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## Creator

[Satoru Fujii](https://orcid.org/0009-0004-0324-8949), [Ryo Tamura](https://orcid.org/0000-0002-0349-358X), [Masato Sumita](https://orcid.org/0000-0002-3506-1028), [Kei Terayama](https://orcid.org/0000-0003-3914-248X)

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[Efficient and scalable expansion of property limits                    <i>via</i>                    novelty-guided exploration](https://mdr.nims.go.jp/datasets/fa25c6e2-589c-43bd-af64-6fa6a7099c71)

## Fulltext

DigitalDiscoveryPAPERPublished on 21 July 2026Licensed under CC-BY 4.0Efficient and scaaGraduate School of Medical Life ScienSuehiro-cho, Tsurumi-ku, Yokohama, Kanark@yokohama-cu.ac.jp; terayama@yokohambCenter for Basic Research on Materials, NaNamiki, Tsukuba, Ibaraki, 305-0044, JapancGraduate School of Frontier Sciences, The UKashiwa, Chiba, 277-8561, JapandRIKEN Center for Advanced Intelligence Pro103-0027, JapaneMolNavi LLC, 402 Wizard Building, 1Kanagawa, 220-0072, JapanfDepartment of Life Science and TechnoNagatsuta-cho, Midori-ku, Yokohama, KanaCite this: Digital Discovery, 2026, 5,3756Received 19th May 2026Accepted 2nd July 2026DOI: 10.1039/d6dd00294crsc.li/digitaldiscovery3756 | Digital Discovery, 2026, 5, 37lable expansion of property limitsvia novelty-guided explorationSatoru Fujii, *a Ryo Tamura, bcd Masato Sumita de and Kei Terayama *adefFinding diverse and high-quality candidates in vast design spaces remains an important challenge inscientific research, including molecular design and material discovery. A recent line of work treatsobserved properties as samples from an unknown distribution and selects candidates that promote moreuniform coverage of the property space using Stein discrepancy as the metric. However, these methodsdo not explicitly account for the information gain of newly acquired data, which can limit exploration ofnovel regions. In addition, they are not designed for efficient batch selection and may sufferperformance degradation when applied in batch settings. Moreover, they incur substantial computationalcost due to both large per-iteration overhead and increasing cost as the number of observations grows.To address these limitations, we incorporate predictive uncertainty into the objective function andintroduce diversity-aware batch selection strategies to promote informative and diverse candidates. Inaddition, we propose a sampled Stein novelty estimator and efficient tensor calculations that significantlyreduce computational overhead. Performance and runtime evaluations on molecular and materialsdatasets show that our method enables scalable and sample-efficient expansion of property-spacecoverage.1 IntroductionNavigating vast design spaces to identify candidates with a widerange of desirable properties remains an important challenge inscientic research, for example, in molecular design andmaterials discovery, where machine learning and generativemodels have increasingly been used to guide the search fornovel structures and functionalities.1–5 In practical applications,it is oen desirable not only to optimize specic target prop-erties but also to discover out-of-distribution candidates thatcover distinct regions of the property space or Pareto front.6,7 Inmulti-property optimization settings, for example, the objectivefunction is oen difficult to dene unambiguously. Moreover,even when explicit objectives are available, objective-freeexploration can in some cases outperform objective-drivenapproaches.8 Such exploration paradigms have also been usedce, Yokohama City University, 1-7-29,gawa, 230-0045, Japan. E-mail: fujii.sat.a-cu.ac.jptional Institute for Materials Science, 1-1niversity of Tokyo, 5-1-5 Kashiwa-no-ha,ject, 1-4-1, Nihonbashi, Chuo-ku, Tokyo,-4-3 Sengen-cho, Nishi-ku, Yokohama,logy, Institute of Science Tokyo, 4259gawa, 226-8501, Japan56–3765to obtain representative samples that provide a holistic view ofproperty space,9–11 to discover diverse behaviors in robotics,12and to efficiently acquire labeled samples that improve predic-tive models.13,14 As illustrated in Fig. 1(a), the overarching goal isto expand coverage beyond densely sampled regions and revealpreviously unexplored areas of the property space. Motivated bythis background, efficient exploration methods, includingactive learning15,16 and generative models,17,18 have beenproposed to navigate large design spaces and identify novelmaterials or molecules with diverse properties.Since data distributions in property space are oen highlybiased, naive sampling tends to yield points concentrated ina