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Large Discovery Models: Empirically-grounded Model-Based Open-Ended Search

Zhongwei Yu, Yan Song, Xue Yan, Anjie Liu, Xingyu Lu, Yihang Chen, Huichi Zhou, Siyuan Guo, Luoyang Sun, Sihan Chen, Xiangning Yu, Jun Wang

arXiv:2608.15669v1cs.LG

TL;DR

Scientific discovery requires searching vast, costly, open-ended design spaces, but LLM confidence and likelihoods do not provide calibrated external value signals. LDM couples an LLM generative prior with an uncertainty-aware Bayesian surrogate and outperforms LLM-only and Bayesian-optimisation baselines across three domains, with sustained gains from expanding the search frontier.

  • Problem

    Scientific discovery lacks calibrated external value signals for searching vast, costly, noisy, and incompletely specified hypothesis spaces.

  • Method

    LDM couples an LLM generative prior with a Bayesian non-parametric surrogate in a sequential loop of generation, evaluation, uncertainty-aware selection, and updating.

  • Results

    Across three heterogeneous domains, LDM outperforms reported LLM-only and Bayesian-optimisation baselines, while uncertainty-aware acquisition and search-frontier expansion improve performance.

  • Takeaways & Limitations

    LDM provides a general framework for effective search over open-ended scientific design spaces within the reported evaluation settings.

  • Takeaways & Limitations

    Scientific domains usually lack the rich feedback data or ground-truth answers commonly used to guide test-time compute and reinforcement learning.

Abstract

from arXiv · show

Scientific discovery often involves optimising expensive-to-evaluate objectives over vast, structured, and open-ended hypothesis spaces, such as molecules, protein sequences, and computer programs. Generative models such as large language models (LLMs) provide expressive priors over such spaces, but their likelihoods and self-assessments are unreliable proxies for the objectives and calibrated epistemic uncertainty, especially for novel candidates outside the observed data distribution. We introduce the Large Discovery Model (LDM), an empirically grounded recurrent architecture that couples a generative model with a Bayesian non-parametric reward surrogate model. The generative model proposes and refines candidate designs, while the surrogate predicts their performance and quantifies uncertainty, yielding an uncertainty-aware value that guides candidate generation, refinement, and selection. The discovery memory and the surrogate model are continually updated as each new experimental observation arrives. We evaluate LDM on three scenarios spanning different design modalities and objectives, including neural-network training, antibody design, and molecular optimisation. Compared to LLM-only reflection or traditional statistical search across these domains, LDM achieves a $2.4\times$ greater reduction in validation BPB, an $18.2\%$ relative decrease in binding energy, and more than $60\%$ relative gains in molecular multi-objective performance. These results suggests that LDM could serve as a general-purpose discovery engine for effective search over open-ended hypothesis spaces.

1 Introduction

Scientific discovery is framed as sequential search over vast, structured design spaces where evaluations are costly, limited, delayed, or noisy. The proposed approach combines LLM-based candidate generation with empirically grounded, uncertainty-aware selection to expand the search frontier while allocating experimental resources effectively.

  • Problem formulation: Vast, structured, and open-ended candidate spaces make discovery difficult because feedback is expensive, delayed, noisy, and available for only a small fraction of candidates.The agent must learn an unknown objective and allocate evaluations under a limited budget.
  • Problem formulation: Scientific discovery requires generating hypotheses or designs, selecting a limited subset for external evaluation, and updating beliefs from empirical observations.The external evaluator may involve physical experiments, simulations, computational tests, or other evidence sources.
  • Limitations of existing methods: LLMs can generate and modify structured candidates but do not reliably estimate their externally measured scientific value or determine which ideas merit costly evaluation.Candidate likelihood or plausibility under the learned distribution need not correlate with the scientific property being optimized.
  • Limitations of existing methods: Bayesian optimisation grounds selection in empirical observations and uncertainty, but depends on representations and search procedures that may fail to expose candidates in structured combinatorial spaces.This limitation applies to spaces such as molecules, proteins, programs, and experimental protocols.
  • Proposed approach: The paper formulates discovery as inference-time search over a dynamic, structured design space guided by an uncertainty-aware value model grounded in empirical observations.Its acquisition-tilted policy combines an LLM’s structured prior with inference-time computation and sequential experimental feedback.
  • Results: 2.4× larger absolute validation-BPB reduction is achieved by LDM than by LLM-only reflection from a common starting point on AutoResearch.The introduction also reports improvements over LLM-only and BO-only baselines in multi-objective molecular design.

