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

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

arXiv:2610.32195v1cs.LGcs.AI

TL;DR

Scientific principles can be unknown in complex discovery, while constructing them from observations requires substantial expertise and effort. PRINCIPIA forms comparative hypotheses, generalizes them into principles, and revises this knowledge as new observations arrive. Across several scientific tasks, it outperforms knowledge- and experience-based baselines, with analyses also reporting fewer oracle evaluations than an experience-summary baseline.

  • Problem

    Constructing and continually refining empirical principles from accumulated observations remains underexplored, and doing so requires substantial expertise, time, and effort.

    Source: §1 · pp. 1–2

  • Method

    PRINCIPIA compares related inputs and outcomes to form hypotheses, generalizes recurring relationships into principles, and revises hypotheses using new observations.

    Source: §1 · p. 2

  • Results

    PRINCIPIA outperforms baselines relying on internal knowledge, experience summaries, or external knowledge across molecular, protein, and gene optimization and molecular property prediction; it matches ExLLM’s final performance with approximately 55% fewer oracle evaluations.

    Source: §1 · p. 2, §4.3 · p. 9, §5 · p. 10

  • Takeaways & Limitations

    The results support test-time hypotheses-to-principle construction as a way for accumulated observations to continually inform subsequent scientific investigation.

    Source: §5 · p. 10

Abstract

from arXiv · show

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.

1 INTRODUCTION

Scientific principles are often unknown in complex discovery, and constructing them from observations demands substantial expertise and effort. PRINCIPIA builds and revises principles from accumulated observations; the paper reports stronger benchmark performance and reduced experimental budgets.

1 INTRODUCTION

  • Constructing empirical principles from observations requires substantial domain expertise, time, and effort, slowing their translation into scientific knowledge.The paper describes this translation as a bottleneck in scientific discovery.Source: §1 · p. 1
  • Principle construction and continual refinement from accumulated observations remain underexplored despite broader LLM efforts in scientific research.The paper identifies two challenges: single input–outcome pairs provide limited evidence for distinguishing explanations, and sparse observations can yield incomplete hypotheses that need revision as evidence grows.Source: §1 · p. 2
  • PRINCIPIA compares related inputs and outcomes to form causal hypotheses, generalizes recurring relationships into principles, then revises hypotheses and reconstructs principles using new observations.The resulting hypotheses and principles guide subsequent prediction or optimization.Source: §1 · p. 2
  • PRINCIPIA outperforms baselines relying on internal knowledge, experience summaries, or external knowledge across molecular, protein, and gene optimization and molecular property prediction.Qualitative analyses also find its hypotheses capture input–outcome relationships and its principles are consistent with scientific literature.Source: §1 · p. 2

2 RELATED WORKS

Prior work automates stages of discovery, searches candidate spaces, or augments systems with external knowledge and summarized experience. PRINCIPIA instead induces reusable causal principles from observations accumulated during test-time discovery.

Automated Scientific Discovery and Optimization

  • Automated discovery spans tools for idea generation and end-to-end AI scientists, while candidate-search methods use generative models or LLMs to explore scientific spaces.The cited work also uses LLMs as surrogate operators in evolutionary algorithms for iterative search.Source: §2 · p. 3

Knowledge-Augmented Scientific Discovery

  • PRINCIPIA addresses the underexplored task of constructing reusable causal principles from test-time observations, rather than relying only on retrieved literature or summarized experience.It forms explicit hypotheses about how input characteristics may contribute to outcomes and generalizes recurring relationships into principles.Source: §2 · p. 3
  • External literature, knowledge bases, search agents, and summarized experience have been used to inform scientific discovery and subsequent optimization.Other approaches reuse preconfigured knowledge or construct memories from earlier discoveries or heterogeneous tasks.Source: §2 · p. 3

3 PRINCIPIA: TEST-TIME HYPOTHESES TO PRINCIPLE CONSTRUCTION

PRINCIPIA uses accumulated observations to build hypotheses and principles that guide prediction or optimization, then updates this knowledge with new observations. Its pipeline spans task settings, comparative hypothesis formation, principle induction, and hypothesis revision.