limited region of the property space. One way to address thisissue is to treat observed property values as samples from anunknown distribution and iteratively select candidates thatmove this empirical distribution toward a uniform distributionover the property space, as illustrated in Fig. 1(b). In particular,methods such as BLOX19 iteratively select candidates whosepredicted properties maximize a quantity called Stein novelty,which measures how much a new point contributes to movingthe empirical distribution closer to a uniform distribution, asquantied by the kernelized Stein discrepancy.20 This calcula-tion does not require knowledge of the explicit bounds of thedistribution, making it suitable for problems in which the rangeof the property space is unknown or difficult to estimate.However, several practical challenges remain. One limitationis that diversity among candidates in the underlying input space(e.g., molecular descriptors or material features) is not explicitly© 2026 The Author(s). Published by the Royal Society of Chemistryhttp://crossmark.crossref.org/dialog/?doi=10.1039/d6dd00294c&domain=pdf&date_stamp=2026-09-11http://orcid.org/0009-0004-0324-8949http://orcid.org/0000-0002-0349-358Xhttp://orcid.org/0000-0002-3506-1028http://orcid.org/0000-0003-3914-248Xhttps://creativecommons.org/licenses/by/4.0/Fig. 1 Overview of property-space coverage expansion. (a) Conceptual illustration of expanding the property space for novel discovery, moreefficient learning of accurate predictive models, and better understanding of the data. (b) Illustration of boundary expansion in property space bydriving the distribution of observed points toward a uniform distribution. (c) Illustration of improving property-space expansion by combininginput-space strategies, including predictive uncertainty and in-batch diversity. Note that although both spaces are shown in two dimensions inthis figure, the input space typically has much higher dimensionality than the property space.Paper Digital Discoveryconsidered when selecting new candidates. Incorporating suchinformation has also been studied in prior work,13,21 and can bebenecial for two reasons. First, sampling informative pointscan accelerate the improvement of the predictive model andincrease sample efficiency. Second, candidates that are unusualin the input space may correspond to unexplored or extremeregions in the property space. Therefore, considering input-space diversity can help guide exploration toward novelregions of the property space. In this context, we incorporatepredictive uncertainty into the objective function to prioritizecandidates whose experimental assay is expected to providehigh information gain. In addition, we introduce diversity-aware batch proposal strategies that prevent simultaneouslyproposed candidates from becoming overly similar in the inputspace. Fig. 1(c) provides an overview of this coverage expansionstrategy.Another challenge is the computational cost of Stein noveltycalculations, which grows with the number of observedsamples,19 and limits the applicability of the method to largedatasets. Because Stein novelty involves interactions betweencandidate points and previously observed samples, thecomputational cost increases linearly as the explorationproceeds. To address this, we propose a sampled Stein novelty© 2026 The Author(s). Published by the Royal Society of Chemistryestimator that reduces the asymptotic computationalcomplexity of the algorithm while maintaining the performanceof the method. In addition, we implement chunked tensorcomputations that substantially reduce the runtime of themethod.We evaluate the proposed framework on photo-functionalmolecules19 and electronic materials22 in terms of coverage-expansion efficiency and runtime, and show that it enablescomputationally scalable, sample-efficient exploration. Theseresults highlight the practical utility of the framework forproperty-space exploration in both sample-limited and large-scale settings. Our framework is freely available as BLOX2 athttps://github.com/ycu-iil/BLOX2.2 Methods2.1 OverviewOur method builds on approaches that select points to expandthe empirical property distribution toward a more uniform one,and extends this paradigm in two directions. First, we improvedata acquisition by incorporating input-space informationthrough two methods: uncertainty-aware scoring and diversity-aware batch proposal. Second, we accelerate the computation ofDigital Discovery, 2026, 5, 3756–3765 | 3757https://github.com/ycu-iil/BLOX2Digital Discovery Paperthe novelty score using two techniques: chunked tensorcomputation