2 Search and Discovery in Open-Ended Design Spaces

Open-ended scientific discovery searches an evolving, incompletely specified hypothesis space for high-reward designs under costly, noisy, black-box evaluation. The framework distinguishes epistemic regimes and assigns exploitation, exploration, and discovery to progressively different search transitions.

  • Open-Ended Search: The search targets high unknown reward R(x) over an evolving hypothesis universe X that must be progressively constructed during discovery.Evaluating R is costly, black-box, and potentially noisy, while the relevant search space is not fully specified in advance.
  • Epistemic Regimes: A probabilistic surrogate posterior p(R | D_t) summarizes empirical knowledge through expected reward µ_t(x) and predictive uncertainty σ_t(x), but does not enumerate X.The posterior is conditioned on previously evaluated designs and their noisy feedback.
  • Epistemic Regimes: The framework partitions hypotheses into known knowns, known unknowns, unknown knowns, and unknown unknowns according to uncertainty, reachability, modelling support, and contextual availability.Unknown knowns require explicit retrieval, while unknown unknowns lie beyond the search’s current effective reach or calibrated surrogate support.
  • Search Operations: Exploitation selects known knowns with high predicted reward and low uncertainty, whereas exploration evaluates reachable uncertain designs to reduce posterior uncertainty.Exploration can turn known unknowns into known knowns.
  • Search Operations: Discovery expands the search frontier by formulating previously unreachable hypotheses, converting unknown unknowns into known unknowns for subsequent evaluation.The three transitions are discovery from unknown unknowns to known unknowns, exploration from known unknowns to known knowns, and exploitation within known knowns.

3 The Large Discovery Model

LDM is a sequential inverse-design policy combining a generative foundation model, probabilistic surrogate, and model-based acquisition function. It uses the generative prior to propose structured candidates, empirical Bayesian uncertainty to ground reward estimates, and acquisition value to balance exploration with exploitation and guide search decisions.

  • Core architecture: LDM combines a generative foundation model, probabilistic surrogate, and model-based acquisition function for sequential inverse design.These three components interact as the core policy architecture.
  • Generative foundation model: The generative model supplies a structured prior that generates plausible candidates without explicitly enumerating the design space.Context and inference changes can expand or reshape the candidates reachable by search.
  • Probabilistic surrogate: The surrogate estimates expected reward with predictive mean µt(x) and quantifies epistemic uncertainty with σt(x).This uncertainty reflects weak evidential support and can be reduced through additional informative evaluations.
  • Acquisition-guided search: The acquisition function assigns candidates a scalar decision value that can combine predicted reward and epistemic uncertainty to mediate exploitation and exploration.Unlike a conventional reward-model score, it values allocating computation or costly empirical evaluation and governs candidate selection and refinement.
  • Policy formulation: The optimal policy exponentially tilts the generative reservoir toward candidates judged valuable by acquisition value.As η →0, search follows the raw generative reservoir; as α →0 and η becomes large, it recovers classical Bayesian optimisation.
  • Recurrent search–learn cycle: LDM’s search–learn cycle uses accumulated search states, candidate pools, and acquisition decisions as experience for improving the proposal model.The proposal adapts to the current empirical posterior while parameter learning consolidates recurring improvements across states and tasks.

4 The Algorithm

The LDM applies an iterative experimental-design loop that reweights an LLM proposal distribution with a Gaussian-process surrogate’s acquisition function, evaluates selected candidates, and updates its data and generative context. It supports direct or indirect candidate generation, adaptive active search domains, and extensions for constraints, costs, uncertainty feedback, multi-objective optimisation, and batch selection.

