PaperlayerView exact revision on arXiv

Source-linked AI summary

Simulated petrological labels enable probabilistic mineralogy prediction from whole-rock geochemistry

Matthew J. Liu, Aaron D. Kaplan, Michael L. Whittaker, Kristin A. Persson

arXiv:2610.36429v1cs.LG

TL;DR

Whole-rock chemistry is easier to obtain than modal mineralogy, but paired labels are sparse and a composition can correspond to multiple assemblages. The paper trains probabilistic predictions on simulated labels and recalibrates them against measured rocks; zero-shot predictions discriminate mineral presence, while few-shot recalibration improves likelihood more quickly than abundance error.

  • Problem

    Modal-mineralogy measurements are time-intensive, paired geochemistry labels are sparse, and one composition can correspond to multiple assemblages.

    Source: §1 · pp. 1–2

  • Method

    The model combines a composition-pretrained transformer, probabilistic heads trained on simulated assemblages, and an optional recalibration layer fit to measured mineralogy.

    Source: §1 · p. 2, §2 · p. 2

  • Results

    Zero-shot AUROC ranged 0.575 to 0.870 across categories, while about 25-rock recalibration recovered 76 percent of validation joint NLL reduction; abundance error fell from 11.0% zero-shot to 9.5% on the full fitting set.

    Source: §3 · pp. 4–5

  • Takeaways & Limitations

    Different geological simulators can re-supervise prediction heads without changing the latent representation.

    Source: §3 · p. 5

    The benchmark compares phenocryst modes from two adjacent volcanic fields with equilibrium solids at 50 and 30 wt% residual melt.

    Source: §3 · p. 5

Abstract

from arXiv · show

Modal mineralogy, the mineral identities and abundances in rocks, guides geological studies and industrial resource extraction. While measuring modal mineralogy is time-intensive, whole-rock chemical measurements furnish elemental concentrations at higher throughput. Predicting mineralogy from elemental data, however, poses a one-to-many inverse problem, and labeled mineralogical datasets are too sparse to train on at scale. We address both challenges by simulating petrological labels that express multiple formation conditions per composition and at a scale unattainable by measurements. Nearly one million simulated labels supervise the middle component of a three-part model: a transformer encoder self-supervised on roughly 788,000 whole-rock compositions, the simulation-trained heads that predict distributions over mineral assemblages, and a recalibration layer that aligns the predictions with measured mineralogy. Zero-shot on 640 volcanic rocks, the model discriminates the presence of most mineral categories and predicts which rocks are richer in each mineral. However, the predicted abundances are systematically offset from measured values. Recalibration fit on as few as 25 labeled rocks recovers 76 percent of the likelihood improvement from fitting on the full 368-rock fitting set, while abundance error responds more slowly (11.0% zero-shot and 9.5% with the full fitting set). This work demonstrates how a machine learning model in the geochemical sciences can both leverage an imperfect simulator and mitigate its systematic biases.

1 Introduction

Modal mineralogy informs geological investigation and resource extraction, but measuring it is slower than obtaining whole-rock chemistry. Prediction is constrained by sparse paired labels and by the many assemblages that can arise from one composition; thermodynamic simulation offers a scalable but imperfect source of labels.

1 Introduction

  • Modal mineralogy informs geological studies and mining decisions, while microscopy and X-ray diffraction require prepared samples and expert effort compared with higher-throughput whole-rock chemistry.Mineral assemblages reflect magma evolution and inform flowsheet design and extraction methods for critical materials.Source: §1 · p. 1
  • Paired modal-mineralogy labels are scarce, and each composition can yield different assemblages under varying formation conditions and geological processes.Relevant factors include temperature, pressure, water content, crystal kinetics, diffusion, exsolution, transport, and separation.Source: §1 · p. 2
  • Thermodynamic simulators can generate diverse equilibrium assemblage labels across candidate conditions, addressing label scarcity and representing the one-to-many mapping at scale.The labels inherit simulator limitations, including omitted kinetics and transport and assumed formation conditions, so they can deviate systematically from measured mineralogy.Source: §1 · p. 2
  • The paper tests simulation-trained prediction with a transformer pretrained on roughly 788,000 compositions and nearly 950,000 simulated assemblages, followed by recalibration on measured rocks.The evaluation uses 640 volcanic rocks.Source: §1 · p. 2

2 Overview of model architecture and evaluation

The model encodes whole-rock compositions, predicts distributions over simulated assemblages, and can recalibrate its predictions using measured mineralogy. Evaluation uses a grouped split of volcanic rocks and scores only the assemblage head against seven mineral categories.