and sampled novelty estimation. An overview ofthe workow is illustrated in Fig. 2.2.2 Stein novelty-based explorationGiven the observed property values, the goal is to select newcandidates whose properties expand coverage of the propertyspace.Following BLOX,19 we quantify this objective using the Steindiscrepancy with respect to a uniform distribution. Thecontribution of a candidate point to moving the empiricaldistribution toward the target distribution is measured by Steinnovelty.In the present setting, the property space is bounded by theniteness of the candidate pool, or the physical and chemicalfeasibility of the candidates in general. Although its boundary isgenerally unknown, the Stein discrepancy depends on densitygradients rather than explicit boundary specication, so noexplicit bound estimation is required during optimization.The surrogate model predicts a property vector for eachcandidate, and the Stein novelty score is calculated from thepredicted properties. Candidates with higher Stein novelties areconsidered to contribute more strongly to expanding thecoverage of the property space. The details of Stein discrepancyand Stein novelty are provided in SI Text T1 and T2. The Steinnovelty score, together with the uncertainty score and the in-batch diversity score when enabled, are calculated for allcandidates. Aer these values are normalized, the acquisitionFig. 2 Workflow of the proposed method. Observed points are used to tcalculated in property space from predicted values, together with predicare then sent to an experimental assay or simulation to obtain new obse3758 | Digital Discovery, 2026, 5, 3756–3765score is computed as a convex combination of them, and thecandidate with the highest score is selected for observation.2.3 Incorporating predictive uncertaintyAlthough maximizing Stein novelty promotes coverage expan-sion in the property space, it does not explicitly account for hownewly acquired data improve the predictive model. In activelearning settings, especially in Bayesian optimization,uncertainty-aware acquisition is a standard and widely usedstrategy.15,23Following this practice, we incorporate predictive uncer-tainty into the acquisition score. In our experiments, predictiveuncertainty was estimated using quantile regression withLightGBM.24 Specically, the difference between the predicted0.9 and 0.1 quantiles was used as an uncertainty score.Uncertainty scores are normalized for each property andthen averaged across properties.2.4 Diversity-aware batch proposalIn many practical settings, each experiment or simulation iscostly, so running evaluations in parallel is desirable to reducewall-clock time. To enable such parallel evaluation, the methodmust propose multiple candidates at each iteration; therefore,we extend the framework to batch proposal.Candidates are selected sequentially within each batch. Oneway to account for candidates already selected within eachbatch is to use virtual observations. Aer a candidate is selected,it is treated as a virtual observation with the predicted propertyvalue. The acquisition score is then recomputed with respect torain the predictor, and new candidates are selected using Stein novelty,tive uncertainty and in-batch diversity control. The selected candidatesrvations for the next cycle.© 2026 The Author(s). Published by the Royal Society of ChemistryPaper Digital Discoverythe augmented set of observations. This procedure is repeateduntil the given batch size is reached.However, when simultaneously proposed candidates areoverly similar, the acquired batch tends to be redundant andless informative for model improvement. Therefore, rewardingdiversity among proposals or penalizing proximity betweencandidates is widely used in active learning settings.25,26 Weadopt the same principle here by introducing a diversity scorebased on proximity in the input space and incorporating it intothe acquisition score instead of using virtual observations.In our experiments, we evaluated three diversity metricsdened on input-space features. Stein-based diversity computesthe Stein novelty in the input space with respect to pointsalready selected in the batch and uses it as a diversity term,while Stein novelty in the output (property) space is computedseparately for acquisition scoring, as in the other settings.Nearest-neighbor diversity calculates the shortest distance topoints already in the batch, similar to greedy sampling,13,21 andits multiplicative inverse is used as the score. SimHash-baseddiversity27 uses random hyperplanes to partition the inputspace and applies a penalty when a candidate falls