  • Iterative discovery loop: Each round fits a Gaussian-process surrogate over A_t and constructs an acquisition function from its posterior mean and uncertainty.The surrogate is fit using the posterior R | D_t ∼ GP(μ_t, k_t).
  • Iterative discovery loop: Candidates are sampled from an acquisition-tilted LLM policy, evaluated with noisy black-box rewards, and added to the dataset for the next round.The policy is π_t ∝ p_θ,α(· | C_t) exp{ηa_t}, and observations update D_t+1 with each candidate–reward pair.
  • Candidate generation and selection: Deterministic top-b selection ranks candidates by acquisition, whereas Gumbel-top-b samples without replacement; pool size N trades inference cost against search quality.The two selection modes operate on the finite candidate pool produced by the LLM or external sampler.
  • Iterative discovery loop: The loop can append LLM reflection feedback when the surrogate detects a stale regime, keeping later proposals aligned with recent mechanistic understanding.This reflection operation is orthogonal to the tilted-search core.
  • Candidate generation and selection: The LLM supports direct generation of complete designs or indirect parameterisation of a search region, with external sampling enabling more efficient scaling of pool size N.Invalid directly generated candidates may be removed by rejection sampling with a validity checker.
  • Active domains and extensions: Indirect parameterisation restricts the GP to an LLM-selected active subspace A_t, simplifying search and surrogate modelling while supporting constrained, cost-aware, decomposed, multi-objective, and batch extensions.For vector-valued objectives, the scalar acquisition can be replaced by Expected Hypervolume Improvement (EHVI).

5 Theoretical Analyses

The theoretical analysis extends Bayesian-optimisation regret reasoning to an LLM-defined, dynamically evolving search space. It decomposes LDM regret into discovery, GP-UCB optimisation, and LDM sampling-shortfall terms, clarifying how the reservoir and acquisition tilt contribute.

  • Dynamic search-space analysis: LDM’s regret analysis allows reachable candidates to depend on the LLM reservoir and evolving discovery context, unlike fixed-domain GP-UCB analyses.This yields a decomposition separating discovery error from optimisation error within the currently reachable region.
  • Regret decomposition: The regret decomposes into a discovery gap and optimisation regret: the former reflects missing near-optimal designs, while the latter measures selection quality within the current reservoir support.The discovery gap is zero whenever the global optimum belongs to the current support.
  • Interpretation: The reservoir controls whether high-quality regions are discovered, while acquisition tilt controls how effectively promising candidates are selected among reachable designs.An informative LLM can reduce the coverage radius and increase near-UCB probability mass, improving the corresponding regret terms.
  • Regret guarantees: Theorem 1 bounds average regret with probability at least 1 −δgp −δsamp under UCB calibration and reservoir coverage/local-regularity assumptions.The bound applies when the near-UCB reservoir mass κt(ζt) is positive and the sampling failure probabilities satisfy the stated conditions.
  • Regret guarantees: The bound separates discovery gap, GP-UCB optimisation, and LDM sampling shortfall, with shortfall decreasing as acquisition tilt sharpens or near-UCB reservoir mass increases.The GP-UCB term captures information gain within the covered region, while sampling shortfall reflects tilted sampling rather than exact UCB maximisation.

6 Experiments

Across neural-network training, antibody design, and molecular optimisation, LDM improves search by combining generative proposals with surrogate-guided acquisition and discovery. Experiments show benefits from expanded test-time search, frontier discovery, and domain-adapted candidate generation, while evaluations remain digital-oracle benchmarks.

  • 6.1.1 Autoresearch: Plateau detection followed by search-space revision enables a second improvement phase after local tuning stalls.This plateau-and-revision pattern recurs across all three domains.
  • 6.1.3 Molecular design: Molecular optimisation proceeds through scaffold identification, substituent screening, objective bifurcation, feature recombination, and fine-tuning while uncovering unrelated backbones.This structural exploration capability is absent from standard Bayesian optimisation and seed-local expansion tools.
  • 6.2 Ablations: Increasing test-time search budgets and using acquisition functions that balance exploitation and exploration improve performance, with larger budgets especially effective for molecular design.EHVI requires a large screening pool, whereas scalarised acquisitions remain effective when the pool is small; higher LLM-decoding and acquisition temperatures generally improve molecular hypervolume.
  • 6.1.1 Autoresearch: 2.4× larger reduction in validation BPB: LDM reaches 0.93421 versus 0.9767 for the no-discover baseline after roughly 255 runs.Both methods share val bpb = 1.0069; LDM reduces validation BPB by 0.0727, compared with 0.0301 for the LLM-only baseline.
  • 6.1.2 Antibody design: Policy-based LDM variants consistently outperform direct generation for antibody design, achieving affinity comparable to AntBO.Direct variants perform only marginally better than standalone LLMs, while policy search generates a larger candidate pool within an LLM-parameterised region.

7 Related Work

Related work establishes complementary strengths and limitations of LLMs and statistical optimisation: LLMs offer powerful generative priors but unreliable calibration, while statistical methods provide principled uncertainty-aware search yet struggle in vast semantic spaces. LDM combines these capabilities by using an acquisition-based value signal to guide LLM-driven inference-time search for scientific discovery.