3 PRINCIPIA: TEST-TIME HYPOTHESES TO PRINCIPLE CONSTRUCTION

  • PRINCIPIA constructs and refines empirical principles from accumulated observations to guide subsequent investigation in optimization and prediction tasks.Optimization seeks an instance best suited to a specified objective through successive modifications; prediction estimates an input's property or characteristic.Source: §3 · pp. 3–4, Figure 2 · p. 4

3.1 COMPARATIVE CAUSAL HYPOTHESIS

  • A comparative causal hypothesis explains how similarities and differences between two related inputs account for their observed outcomes.Comparing related inputs and outcomes provides evidence for distinguishing characteristic contributions beyond a single input–outcome pair.Source: §3.1 · p. 4

3.2 INDUCTIVE PRINCIPLE

  • Similarity-based clustering groups related inputs and their associated hypotheses, from which recurring relationships are generalized into inductive principles.The principles summarize patterns across multiple comparisons and are associated with the input clusters.Source: §3.2 · p. 5

3.3 HYPOTHESIS REVISION VIA NEW OBSERVATIONS

  • Retrieved hypotheses and principles guide task-specific predictions or candidate generation, and new observations support revising hypotheses and reconstructing principles.The framework also adds hypotheses for new observations while retaining the original comparative evidence for revised hypotheses.Source: §3.3 · pp. 5–6

4 EXPERIMENTAL RESULTS

Across molecular, protein, and gene optimization and molecular property prediction, PRINCIPIA constructs task-specific knowledge from experimental observations and outperforms the reported baselines. Analyses examine its component contributions, evaluation efficiency, and the plausibility of its constructed knowledge.

4.1 SCIENTIFIC OPTIMIZATION

  • PRINCIPIA consistently outperforms optimization baselines using no guidance, experience summaries, or external knowledge, and often outperforms PiFlow across molecular, protein, and gene tasks.The comparison covers molecular optimization in Table 1 and protein engineering and gene perturbation in Table 2.Source: §4.1 · p. 6, Table 1 · p. 7, Table 2 · p. 7

4.2 MOLECULAR PROPERTY PREDICTION

  • PRINCIPIA consistently outperforms all baselines across eight molecular property prediction tasks, with results suggesting its constructed knowledge generalizes to unseen molecules.Knowledge is constructed from training observations and evaluated on held-out molecules with different structures.Source: §4.2 · pp. 7–8, Table 3 · p. 8

4.3 ANALYSES

  • Comparative hypothesis generation improves optimization over both unguided optimization and hypotheses generated from a single input and outcome.The authors attribute this to comparative evidence narrowing the factors considered when generating hypotheses.Source: §4.3 · p. 8, Figure 3 · p. 8
  • Removing either principle construction or hypothesis revision reduces performance, supporting both generalization across hypotheses and updating explanations from new observations.The analysis reports that revised hypotheses and reconstructed principles provide up-to-date guidance.Source: §4.3 · pp. 8–9, Figure 4 · p. 8
  • PRINCIPIA matches ExLLM, WebSearch, MolLEO, and DeepEvolve final performance with approximately 55%, 84%, 86%, and 86% fewer oracle evaluations, respectively.PRINCIPIA achieves the best final performance among the compared methods under the extended oracle budget.Source: Figure 5 · p. 8, §4.3 · p. 9
  • Removing LLM-based knowledge retrieval lowers performance; without retrieval, AUC@10 is 0.364, comparable to 0.374 without hypothesis revision.The analysis suggests query-dependent selection helps identify knowledge useful for subsequent investigation.Source: Figure 6 · p. 8, Figure 4 · p. 8, §4.3 · p. 9
  • A qualitative molecular example links recurring epoxide motifs to mutagenicity and distinguishes an aminoalcohol structure lacking a strained electrophile.The induced principle is described as consistent with prior studies linking epoxide-containing compounds to mutagenicity.Source: §4.3 · p. 9, Table 5 · p. 9

5 CONCLUSION

PRINCIPIA turns accumulated observations into comparative causal hypotheses and inductive principles, revising hypotheses and reconstructing principles as new observations arrive. Across four scientific task areas, it outperforms several baseline types, with further analyses supporting reduced oracle evaluations and plausible principles.