2 Overview of model architecture and evaluation

  • A pretrained encoder, simulation-trained probabilistic heads, and an optional measured-mineralogy recalibration layer form the three model components.The heads predict mineral presence and proportions, oxide compositions, and melt pressure, temperature, and water content; the input contains composition data, not formation conditions.Source: §2 · p. 2
  • The CrabNet-based encoder uses masked-element modeling on 787,721 measured whole-rock compositions to learn a latent representation.Each element is a token, and a decoder predicts masked concentrations as standardized log values.Source: §2 · p. 2
  • Three heads trained on simulated labels predict distributions because each of 9,946 measured compositions is simulated under 48 sampled formation conditions.The assemblage head factors mineral presence from abundances conditional on presence; the model also predicts oxide compositions and formation conditions.Source: §2 · pp. 2–3
  • The optional recalibration layer fits a small set of labeled rocks while keeping the encoder and prediction heads fixed, adjusting presence logits and Dirichlet concentrations.Its parameters apply an affine map to presence logits and a multiplicative rescaling to concentrations.Source: §2 · p. 3
  • Evaluation uses 640 volcanic rocks split by stratigraphic unit, with mineral presence assessed by AUROC and assemblage predictions scored by joint NLL and absolute abundance error.The resulting train, validation, and test sets contain 368, 111, and 161 rocks; evaluation collapses predictions onto seven mineral categories and scores only the assemblage head.Source: §2 · p. 3

3 Results and discussion

The pretrained representation improves mineral-presence predictions over raw geochemistry, while simulation-trained heads recover mineral ordering zero-shot but systematically misestimate abundance. Recalibration improves likelihood substantially with few measured rocks, though abundance error improves more slowly.

3 Results and discussion

  • The pretrained representation preserved geochemical structure, with median log-space R2 of 0.89 across 8 major elements and 0.84 across 13 trace elements.These imputation scores were measured on 157,544 held-out compositions.Source: §3 · p. 3
  • Across fitting sizes, latent-representation heads outperformed raw-geochemistry heads by 0.50 to 0.67 nats of joint NLL, primarily through the presence factor.A head given no chemistry converged to the same abundance factor.Source: §3 · p. 3
  • Zero-shot presence AUROC ranged from 0.575 to 0.870 across mineral categories, and predicted abundances positively ranked measured abundances for 6 of 7 categories.Abundances nevertheless showed category-specific bias, with feldspar and quartz most often over-predicted.Source: §3 · p. 4, Figure 1 · p. 4
  • 25-rock recalibration reduced test-set joint NLL from 9.36 to 1.58 nats, with 71 percent of the reduction in the abundance factor.For the illustrated rhyolite, recalibration shifted predicted quartz and biotite abundances toward their measured values.Source: §3 · p. 4, Figure 2 · p. 5
  • 25 rocks recovered 76 percent of the validation joint NLL reduction, reaching 3.97 nats versus 13.4 nats zero-shot; 368 rocks reached 0.97 nats.Abundance error declined more slowly, from 11.0% zero-shot to 9.5% with the full fitting set.Source: §3 · p. 5
  • The benchmark compares phenocryst modes from two adjacent volcanic fields with equilibrium-solid labels at 50 and 30 wt% residual melt.The authors also note that composition alone may under-determine polymorphs and solid solutions, where errors concentrate.Source: §3 · p. 5

A Related Works

Geochemical mineral prediction faces sparse measured labels and a one-to-many mapping from composition to assemblage. Prior approaches address parts of the problem, while this work combines simulation-generated supervision, probabilistic predictions, and recalibration on measured mineralogy.