  • Large language models: Scaling laws and test-time compute have driven major LLM progress, including improved reasoning through additional inference-time computation and verifiable rewards.The reviewed milestones include Transformer, GPT-1, BERT, GPT-3, scaling laws, verifiers, and RLVR.
  • Large language models: LLMs remain poorly calibrated for scientific decisions and cannot yet reliably discover novel, high-quality solutions in end-to-end execution benchmarks.Their internal confidence does not reliably reflect uncertainty about external properties, motivating an external value signal.
  • Statistical optimisation: Bandits and Bayesian optimisation provide principled exploration–exploitation and uncertainty-aware search for noisy, costly black-box objectives, including scientific discovery.The literature covers UCB, infinitely-armed bandits, probabilistic surrogates, GP-UCB, and domain-specific BO applications across chemistry, materials science, and biology.
  • Statistical optimisation: Pure statistical methods struggle to propose valid candidates in vast unbounded spaces, incorporate high-level semantic knowledge, and respond to user-specified constraints or preferences.These limitations create an opportunity for complementarity with generative models that propose semantically meaningful candidates.
  • Hybrid methods: LDM bridges LLM generation and statistical search by making the acquisition function the value signal for an LLM-driven inference-time discovery process.This addresses the contrast between generative priors lacking calibration and statistical methods lacking semantic candidate generation; designs can also provide value for future information gain.

8 Conclusion, Limitations, and Outlook … A Notation

The LDM couples LLM generative priors with Gaussian-process value and uncertainty signals to search open-ended scientific design spaces, while its evaluation demonstrates broad applicability and its limitations motivate scalability, automation, and knowledge-integration work.

  • 8 Conclusion, Limitations, and Outlook: LDM couples LLM generative priors with Gaussian-process surrogate value signals in an experiment-grounded recurrent architecture for open-ended scientific design.The framework addresses costly evaluation budgets and complementary weaknesses of LLMs and Bayesian optimisation.
  • 8 Conclusion, Limitations, and Outlook: LDM formulates search as KL-regularised, acquisition-guided optimisation with a closed-form acquisition-tilted distribution spanning exploitation, exploration, and discovery.This framework unifies generative priors and empirical value signals mathematically.
  • 8 Conclusion, Limitations, and Outlook: Evaluation across neural-network training, antibody CDRH3 design, and multi-objective molecular optimisation supports the generality of LDM and the complementarity of its components.The supplied passage states that integrated performance outperforms reported LLM-only and traditional approaches, though the excerpt does not provide the associated figures.
  • 8 Conclusion, Limitations, and Outlook: The Gaussian-process surrogate has cubic computational complexity in observations, while batch candidate sampling creates substantial LLM inference overhead at test time.These constraints limit scalability under large experimental budgets.
  • 8 Conclusion, Limitations, and Outlook: Domain-specific kernel functions and surrogate representations require manual customisation, limiting automation across scientific domains.Future work targets end-to-end surrogate specification so the LLM can learn these components autonomously.
  • 8 Conclusion, Limitations, and Outlook: Future directions include memory retrieval and federated discovery to incorporate external knowledge bases, published results, and parallel exploration data into the search loop.Sparse Gaussian processes are also identified as a way to address scalability.
  • A Notation: The notation defines the design space X, candidate design x, global maximiser x⋆, unknown reward R(x), evaluation history Dt, search context Ct, and base distribution pθ.It also introduces the effective proposal pθ,α, surrogate mean µt(x), standard deviation σt(x), acquisition value at(x), policy πt, tilt strength η, and search parameters.

B Detailed Proofs … B.3 Proof of Theorem 1

The detailed proofs establish Proposition 1, Lemma 1, and Theorem 1. They derive the variational identity, a conditional sampling tail bound, and a regret guarantee by combining discovery coverage, UCB calibration, information gain, and high-probability events.