into a parti-tion that already contains selected points.2.5 Accelerating Stein novelty computationThe computational cost of Stein novelty increases as thenumber of observed samples grows, because each candidatescore depends on interactions with the observed set. To main-tain scalability on large datasets, we introduce two comple-mentary acceleration techniques that reduce computationaltime.2.6 Chunked tensor computationThe dominant cost of Stein novelty computation comes frompairwise interactions between each candidate and the observedsamples, which are largely reduced to pairwise distance calcu-lations. In our implementation, these distance calculations areevaluated for chunks of candidate points at once by rewritingthe nested loops in the original BLOX implementation as vec-torized 3D tensor operations. Although this does not change theasymptotic complexity of the Stein novelty calculation, itsubstantially reduces computation time in settings where Steinnovelty computation becomes a bottleneck. The details of thiscalculation are provided in SI Text T3.2.7 Sampled Stein noveltyWe further introduce a sampled estimator of Stein novelty.Here, n denotes the number of observed samples, vp a candidatepoint, vi the i-th observed sample, and u(vp, vi) the pairwiseinteraction term in the Stein novelty computation. Instead ofusing all observed samples, we randomly select a subset S3 {1,., n} of size m for each computation and approximate the fullsum by a sum over S. Because a uniformly sampled subsetsatises© 2026 The Author(s). Published by the Royal Society of ChemistryES"nmXi˛Su�vp; vi�# ¼Xni¼1u�vp; vi�;the subsampled objective is an unbiased estimator of the fullobjective, and the multiplicative constantnmdoes not affect theminimizer. This approximation reduces the per-iterationcomputational cost of the Stein novelty estimation from O(N)to O(1) with respect to the number of observations N. A detaileddescription is provided in SI Text T4.2.8 DatasetsTo evaluate the proposed method in representative multi-objective molecular and materials design settings, we usedtwo benchmark datasets: one for photo-functional moleculesand the other for electronic materials. Although the envisionedapplication is an iterative proposal-to-experimental-assay loop,these xed datasets allow controlled comparison amongmethods under the same conditions.The rst dataset comprises 87 268 molecules from the ZINCdatabase,28 with absorption wavelength (nm) and intensityvalues precomputed by density functional theory (DFT) simu-lations29 at the B3LYP/6-31G* level. These two properties aredirectly relevant to the design of photo-functional molecules,where both spectral position and transition intensity areimportant. As input features, we used Morgan ngerprints withradius 2 and 2048 bits,30 together with RDKit descriptors,31resulting in a total input dimensionality of 2265.The second dataset consists of 1277 materials obtained froma public database.22 The target properties are band gap (eV) andpermittivity, which are fundamental quantities for electronicand dielectric material design. For these materials, we used 132composition-based physical-property features generated byMagpie.322.9 MetricsTo quantify coverage, we compute the area of the union of 3-neighborhoods around observed samples in the property space.For each dataset, the property space is rst normalized using allavailable true property values, and the resulting area is furtherdivided by the maximum area computed from all available trueproperty values so that coverage takes values in [0, 1]. The use of3-neighborhoods is a commonly adopted formulation.33Throughout this paper, we refer to this quantity simply ascoverage.In the main text, we report comparisons for 3 = 1 in thenormalized property space. Fig. 3 compares the coverage ob-tained by the proposed method and by random candidateselection, showing that the metric is consistent with the visualextent of the covered region.When ner local lling behavior is of primary interest,smaller 3 values may be more appropriate. We also evaluatedthe methods with 3 = 0.1 and using other evaluation metrics,such as the kernelized Stein discrepancy and convex-hull area,and found broadly similar overall trends across metrics. Thecorresponding results are provided in SI Fig. S1–S3.Digital Discovery, 2026, 5, 3756–3765 | 3759Fig. 3 Illustrative comparison between the proposed method (denoted as “With exploration”) and random candidate selection (denoted as“Random”), demonstrating that the defined coveragemetric is consistent with the visual extent of explored regions in the property space. In