A Related Works

  • Site-specific supervised models can perform well locally, but each new element, mineral, or lithology requires its own labeled dataset, limiting their use as general predictors.Their evaluation often uses held-out samples from the same site.Source: A Related Works · p. 11
  • Grain-scale classifiers identify minerals from individual-grain chemistry but do not predict whole-rock modal abundance.Normative calculations return a single assemblage independent of formation conditions, while probabilistic mass-balance methods are fitted study by study and require a predefined mineral list.Source: A Related Works · p. 11
  • Thermodynamic simulators can address label scarcity and the one-to-many mapping by generating labels at scale across sampled formation conditions.Earlier work largely used simulator outputs as study deliverables rather than as model training signals.Source: A Related Works · p. 11
  • The framework combines a composition transformer, masked pretraining, simulator-generated supervision, and measured-mineralogy recalibration to predict distributions over assemblages across rock types.Recalibration on a small measured set adjusts systematic prediction errors and can account for overconfidence while preserving mineral rankings.Source: A Related Works · pp. 11–12
  • The paper situates its approach among four model families—site-specific models, grain-scale classifiers, normative calculators, and simulators—each addressing distinct challenges.The combined use of self-supervised pretraining, simulated labels, and post-hoc recalibration is presented as not previously reported for geochemical-science machine learning.Source: A Related Works · pp. 11–12

B Implementation Details

The implementation adapts a composition transformer to fixed elemental inputs and uses distinct token states to represent measured, missing, masked, and redox information. The redox ratio is used in pretraining but padded for benchmark head training and evaluation.

B.1 Input representation and tokenization

  • The CrabNet adaptation fixes the element-row vocabulary across rocks and uses a reserved padding value for unreported elements instead of zero abundance.The fixed rows make each row denote the same element in every rock; padding supports masking measured concentrations during pretraining.Source: §B.1 · p. 13
  • The encoder input has 23 fixed rows: 9 major elements, 13 trace elements, and an Fe3+/total-Fe ratio; formation conditions are not inputs.Trace elements were selected for prevalence in the compilation and usefulness in distinguishing rocks with similar major-element chemistry.Source: §B.1 · p. 13
  • Each row is encoded as an element identity and rescaled abundance, with separate states for padding, populated, masked, and redox tokens.Masked rows remain attended during pretraining, whereas padding is excluded from attention; compilation blanks are treated as missing rather than measured zeros.Source: §B.1 · p. 13
  • The redox row is populated only during pretraining and padded for head training and benchmark evaluation because benchmark rocks do not report both FeO and Fe2O3.The authors note that datasets reporting both iron concentrations could support heads that use measured oxidation state.Source: §B.1 · p. 14

B.2 Encoder architecture

The encoder combines element embeddings and abundance encodings before a transformer produces a pooled latent vector for each rock. Its configuration includes searched architectural choices and fixed featurization conventions.

B.2 Encoder architecture

  • Each token sums a mat2vec element embedding with two sinusoidal abundance encodings, one based on linear frac and one on log10 frac.The embedding table is initialized from published 200-dimensional embeddings and remains trainable during pretraining; the padding embedding is fixed at zero.Source: §B.2 · p. 14
  • The encoder uses a 256-dimensional representation and four transformer layers, with width, layer count, head count, and dropout selected by hyperparameter searches.Table B3 reports the encoder configuration; the remaining values are fixed conventions informed by the original CrabNet implementation.Source: §B.2 · p. 14, Table B3 · p. 14
  • For a batch of rocks, the input and contextualized token grids have shape [B, 23, 256], and pooling yields one [B, 256] latent representation per rock.The checkpoint has 4,514,699 tensor entries, including 3,234,699 trainable parameters.Source: §B.2 · p. 14

B.3 Self-supervised pretraining

Masked-element pretraining uses standardized log-concentration regression to recover hidden elements from whole-rock compositions. The tested log-space objective improved trace-element imputation relative to a linear-space objective without reducing major-element performance.