  • B.1 Proof of Proposition 1: Proposition 1 follows from KL nonnegativity, with equality if and only if q = πt.The normalising constants combine into Zt to obtain the stated result.
  • B.2 Proof of Lemma 1: Lemma 1 fixes a round and history, treating the reservoir support, proposal, and acquisition function as fixed.The acquisition function is at(x) = µt(x) + √βtσt(x).
  • B.2 Proof of Lemma 1: Lemma 1 derives a tail bound and converts it into a conditional probability of at least 1 − ρt by choosing η using ρt and κt(ζt).The resulting z is non-negative because ρt ∈ (0, 1) and κt(ζt) ≤ 1.
  • B.3 Proof of Theorem 1: Theorem 1 decomposes regret into discovery and optimisation terms, controlling the latter through UCB calibration and Lemma 1.The proof first bounds the discovery gap and then constructs a simultaneous sampling event.
  • B.3 Proof of Theorem 1: The discovery price is exactly controlled by the current reservoir coverage radius.This follows from Assumption 2 for every x ∈ At.
  • B.3 Proof of Theorem 1: Applying Lemma 1 at each round and a union bound yields a simultaneous sampling event with conditional failure probability at most ρt.The optimisation bound is then established on the intersection of the sampling event and the event in Assumption 1, using UCB optimism.
  • B.3 Proof of Theorem 1: The optimisation bound uses the sampled-point lower side of (23), the GP-UCB information-gain variance bound, and Cauchy–Schwarz.Combining these inequalities gives the per-round bound and the theorem’s final high-probability conclusion after a final union bound.
  • B.3 Proof of Theorem 1: Theorem 1 concludes by combining the good-event probabilities from Assumption 1 and the sampling argument through a final union bound.The proof then completes the theorem.

C Technical Implementation Details … C.3 Batch Acquisition Sampling

The appendix specifies LDM’s GP surrogate, acquisition functions, and finite-pool batch sampling, with continual model updates grounding search in predictive reward and uncertainty. It details single- and multi-objective acquisition values and weighted without-replacement selection for parallel evaluation.

  • C.1 Gaussian Process Surrogate: LDM uses a Gaussian Process surrogate to fit black-box rewards from historical experiments and provide calibrated predictive means and epistemic uncertainty for acquisition computation.The implementation follows the acquisition-tilted search framework and expands its surrogate-training and sampling logic.
  • C.1.1 Prior Specification: The GP prior uses a constant mean m(x) = m0 and a design-adapted positive-definite kernel, such as RBF for continuous spaces or string kernels for sequences.Kernel hyperparameters, observation noise variance σ2 n, and m0 are estimated from data.
  • C.1.2 Posterior Inference: The posterior reward distribution is Gaussian, with its posterior mean estimating expected reward and posterior variance quantifying epistemic uncertainty for each candidate.Posterior inference conditions on the cumulative historical observation dataset and uses the GP kernel matrix and cross-covariance vector.
  • C.1.3 Hyperparameter Estimation: GP hyperparameters are fitted by Type-II maximum likelihood using gradient-based optimisation such as L-BFGS, and re-optimised after each iteration with new observations.The optimised parameters include kernel lengthscales, output variance, observation noise variance σ2 n, and prior constant m0.
  • C.2 Acquisition Functions: Acquisition functions combine GP posterior mean and uncertainty into experimental-value signals that guide search and balance exploitation with exploration.LDM supports three acquisition functions for single- and multi-objective settings within the acquisition-tilted search framework.
  • C.2.1 Expected Improvement; C.2.2 Upper Confidence Bound: Expected Improvement measures expected gain over the best observed reward, while UCB combines predictive mean and uncertainty through an exploration weight βt.Adjusting βt moves UCB between exploitation-biased and exploration-biased search.
  • C.2.3 Expected Hypervolume Improvement: For multi-objective optimisation, EHVI replaces the scalar acquisition value with expected hypervolume gain while leaving the core acquisition-tilted search framework unchanged.The appendix also describes model-assisted S-metric selection based on hypervolume contribution.
  • C.3 Batch Acquisition Sampling: For parallel evaluation, LDM applies Gumbel-top-k to acquisition-tilted candidate weights, ranks log wi + gi, and selects the top k candidates without replacement.The resulting ordered batch follows a Plackett–Luce weighted without-replacement distribution, preserving acquisition weighting and preventing duplicate selections.

D Ablation Studies

The ablations test both the limits of a pure current-agent research loop without calibrated Bayesian-optimization value and LDM’s test-time search settings. They span multi-turn code editing, single-step molecular and CDRH3 proposal tasks, and varying search or proposal budgets.

