hERG		Ames		Skin		CYP1A2		CYP2C9		CYP2D6		CYP3A4		Avg.
Methods	Acc	F1	Acc	F1	Acc	F1	Acc	F1	Acc	F1	Acc	F1	Acc	F1	Acc	F1	Acc	F1
Direct	52.43	44.11	51.33	37.27	58.33	57.51	45.12	43.54	63.33	60.18	67.33	64.73	68.33	66.64	60.00	54.26	58.28	53.53
[0.5pt/1pt] Few-shot ( $k{=}1$ )	59.72	54.68	58.67	53.16	59.33	59.02	52.03	51.30	66.33	64.98	68.00	66.95	69.33	68.93	59.00	57.21	61.55	59.53
Few-shot ( $k{=}3$ )	62.15	57.95	62.00	59.76	62.33	61.03	52.85	51.49	64.67	63.06	70.33	69.75	71.33	71.31	61.00	59.63	63.33	61.75
Few-shot ( $k{=}5$ )	62.85	57.82	64.67	62.83	62.00	60.53	50.81	49.62	67.67	66.00	66.67	66.18	71.67	71.53	62.00	60.42	63.54	61.87
Few-shot ( $k{=}7$ )	62.15	57.74	64.00	62.60	62.33	60.94	50.81	48.40	66.33	64.65	69.67	69.42	71.67	71.65	64.67	62.97	63.95	62.30

Table 3: Comparison of Principia with direct prediction, few-shot prediction, and knowledge-augmented baselines on molecular property prediction tasks. We report averaged values over three different runs for each metric. The best results are highlighted in bold .

(A) Comparative evidence	(B) Causal hypotheses	(C) Inductive principle
Mutagenic (+) $\rightarrow$ Mutagenic (+)	The shared aryl ether epoxide motif, … is the most plausible mutagenicity driver because it is retained in both compounds.	Positive pattern Epoxide/oxirane-bearing aryl ether motifs recur as a likely mutagenicity driver, especially Ar-O-CH2-CH … Negative pattern More polar aminoalcohol side chains … are often tolerated when they do not contain a strained electrophile.
Mutagenic (+) $\rightarrow$ Non-mutagenic ( $-$ )	mutagenicity is driven by its epoxide/oxirane-like ring … has open-chain alcohol/amine side chain , which is far less prone to covalent DNA damage …

Table 5: An example of comparative hypotheses and an induced principle. Matching colors link epoxide rings (blue), phenoxy groups (green), and aminoalcohol side chains (red) to their descriptions. Arrows indicate reference-to-target comparisons, and labels are dataset observations.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Reference & Target	Original Hypothesis
$\rightarrow$ Non-inhibitor Inhibitor	Compared with the reference’s thiourea linker , the target’s benzamide linker and substituted aromatic scaffold may contribute to CYP2C9 inhibition.
New Observation	Revised Hypothesis
Predicted: Inhibitor Observed: Non-inhibitor	An amide motif alone does not reliably explain inhibition; its role must be considered in the context of the surrounding aromatic arrangement .

Appendix

Table 8: Hypothesis revision via new observations. A comparison between a non-inhibitor and an inhibitor yields comparative causal hypotheses about CYP2C9 inhibition. These hypotheses were retrieved when predicting a new molecule, whose observed label differed from the prediction. After incorporating new observations, including this case, the revised hypotheses explicitly limit the explanatory role of the amide motif alone. Matching colors link molecular features to their mentions in the text: thiourea (red), amide (blue), and aromatic rings with selected substituents (green). Hypothesis text is summarized; the revision qualifies the existing explanation rather than replacing it entirely.

Panel of Figure 8 — Figure 8: Additional Top-100 average score trends for Principia across different backbone models and optimization tasks. For each task and backbone model, lines represent the mean fitness values over three random seeds, and shaded regions indicate the standard deviation.

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