B.3 Self-supervised pretraining

  • The pretraining set contains 787,721 filtered compositions from a global compilation, after removing implausible oxide totals, sparsely populated rows, and duplicate tokenized compositions.The split held out 20% for validation and 20% for testing by row, assigning downstream compositions to the test split to prevent encoder pretraining on them.Source: §B.3 · pp. 14–15
  • For each rock, a new random subset of populated rows is masked each epoch, and the decoder predicts standardized log concentrations only at masked positions.Log space addresses the large magnitude gap between major and trace elements; element-wise standardization accounts for differences in log-concentration variance.Source: §B.3 · p. 15
  • 0.88 versus 0.84 median R2 across the thirteen trace elements: standardized log-space regression improved over the linear-space objective, with no loss on major elements.The comparison is from a held-out imputation benchmark; Table B4 reports the pretraining configuration and outcome.Source: §B.3 · p. 15, Table B4 · p. 15
  • Hyperparameter tuning used two Bayesian searches ranked by validation loss, with architecture choices from an igneous-only configuration reused for the all-rock encoder.The second search retuned optimization settings after adopting the standardized log-space objective; adding all rock types and the redox row came later without further tuning.Source: §B.3 · pp. 15–16

B.4 Simulated label corpus

The simulated corpus pairs measured igneous compositions with MAGEMin assemblages across sampled formation conditions, then converts solver outputs into targets for three probabilistic prediction heads. The corpus and heads are designed to represent multiple possible assemblages while predicting mineral presence, abundance, composition, and formation conditions.

B.4 Simulated label corpus

  • Each label pairs a measured whole-rock composition with a MAGEMin equilibrium assemblage calculated at specified temperature and pressure.The corpus covers igneous compositions.Source: §B.4 · p. 16
  • The corpus excludes compositions outside defined volcanic, chemical-range, and analysis-completeness criteria, including silica above 80 wt% or magnesia above 18 wt%.Foidites are omitted because the solver failed to converge across sampled conditions.Source: §B.4 · p. 16
  • Simulations follow cooling paths and record assemblages at 50 and 30 wt% residual melt, excluding near-solidus conditions.Solids are renormalized as the assemblage target; oxide compositions and formation conditions also supervise their respective heads.Source: §B.4 · p. 16
  • Pressure and dissolved water are sampled broadly, but rhyolitic solubility applied to every composition undersamples wet, low-pressure conditions for phonolitic melts.The authors identify a composition-aware solubility model as a possible improvement.Source: §B.4 · p. 17
  • The 21-phase vocabulary collapses silica polymorphs and splits solver-lumped feldspar into plagioclase or alkali feldspar according to composition.Chlorite and ferropericlase are dropped because they occur in only about 1 to 2 of every 10,000 draws; labels use a 0.1 wt% presence threshold.Source: §B.4 · pp. 17–18

B.5 Prediction heads

  • The assemblage head factorizes phase presence from abundance, allowing absent phases while modeling abundances only over the predicted support.The composition head predicts each present phase’s oxide composition, while the conditions head predicts temperature, pressure, and dissolved water distributions.Source: §B.5 · pp. 18–19
  • A mass-balance term reconstructs the input composition from predicted solids plus melt and fluid fractions and compositions taken from the label.Predicted solid abundances and compositions are adjusted to reduce reconstruction mismatch.Source: §B.5 · p. 19

B.6 Training

The prediction heads are trained jointly with likelihood terms for presence, abundance, composition, and conditions, plus a mass-balance penalty. Recalibration fits a map to measured mineralogy, with a mixture component that can widen uncertainty for a minority of rocks without widening every prediction.

B.6 Training

  • The joint objective combines four predictive-factor negative log-likelihoods with a mass-balance penalty.The terms score presence, abundance, composition, conditions, and the squared reconstruction residual.Source: §B.6 · p. 19
  • Hyperparameters are selected by Bayesian search using validation assemblage loss, with sampled supports used to break ties among leading trials.The winning trial is retrained to a 120-epoch ceiling.Source: §B.6 · pp. 19–20