  • Ablation design: The regimes stress different framework components: autoresearch supports persistent code editing and changing the search-space representation, whereas molecule and CDRH3 tasks use single-step candidate proposals.In the latter tasks, surrogate acquisition selects from each proposed candidate pool before expensive oracle evaluation.
  • D.1 Pure LLM loop: §D.1 removes calibrated BO value from the nanoGPT research loop to test how far an LLM can progress using logs and reflection alone.The agent cannot search against a surrogate posterior in this ablation.
  • D.2 LDM test-time search: §D.2 retains the value model and varies LDM test-time search through inner-search budgets, discovery mechanisms, and acquisition choices.For molecules and CDRH3, the ablation tests whether open-source LLM proposers benefit from larger proposal and acquisition-selection budgets in single-step rounds.
  • D.1 Pure LLM loop: 875 no-BO, no-acquisition experiments track validation val bpb, with lower values better, using individual trials, best-so-far steps, and self-reflection checkpoints.The figure depicts staged progress across research regimes, including dense scaling, sparse-memory invention, and compute rebalancing around sparse memory.

D.1 Pure LLM-based research loop · D.2 Test-time Search for LDM · D.2.1 Small-molecule drug discovery

The pure LLM loop makes coherent, stateful research progress but plateaus without a searchable value landscape, whereas LDM’s test-time search improves when proposal and calibrated acquisition budgets scale together. In molecular design, balanced inner-loop scaling favors proposer64 bo64, while EHVI becomes effective only with larger screening budgets.

  • D.1 Pure LLM-based research loop: The pure LLM loop reaches val bpb ≈0.956 after coherent multi-stage experimentation, improving on the no-discover Karpathy baseline at 0.9767 but trailing LDM at 0.93421.Its progress includes dense scaling, sparse memory, rebalancing, confirmation, and grid search around the 512-sparse frontier.
  • D.1 Pure LLM-based research loop: The loop accumulates procedural knowledge by testing code interventions, preserving successes and failures, labelling regimes, and selecting later experiment families from retrieved memories.It performs causal ablations, estimates noise floors with restored anchors, and tracks trajectory diagnostics including steps, tokens, MFU, train/eval gap, and loss slopes.
  • D.1 Pure LLM-based research loop: After the third breakthrough, ≈500 experiments mostly confirm and grid-search the same frontier, revealing a nearly flat envelope rather than continued discovery.The limitation is value: without µt, σt, and acquisition at, the run log remains narrative memory instead of a searchable value landscape.
  • D.2 Test-time Search for LDM: LDM test-time search varies only cheap inner-loop budgets while holding the outer evaluation budget fixed, including proposer count and acquisition-scoring capacity.The theory predicts reduced sampling shortfall when increased near-acquisition mass is evaluated by a calibrated value model rather than language plausibility alone.
  • D.2.1 Small-molecule drug discovery: The molecular ablation evaluates two-objective KRAS G12D discovery using dominated Pareto hypervolume under Vina/activity objectives, with Qwen3.5-9B proposing SMILES and BO/EHVI scoring candidates.The proposerK boM label denotes K proposed candidate strings and an inner loop allowed to score up to M candidates.
  • D.2.1 Small-molecule drug discovery: proposer64 bo64 makes the largest early jump and achieves the highest final hypervolume, while proposer32 bo32 dominates smaller budgets through most of the run.The asymmetric proposer64 bo32 performs worse, indicating that broader proposals require correspondingly greater acquisition-scoring bandwidth.
  • D.2.1 Small-molecule drug discovery: At small budgets, mean- or UCB-style acquisitions outperform strict EHVI, but as n grows, EHVI overtakes them and continues improving.Mean- and UCB-style acquisitions use a 0.5/0.5 weighted scalarisation of the Vina and activity objectives.
  • D.2.1 Small-molecule drug discovery: EHVI requires a large screening budget because strict Pareto-frontier improvements are sparse, whereas scalarised acquisitions can smooth optimisation under thin screening budgets.Mean-style acquisitions degrade or stagnate as budgets increase, while EHVI benefits from greater screening bandwidth.

D.2.2 Antibody CDRH3 design

In antibody CDRH3 design, calibrated acquisition functions outperform mean-style and random baselines, while larger proposer budgets generally improve attainable binding-energy plateaus across antigen targets. However, the best budget is target-dependent, showing that test-time scaling helps when additional candidates are filtered by a calibrated value model.