eachrow, the left two panels show the observed-property distributions after 50 and 200 proposals, together with the corresponding coverage regions(3 = 1). Here, coverage denotes the area of the union of 3-neighborhoods around observed samples. The right panel shows the trajectory ofcoverage over steps.Digital Discovery Paper3 Results3.1 Experimental setupIn the proposed method, a surrogate model is trained on theobserved data, and new candidates are iteratively proposed bymaximizing Stein novelty computed from the predicted prop-erty values. In this section, we evaluate how incorporatingpredictive uncertainty and in-batch diversity into this selectioncriterion affects coverage expansion performance, and thenassess the computational speedups obtained by the proposedStein calculation techniques.All experiments were conducted on the molecular andmaterials datasets introduced above. For the coveragecomparisons, each run was initialized with 10 randomlyselected observed points shared across all methods withina seed. We used 5 seeds and 2000 proposals for the moleculardataset, and 20 seeds and 400 proposals for the materialsdataset. All samples that were not selected as the initialobserved points were used as the candidate pool, and selectedcandidates were removed from the candidate pool aer their3760 | Digital Discovery, 2026, 5, 3756–3765property values were revealed. The reported coverage trajecto-ries are averaged across seeds, and the shaded regions indicatestandard deviation. Details of the used hyperparameters areprovided in the SI Text T5.3.2 Effect of predictive uncertaintyWe rst evaluate the effect of incorporating predictive uncer-tainty into the acquisition score. In this experiment, uncertaintyis dened as the LightGBM quantile spread (q0.9–q0.1). Thepredictive uncertainty-to-Stein novelty ratio was set to 0.75 forboth datasets.Fig. 4(a) compares the coverage trajectories of two strategiesfor the molecular dataset: selection without model condence(Stein novelty only) and selection with predictive uncertainty.Fig. 4(b) shows the corresponding results for the materialsdataset. The coverage values are averaged across seeds for eachdataset.Across both datasets, incorporating model condenceimproved coverage expansion performance. This result© 2026 The Author(s). Published by the Royal Society of ChemistryFig. 4 Results of the predictive-uncertainty and in-batch-diversity experiments on the molecular and materials datasets: (a) predictiveuncertainty on the molecular dataset, (b) predictive uncertainty on the materials dataset, (c) in-batch diversity on the molecular dataset, and (d)in-batch diversity on thematerials dataset. The curves show themean coverage trajectories across seeds, and the lightly shaded regions indicatethe standard deviation.Paper Digital Discoveryindicates that condence-aware acquisition provides moreinformative samples and therefore achieves effective explora-tion of the property space.3.3 Effect of diversity-aware batch proposalWe next examine batch selection, which is important in prac-tical settings where multiple candidates can be evaluated inparallel. For a fair comparison, predictive uncertainty wasdisabled in these experiments. We set the diversity-to-Steinnovelty ratio to 0.25 for the molecular dataset and 0.50 for thematerials dataset, xed the batch size at 100, and evaluated thefollowing methods:� Virtual observation baseline without diversity score.� Stein-based diversity.� Nearest-neighbor diversity.� SimHash-based diversity.Fig. 4(c) shows that incorporating diversity within the batchimproves coverage expansion performance compared to rawbatch selection for the molecular dataset, and Fig. 4(d) showsthe corresponding results for the materials dataset. Becausecandidate evaluations can oen be performed in parallel, batchproposal can further reduce the number of learning iterationsrequired for exploration in practice.Among the tested methods, Stein-based diversity achievedthe best performance. However, because the computational costof the Stein novelty increases proportionally with the number oftarget dimensions, it can become expensive in high-© 2026 The Author(s). Published by the Royal Society of Chemistrydimensional input spaces. A similar computational-costconcern also applies to the nearest-neighbor distance,although algorithmic renements may partially mitigate thisissue. In contrast, SimHash-based diversity required almost thesame computation time as raw batch selection without in-batchdiversity, while still improving performance over the raw base-line in both datasets. Considering this practical