5 CONCLUSION

  • PRINCIPIA forms comparative causal hypotheses, generalizes recurring relationships into inductive principles, then uses new observations to revise hypotheses and reconstruct principles.Source: §5 · pp. 9–10
  • Across molecular optimization, protein engineering, gene perturbation, and molecular property prediction, PRINCIPIA outperforms baselines relying on internal knowledge, experience summaries, or external knowledge.Further analyses support reduced oracle evaluations and the plausibility of its constructed principles.Source: §5 · p. 10
  • The work frames test-time hypotheses-to-principle construction as a direction for LLM-based scientific discovery, with accumulated observations informing subsequent investigation.Source: §5 · pp. 9–10

A IMPLEMENTATION DETAILS OF PRINCIPIA

PRINCIPIA stores comparative evidence and hypotheses, clusters inputs to induce principles, retrieves relevant knowledge for task queries, and revises used hypotheses with new observations.

Comparative Evidence and Hypothesis Generation

  • For scientific optimization, PRINCIPIA compares candidate-generation inputs with evaluated candidates; for property prediction, it pairs each new target with up to three similar reference molecules.Prediction references are ranked by Tanimoto similarity; reference selection does not filter by label.Source: A IMPLEMENTATION DETAILS OF PRINCIPIA · p. 14

Similarity-based Clustering and Principle Induction

  • Inputs are clustered using domain-specific distances, and an LLM generalizes recurring relationships across cluster-linked hypotheses into inductive principles.The stated distances differ across molecules, proteins, and genes; clustering targets about ten inputs per cluster.Source: A IMPLEMENTATION DETAILS OF PRINCIPIA · p. 14

Knowledge Retrieval

  • PRINCIPIA retrieves relevant hypothesis records and principles from separate memories, using query-related candidate pools before LLM selection.Optimization retrieves up to three records and one principle per query; prediction allows configurable record counts.Source: A IMPLEMENTATION DETAILS OF PRINCIPIA · p. 14

Hypothesis Revision via New Observations

  • For each selected hypothesis record, an LLM can retain, revise, remove, or add hypotheses after considering up to five sampled new observations.The updated hypotheses replace those in the record while its original comparative evidence is retained.Source: A IMPLEMENTATION DETAILS OF PRINCIPIA · pp. 14–15

B TASK-SPECIFIC EXPERIMENTAL SETTINGS

This section describes the datasets, task applications of PRINCIPIA, and experimental configurations.

B TASK-SPECIFIC EXPERIMENTAL SETTINGS

B.1 SCIENTIFIC OPTIMIZATION

The scientific-optimization setup specifies the backbone model, shared population-based procedure, and schedule for updating PRINCIPIA’s knowledge.

B.1 SCIENTIFIC OPTIMIZATION

  • Scientific optimization uses GPT-5-mini-2025-08-07 at temperature 1.0, with mean results reported across three random seeds.Source: §B.1 · p. 15
  • The shared optimization procedure maintains a population of top-scoring distinct inputs, samples a fitness-weighted mating pool, and adds newly evaluated candidates to the accumulated records.Previously evaluated inputs reuse recorded scores.Source: §B.1 · p. 15
  • PRINCIPIA begins with empty hypothesis and principle memories; after evaluation it generates comparisons, then revises used hypotheses and reconstructs principles for later generations.Source: §B.1 · p. 15

B.1.1 MOLECULAR OPTIMIZATION

Molecular optimization evaluates five PMO tasks using task-specific objectives and scoring oracles. PRINCIPIA applies crossover and mutation while updating its knowledge from observed outcomes, under a shared 1,000-evaluation budget.