  • Acquisition functions: Calibrated acquisitions, including EI and UCB variants, broadly outperform mean-style and random baselines across five antigens at proposer budget 300.This benefit persists despite the open-source LLM’s weak biological priors.
  • Proposer budget scaling: Budget 36 improves early but usually plateaus higher, whereas budgets 150 and 300 achieve the best final result on all five antigens.Budget 75 already improves final binding energy on most targets.
  • Proposer budget scaling: Budget 150 is best on 1ADQ A, 1NSN S, and 1OB1 C, while budget 300 is best on 1FBI X and 1H0D C.The target-dependent optimum reflects a rugged sequence landscape, finite seeds, and a noisy surrogate.
  • Candidate-pool expansion: Expanding the candidate pool makes additional inference-time candidates useful once the LDM pipeline can expose enough sequences or neighbourhoods to acquisition filtering.Direct token-level generation underperforms policy-mode LDM because emitting a few complete CDRH3 loops provides insufficient reservoir mass for Bayesian optimisation.
  • General implication: Test-time scaling is useful for single-step design only when added samples are evaluated by a calibrated value model, with sparse biological sequence spaces requiring sufficient coverage before acquisition filtering works.This contrasts with richly pretrained SMILES models, which can absorb large direct proposal batches.

D.3 Hyperparameter ablations for LDM. … E.3 Supplementary Quantitative Tables

The appendix examines LDM hyperparameter sensitivity and extends the analysis to fine-tuning as value distillation, cross-molecule transfer, and supplementary quantitative results. Together, these sections describe acquisition-guided search, its distillation into a student proposer, and positive transfer across molecular tasks.

  • D.3 Hyperparameter ablations for LDM.: The ablations vary LLM sampling temperature for LDMDirectSoftmax and acquisition temperature for LDMPolicySoftmax, including uniform selection and acquisition-function argmax limits.For LDMDirectSoftmax, TLLM ∈ {0.25, 0.5, 0.75, 1, 1.25} with η = 1; for LDMPolicySoftmax, TLLM = 1 and η ∈ {0, 0.5, 1, 2, 4, ∞}.
  • D.3 Hyperparameter ablations for LDM.: D.3 evaluates LDM hyperparameter sensitivity on antibody design using five random seeds and mean best-so-far Absolut energy curves.Lower Absolut energy is better, and shaded regions represent one standard deviation.
  • D.3 Hyperparameter ablations for LDM.: Policy variants dampen near-random proposals by expanding candidate neighborhoods around promising incumbents rather than committing to a single sequence.The open-source LLM lacks biological sequence domain priors over the 2011 CDRH3 space.
  • E Additional Fine-Tuning Analyses: E frames the appendix as complementary evidence for distilling high-budget LDM test-time search into a student proposer across AutoResearch, antibody design, and small-molecule discovery.The main fine-tuning results are reported in Section 6.4, while this appendix supplies additional analyses.
  • E.1 Fine-Tuning as Value Distillation: LDM fine-tuning distills epistemic acquisition value: high-budget search generates candidates, reasoning augmentation translates Bayesian-optimisation statistics into rationales, and supervised training produces a fast student proposer.The student is trained on CoT targets using standard next-token prediction, compiling the search policy into amortised inference.
  • E.2 Cross-Molecule Transfer without Reasoning Augmentation: 22.279±3.828 final hypervolume was achieved by the fine-tuned model versus 16.489±5.867 for the base Qwen3.5-9B LDM under cross-molecule evaluation.The source and target molecular optimisation tasks differed, so the improvement is attributed to transfer of acquisition-weighted research-management policy rather than memorisation of source-task molecules.
  • E.3 Supplementary Quantitative Tables: E.3 consolidates supplementary quantitative evidence, retaining G12C results and collecting the numerical cross-domain comparisons underlying the three main-text figures.Table 6 reports reasoning-augmentation ablation hypervolume at evaluation budget 80 averaged over five seeds; Table 7 reports terminal metrics for three fine-tuning studies.

E.4 In-Distribution Single-Task Fit · E.5 Case-level Out-of-distribution Generalisation

The single-task policies achieve faithful in-distribution fits, with training and held-out losses converging closely across autoresearch, small-molecule, and antibody design. When evaluated on unseen antibody targets, the distilled acquisition policy matches or exceeds in-distribution performance and outperforms Qwen3.5-9B baselines, demonstrating transfer beyond memorised antigen-specific patterns.