trade-off,SimHash-based diversity may be a practical default choice.Fig. 5 further shows the effect of Stein-based in-batch diversityon the materials dataset across batch sizes from 1 to 256. Theseresults show that in-batch diversity can substantially suppressthe performance degradation associated with increasing batchsize, highlighting its importance in large-batch settings.3.4 Acceleration of Stein novelty computationNext, we evaluate the effect of the chunked tensor calculation ofthe Stein novelty. The experiments were conducted on the samemachine for fair comparison. Because the materials dataset hasboth lower input dimensionality and fewer data points, itscomputation time is trivial and not a practical bottleneck;therefore, the experiments in this section use only the molec-ular dataset.Fig. 6(a) shows that our implementation achieves more thana 300-fold speedup of Stein novelty computation compared tothe original implementation,19 enabling efficient evaluation oflarge candidate sets. Fig. 6(b) presents the same results ona logarithmic scale, showing that the computation time stillDigital Discovery, 2026, 5, 3756–3765 | 3761Fig. 5 Effect of Stein-based in-batch diversity as the batch size increases from 1 to 256. Panels (a) and (b) show the mean coverage trajectoriesacross seeds with and without in-batch diversity (Stein-based), respectively, and the lightly shaded regions indicate the standard deviation.Digital Discovery Paperincreases approximately in proportion to the number ofobserved points in both implementations.Next, we evaluate the sampled Stein novelty estimator.Fig. 6(c) compares the case with sampled Stein novelty (samplesize 500) and the case without sampling, showing that sampledStein novelty makes the computation time constant with respectto the number of observed points. Fig. 6(d) shows that thesampled Stein novelty largely preserves coverage expansionFig. 6 (a) Comparison of selection time for Stein novelty computation bimplementation, measured on the samemachine. (b) Shows the same resfor Stein novelty computation with and without sampling (sample sizetrajectories with and without sampling in Stein novelty computation fodeviation across seeds.3762 | Digital Discovery, 2026, 5, 3756–3765performance. Even with a sample size of 100, the performancedegradation remains small.4 DiscussionIn this study, we extended Stein novelty-based property-spaceexploration by incorporating input-space information andimproving the computational efficiency of novelty calculation.Across molecular and materials datasets, the proposedetween the original BLOX implementation19 and our chunked-tensorults as (a), but on a logarithmic y-axis. (c) Comparison of selection time= 500, 100) for the molecular dataset. (d) Comparison of coverager the molecular dataset. The lightly shaded regions indicate standard© 2026 The Author(s). Published by the Royal Society of ChemistryPaper Digital Discoveryframework achieved sample-efficient coverage expansiontogether with substantially improved runtime, supporting itspractical use in both sample-limited and large-scale settings.Our method incorporates information from the input spacein order to improve the value of the acquired data. In particular,predictive uncertainty is used as a proxy for data value in theacquisition process. An alternative approach is to calculate theStein novelty directly in the input space. However, its compu-tational cost increases linearly with the dimensionality of theinput feature vectors, making it less suitable for high-dimensional datasets. Although we used LightGBM24 in thisstudy due to its favorable balance between accuracy and speed,the framework is not tied to a specic predictor. For example,TabPFN,34 which directly outputs predictive distributions,might further improve exploration quality while also providinguncertainty estimates without separate quantile models, albeitat a higher base computational cost. In our experiments, thisstrategy produced performance comparable to uncertainty-based selection; details are provided in the SI Fig. S4.The main practical risk in batch proposal is selecting overlysimilar candidates. The diversity score introduced in this workmitigates this issue by encouraging exploration within eachbatch. The computational cost of diversity penalties can bereduced using dimensionality reduction techniques such asprincipal component analysis (PCA). The squared distance inthe original space can be decomposed into the sum of squareddistances along the retained and discarded PCA components.Since Stein novelty relies on pairwise distances, its accuracydepends on the