Datasets and Objectives

  • The five PMO tasks are JNK3, GSK3β, Median1, Median2, and Valsartan SMARTS, each scored by its benchmark oracle.The objectives cover inhibitory activity, similarity to reference molecules, and target-substructure plus physicochemical requirements.Source: §B.1.1 · p. 15

Task Execution and Application of PRINCIPIA

  • Each generation applies rule-based crossover followed by LLM mutation, and both intermediate products and offspring are oracle-evaluated.Parent-to-crossover and crossover-to-offspring comparisons provide observed evidence for the generation-end knowledge update.Source: §B.1.1 · p. 15

Experimental Configuration and Evaluation

  • Runs begin with 200 molecules and allow 1,000 distinct oracle evaluations, including initialization.Performance is reported using AUC@10 and Avg@100.Source: §B.1.1 · p. 16

B.1.2 PROTEIN SEQUENCE ENGINEERING

Protein sequence engineering evaluates three fitness-oracle tasks. PRINCIPIA uses sequence-preserving crossover and mutation, retaining observed outcomes from both intermediate and final sequences for knowledge updates.

Datasets and Objectives

  • Syn-3bfo, AAV, and GB1 use task-specific fitness oracles, with synthetic, pretrained-predictor, and experimentally measured fitness sources, respectively.Each task maximizes fitness over fixed-length amino-acid sequences using the 20 standard amino acids.Source: §B.1.2 · p. 16

Task Execution and Application of PRINCIPIA

  • Each generation applies length-preserving uniform crossover followed by LLM mutation under task-specific sequence constraints.Observed outcomes for crossover sequences and mutated offspring support comparisons used in the generation-end knowledge update.Source: §B.1.2 · p. 16

Experimental Configuration and Evaluation

  • Runs start from 48 sequences and use a budget of 200 distinct oracle evaluations, including initialization.The section reports AUC@10 and Avg@50; Syn-3bfo scores are normalized to [0, 1] before AUC computation.Source: §B.1.2 · p. 16

B.1.3 GENE PERTURBATION

Gene perturbation evaluates two CRISPR-screen tasks with recorded perturbation-effect scores. PRINCIPIA proposes genes directly from selected genes and their retrieved hypotheses and principles, without a separate crossover.

Datasets and Objectives

  • Scharenberg22 maximizes its recorded screen score, while IFNG maximizes the absolute recorded effect to reward strong increases and decreases.IFNG has a larger gene search space than Scharenberg22.Source: §B.1.3 · p. 16

Task Execution and Application of PRINCIPIA

  • Given selected genes and scores, the LLM directly proposes another gene without a separate crossover operation.Previously proposed genes are included to reduce duplicates, and selected-to-proposed comparisons support the generation-end knowledge update.Source: §B.1.3 · p. 16

Experimental Configuration and Evaluation

  • Oracle budgets are 192 genes for Scharenberg22 and 768 for IFNG, counting initialization.AUC@10 measures optimization trajectories; Hit Ratio measures recall among distinct newly proposed genes and excludes the initial population.Source: §B.1.3 · p. 17

B.2 MOLECULAR PROPERTY PREDICTION

The molecular property prediction setup uses sequentially accumulated task-specific knowledge and evaluates fixed memories on held-out molecules. The accompanying optimization and prediction baselines vary in whether they supply retrieved, summarized, internal, or external guidance.