  • E.4 In-Distribution Single-Task Fit: E.4 In-Distribution Single-Task Fit: Training and held-out losses for autoresearch, small-molecule KRAS design, and antibody CDRH3 design converge within a few dozen steps.The held-out curves closely track the training curves across all three domains.
  • E.4 In-Distribution Single-Task Fit: E.4 In-Distribution Single-Task Fit: Held-out losses are 0.06 for autoresearch, 0.38 for small-molecule design, and 0.70 for antibody CDRH3 design.
  • E.4 In-Distribution Single-Task Fit: E.4 In-Distribution Single-Task Fit: Figure 27 confirms a faithful in-distribution fit before acquisition-loop evaluation.The figure compares training loss with held-out evaluation loss over training steps for all three policies.
  • E.5 Case-level Out-of-distribution Generalisation: E.5 Case-level Out-of-distribution Generalisation: Two antibody targets, 1FBI X and 1H0D C, were held out entirely during training and evaluated within the same acquisition-guided loop.The mixed-task model was fine-tuned on the other three of five antibody targets.
  • E.5 Case-level Out-of-distribution Generalisation: E.5 Case-level Out-of-distribution Generalisation: The out-of-distribution model matches or exceeds the in-distribution model on both held-out targets and clearly beats base models.
  • E.5 Case-level Out-of-distribution Generalisation: E.5 Case-level Out-of-distribution Generalisation: −110.57 on 1FBI X beats the base −109.5 but trails the in-distribution −113.4.
  • E.5 Case-level Out-of-distribution Generalisation: E.5 Case-level Out-of-distribution Generalisation: −95.4 on 1H0D C surpasses the in-distribution model at −94.6 and the base at −90.9.
  • E.5 Case-level Out-of-distribution Generalisation: E.5 Case-level Out-of-distribution Generalisation: Because the model never observed these antigens, the gain cannot be attributed to memorisation.The distilled acquisition policy transfers to unseen targets.

E.6 Task-level Out-of-distribution Generalisation · E.7 Distilling Acquisition Value into the Weights

Task-level distillation transfers acquisition-guided exploration and exploitation across domains, but not de novo protein design, explaining strong performance on four of five antibody targets and failure on a narrow, shallow landscape. Hiding Gaussian-process values trains the model to infer epistemic state from observed outcomes, with reasoning largely unchanged and performance improved.

  • E.6 Task-level Out-of-distribution Generalisation: On four of five antibody targets, the task-level OOD model performs on par with an in-distribution model trained directly on the tested antigens.It reaches −113.1 on 1FBI X against −113.4, −110.3 on 1ADQ A against −109.4, −106.6 on 1OB1 C against −105.5, and −104.2 on 1NSN S against −104.7.
  • E.6 Task-level Out-of-distribution Generalisation: −89.4 on 1H0D C is the task-level model’s sole shortfall, matching the base model because its shallow landscape has a narrow optimum requiring deliberate domain-specific design.The best attainable energy is around −95, versus −104 to −113 for the other targets.
  • E.6 Task-level Out-of-distribution Generalisation: The transferred behavior is acquisition-guided: the task-level model conditions on search state, anchors on the best result so far, and proposes moves aimed at improvement.One trace starts from a best sequence at −86.83 and proposes QTFQNDKGLFI using hydrophobic, hydrogen-bonding, and charged residues.
  • E.6 Task-level Out-of-distribution Generalisation: The experiment separates transferable acquisition policy from non-transferable de novo domain design: selection alone suffices on four antigens, whereas protein sequence priors are needed on 1H0D C.The task-level model retreats to the most promising candidate already in the pool, while the in-distribution model composes motifs from scratch.
  • E.7 Distilling Acquisition Value into the Weights: In the adopted reasoning-augmentation regime, GP posterior mean, uncertainty, and acquisition values are hidden, so the model infers epistemic state from tried candidates and real outcomes.The alternative embeds GP values directly in the prompt, while the adopted variant carries only observed history.
  • E.7 Distilling Acquisition Value into the Weights: 1.3% of reasoning-augmented traces explicitly cite a surrogate number, whereas 97.2% reason from observed outcomes such as stall length, noise level, and best-so-far.The same explore decision can therefore be reconstructed from raw history when GP values are omitted.
  • E.7 Distilling Acquisition Value into the Weights: The GP-hidden proposer attains the best average binding energy and the best result on three of five antigens, including −115.9 on 1FBI X.Table 8 compares task-level OOD proposers trained only on nanoGPT and small-molecule trajectories, differing only in whether GP values appear in the prompt.
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