fraction of variance captured by the retainedcomponents. We also empirically evaluated this approximation,and the results are reported in SI Fig. S5. As predictive perfor-mance improves over the course of exploration, the benet ofenforcing in-batch diversity may decrease. Therefore, a sched-uling strategy that gradually reduces the weight of the in-batchdiversity term as the number of steps increases may furtherimprove overall performance.The sampled Stein novelty signicantly reduces the compu-tational cost of novelty estimation. Although the estimator itselfhas constant complexity with respect to the number of obser-vations, the overall runtime may still depend on the predictivemodel used. In many predictive models, retraining the modelaer each iteration scales at least linearly with the number ofobservations. Therefore, when scalability is a primary concern,predictive models that support online learning are preferable.Further improvements may be possible by introducing impor-tance sampling strategies35 that focus on informative regions ofthe property space.We use a Gaussian kernel in Stein novelty, and its bandwidthis a hyperparameter. In our experiments, the bandwidth is xedto s = 1 for consistency between datasets. In the input space,the feature vectors for all candidate points are known inadvance. Therefore, the bandwidth parameters can be esti-mated using statistics such as the average pairwise distance. Incontrast, property values for unobserved candidates areunknown, making such estimation difficult in the propertyspace. Regarding ratios of uncertainty and diversity score, ourexperiments were conducted on only two datasets and therefore© 2026 The Author(s). Published by the Royal Society of Chemistrydo not establish a single set of optimal settings applicable to allpossible datasets. However, from our experience with the testedsettings, an uncertainty-to-Stein novelty ratio of 0.5–0.75 anda diversity-to-Stein novelty ratio of 0.25–0.5 may serve as usefuldefault values.Our method is applicable to datasets with three or moreproperty dimensions. However, because Stein novelty compu-tation scales linearly with the dimensionality of the propertyspace, the computational cost may become substantial in veryhigh-dimensional settings.Author contributionsSatoru Fujii: conceptualization (lead); methodology (lead); so-ware (lead); data curation (equal); writing – original dra (lead);writing—review and editing (lead). Ryo Tamura: data curation(equal); supervision (supporting); methodology (supporting);writing—review and editing (supporting). Masato Sumita: datacuration (equal); supervision (supporting); methodology (support-ing); writing—review and editing (supporting). Kei Terayama:supervision (lead); funding acquisition (lead); methodology (lead);data curation (equal); project administration (lead); conceptuali-zation (lead); writing—review and editing (lead).Conflicts of interestThere are no conicts to declare.Data availabilityThe source code of BLOX2 and the datasets used in this studyare publicly available at https://github.com/ycu-iil/BLOX2. Theversion of the repository corresponding to the experiments re-ported in this manuscript has been archived on Zenodo and isavailable at https://doi.org/10.5281/zenodo.20911113.The datasets used in this study are included under the data/directory of the same archived repository. The material datasetwas derived from a public oxide dielectric database available athttps://github.com/takahashi-akira-36m/oxi_diel_db/tree/master and is provided under the Creative CommonsAttribution 4.0 International License (CC BY 4.0).Supplementary information (SI): detailed descriptions of themethods, experimental settings, hyperparameter settings, andadditional results. See DOI: https://doi.org/10.1039/d6dd00294c.AcknowledgementsThis work was supported by the JST FOREST Program [grant no.JPMJFR232U], JSPS KAKENHI [grant no. 25K01492], and DataCreation and Utilization Type Material Research and Develop-ment Project [grant no. JPMXP1122683430].Digital Discovery, 2026, 5, 3756–3765 | 3763https://doi.org/10.5281/zenodo.20911113https://github.com/takahashi-akira-36m/oxi_diel_db/tree/masterhttps://github.com/takahashi-akira-36m/oxi_diel_db/tree/masterhttps://doi.org/10.1039/d6dd00294chttps://doi.org/10.1039/d6dd00294cDigital Discovery PaperReferences1 A. Baranes and P.-Y. 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Stat., 2010, 2(1), 54–60.Digital Discovery, 2026, 5, 3756–3765 | 3765 Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration Efficient and scalable expansion of property limits via novelty-guided exploration