B.2 MOLECULAR PROPERTY PREDICTION

  • Eight TDC binary-classification tasks cover four toxicity outcomes and inhibition of CYP1A2, CYP2C9, CYP2D6, and CYP3A4.Training and test sets are scaffold-split; training labels arrive over six rounds, while held-out labels are excluded from knowledge construction.Source: §B.2 · p. 17
  • After the initial label-revealing round, each prediction uses retrieved hypotheses and principles before labels are revealed for hypothesis revision and principle reconstruction.The final fixed memories are used for held-out test prediction without further updates.Source: §B.2 · p. 17

C.1 SCIENTIFIC OPTIMIZATION

  • Optimization baselines include REINVENT, Augmented Memory, and Graph GA, with their stated settings aligned to the benchmark protocol and PRINCIPIA where described.Graph GA shares PRINCIPIA’s 200-molecule initial population and uses 100 offspring per generation.Source: §C.1 · pp. 17–18
  • MolLEO uses the shared optimization architecture without PRINCIPIA’s hypothesis and principle guidance, while ExLLM adds rolling experience summaries to that baseline.ExLLM summarizes sampled high- and low-performing candidates and injects the summary into generation-level calls with probability 0.5.Source: §C.1 · p. 18
  • PiFlow is reimplemented with its scoring and agent protocol, while DeepEvolve and WebSearch provide retrieval-based guidance constrained to general scientific principles.DeepEvolve summarizes search results; WebSearch injects retrieved passages directly without LLM-based summarization.Source: §C.1 · pp. 18–19

C.2 MOLECULAR PROPERTY PREDICTION

  • Prediction baselines range from direct prompts and similarity-selected labeled examples to fixed internal or web-derived principles.The few-shot baseline selects examples by Tanimoto similarity, while internal and external principles remain the same for all queries within a task.Source: §C.2 · p. 19
  • The textual-summary baseline sequentially incorporates training molecule-label pairs into one summary, then fixes it for test prediction.It does not maintain separate comparative causal hypotheses and inductive principles.Source: §C.2 · pp. 19–20

D ALGORITHMS

PRINCIPIA’s algorithms apply task-specific procedures to gather observations, then use those observations to generate hypotheses and induce principles, revising knowledge across rounds. Prediction and optimization use different task-application procedures but share knowledge construction and hypothesis revision.

D ALGORITHMS

  • Each round applies task-specific procedures, revises previously used hypotheses from new observations, generates comparative hypotheses, and induces principles; optimization stops when oracle-call budget B is exhausted.The workflow returns hypothesis memory Mh and principle memory Mp.Source: D ALGORITHMS · p. 20
  • Prediction partitions task data into T batches and, after the first round, predicts properties using retrieved hypotheses and principles while recording new observations.The initial task procedure returns no data; later rounds compare predictions with observed outcomes.Source: D ALGORITHMS · p. 20
  • Optimization starts from evaluated inputs, selects parents, creates crossover offspring except for gene perturbation, retrieves hypotheses and principles, and evaluates candidates.The task procedure records comparative evidence and adds new observations to the data.Source: D ALGORITHMS · p. 21
  • The induction procedure clusters inputs into K groups Gk, forms each Ek from hypotheses whose endpoints touch Gk, and applies LLMprinciple(Ek; q) to produce Pk.It produces one Pk per cluster.Source: D ALGORITHMS · p. 21

E SUPPLEMENTARY EXPERIMENTS

The supplementary section examines how retrieval, accumulated observations, and task-specific principles shape test-time discovery, including across objectives and backbone models. It also documents prompts that operationalize hypothesis revision across four task areas, with structurally grounded comparisons, cluster-specific memories, and retrieval for molecular-property prediction.

E SUPPLEMENTARY EXPERIMENTS

  • Retrieving hypotheses associated with both increasing and decreasing fitness yields more effective discovery than using either direction alone, while consistent directional signals outperform random retrieval.PRINCIPIA also outperforms the plain optimization algorithm across the tested retrieval strategies.Source: E SUPPLEMENTARY EXPERIMENTS · p. 22
  • In multi-objective protein engineering, PRINCIPIA improves over plain optimization while other knowledge-augmented methods degrade; it also achieves the highest Hit Ratio on both Scharenberg22 and IFNG gene perturbation tasks.The protein task maximizes Syn-3bfo fitness while minimizing Hamming distance from wild type, with the objectives scalarized using equal weights.Source: E SUPPLEMENTARY EXPERIMENTS · p. 22
  • In CYP2C9 prediction, new observations revise the explanation linking inhibition to a benzamide linker and substituted aromatic scaffold by clarifying that an amide alone does not reliably explain inhibition.The revision follows a molecule predicted to inhibit CYP2C9 but observed to be a non-inhibitor.Source: Table 8 · p. 23, E SUPPLEMENTARY EXPERIMENTS · p. 23
  • Across 16 task–backbone combinations, PRINCIPIA outperforms baselines, with growing advantages in JNK3, GSK3B, and GB1 as observations accumulate and higher Top-100 scores across four backbones.Figure 9 tracks Top-100 Average Scores over oracle calls; Figure 8 shows results across backbone models and tasks.Source: E SUPPLEMENTARY EXPERIMENTS · pp. 22–23, Figure 8 · p. 24, Figure 9 · p. 25

F.1 PROMPT FOR MOLECULAR OPTIMIZATION

  • For molecular optimization, the prompts specify comparative-hypothesis generation, principle induction and retrieval, hypothesis revision, candidate generation, and task properties and objectives.The appendix uses “episodic memories” for hypothesis records and “semantic memories” for inductive principles.Source: §F.1 · p. 26, F PROMPTS · p. 26

F.2 PROMPT FOR PROTEIN SEQUENCE ENGINEERING

  • For protein sequence engineering, the prompts cover comparative-hypothesis generation, principle induction and retrieval, hypothesis revision, candidate generation, and task properties and objectives.The revision prompt asks the model to keep supported hypotheses, revise or remove contradicted ones, and add hypotheses suggested by new patterns.Source: §F.2 · p. 26, §F.4 · p. 34

F.3 PROMPT FOR GENE PERTURBATION

  • For gene perturbation, the prompts cover hypothesis generation, principle induction and retrieval, hypothesis revision, candidate generation, and task objectives, with candidate generation instructed to exclude previously proposed genes.The gene prompt also describes prioritizing shared pathways, complexes, functional families, and recurring links to fitness.Source: §F.3 · p. 26, §F.4 · p. 37

F.4 PROMPT FOR MOLECULAR PROPERTY PREDICTION

  • For molecular property prediction, the prompts specify hypothesis generation and retrieval, principle induction and retrieval, hypothesis revision, and held-out prediction using retrieved hypotheses and principles.The revision prompt incorporates observations from other transformations to refine hypotheses; the listed task set includes eight descriptions, questions, observed labels, and answer formats.Source: §F.4 · pp. 26, 29, 34
  • For gene-perturbation edges, the revision prompt uses additional proposal outcomes to retain supported hypotheses, revise or remove contradicted ones, and add new patterns.The requested output describes a refined causal mechanism and its supporting biological relationships.Source: §F.4 · pp. 38–39, Figure 28 · p. 38
  • Molecular-property hypotheses are generated from one target–reference comparison, grounded in structural differences and the pair’s observed labels.The prompt requests 1–2 hypotheses, treating shared substructures as likely drivers when labels match and differing substructures as likely drivers when labels differ.Source: §F.4 · p. 40, Figure 31 · p. 40
  • Cluster memories prioritize recurring local scaffolds, label-changing substructures, and tolerated variation, distinguishing conserved features from variable ones.The prompt contrasts CHANGED and UNCHANGED comparisons and rejects generic endpoint or pharmacophore descriptions in favor of cluster-specific patterns.Source: §F.4 · p. 41, Figure 32 · p. 41
  • Molecular-property retrieval selects relevant cluster-level memories for a query molecule, prioritizing present reactive or alerting groups even across different scaffolds.The candidate memories summarize patterns among structurally similar training molecules.Source: §F.4 · p. 42, Figure 34 · p. 42
  • For molecular comparisons, hypotheses are similarly refined from evaluation-round prediction outcomes by strengthening supported explanations, revising contradicted ones, or adding new patterns.The comparison includes target and reference molecules, their observed labels, and whether the label changed.Source: §F.4 · p. 43, Figure 35 · p. 43

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