B.7 Recalibration layer

  • Recalibration maps the assemblage head’s presence logits and Dirichlet concentrations across seven benchmark mineral categories.The map adds a silica slope for quartz and amphibole.Source: §B.7 · p. 20
  • A two-component Dirichlet mixture widens predictions for a minority of rocks while leaving the remaining distribution unchanged.The mixture addresses residual overconfidence after predictions are centered on measured abundances.Source: §B.7 · p. 20
  • The recalibration layer is fit by minimizing negative log-likelihood, and its mixture tier has 123 parameters.Weight decay is selected on validation fits at several sample sizes before subsequent fitting.Source: §B.7 · pp. 20–21

B.8 Measured-rock benchmark construction

The measured-rock benchmark retains 640 volcanic rocks with alteration grades 1 or 2 and excludes more altered samples. Its split procedure assigns whole stratigraphic units to sets, then selects a candidate split that matches benchmark mineral-occurrence rates and silica distributions.

B.8 Measured-rock benchmark construction

  • The benchmark includes 640 rocks graded 1 or 2 on the USGS alteration scale, excluding grades 3–5 as hydrothermally replaced assemblages.The authors reason that grades 1 and 2 reflect parent magma without requiring pristine samples.Source: §B.8 · p. 21
  • Train, validation, and test sets contain 368, 111, and 161 rocks, assigned by whole stratigraphic units to reduce overlap among chemically similar rocks.Among 400 candidate splits, the selected split most closely matches benchmark mineral occurrence and silica distributions.Source: §B.8 · p. 21
  • Reported volume-percent abundances are converted to mass fractions using representative mineral densities before categories are collapsed and renormalized.Amphibole’s abundance correction is fixed at zero because its fitted sign changes across plausible density assumptions.Source: §B.8 · p. 21, Table B10 · p. 22

B.9 Presence discrimination

  • Presence discrimination uses AUROC across seven mineral categories, where 0.5 is random classification and 1.0 is perfect discrimination.Uncertainty whiskers bootstrap whole stratigraphic units rather than individual rocks.Source: §B.9 · p. 22

C Composition and conditions predictions

On a held-out simulated andesite, predicted mineral compositions and conditions track the simulated references, although condition-posterior widths reflect the sampling scheme. For a measured rhyolite, the model predicts compositions and conditions, but the benchmark provides no measured counterparts for evaluating them.

C Composition and conditions predictions

  • Predicted oxide compositions agree with simulated labels for the most probable anhydrous and hydrous phases in a validation andesite.The composition head recovers amphibole’s structural water, distinct from dissolved water predicted by the conditions head.Source: C Composition and conditions predictions · p. 23
  • Predicted temperature follows the simulated labels, while pressure and water distributions reproduce the breadth of sampled conditions.Posterior width is set by condition sampling rather than by the rock, which the authors identify as a source of bias.Source: C Composition and conditions predictions · p. 23, Figure C1 · p. 23
  • For a benchmark rhyolite, predicted formation temperatures concentrate at the cool end of the sampled range, but no measured composition or condition counterpart is available.The figure’s points summarize candidate phase compositions, and its condition distributions sample assemblages from the presence branch.Source: C Composition and conditions predictions · p. 23, Figure C2 · p. 24

D Comparing simulated and measured labels

The comparison examines measured-label heads and recalibration across fitting-set sizes, including their confidence and abundance-accuracy tradeoffs. Supplementary materials document the evaluation protocol, model comparisons, and reported metric scopes.

D Comparing simulated and measured labels

  • Fits used whole stratigraphic units to reach sizes of 25, 50, 100, 200, and 400 rocks, with 10 selections per size and evaluation on 111 validation rocks.The fitting set contained 368 rocks; realized fit counts could meet or slightly exceed targets because units were sampled whole.Source: D Comparing simulated and measured… · p. 25
  • The measured-abundance heads used 64-unit hidden-layer MLPs and differed only in input: the frozen 256-dimensional latent, raw geochemistry, or a zero vector.The latent-input and raw-geochemistry heads had 34,839 and 4,887 parameters, respectively; the abundance factor used a two-component Dirichlet mixture.Source: D Comparing simulated and measured… · p. 25
  • At 26 rocks, the latent-input head’s abundance-factor NLL was -1.92 nats, versus -1.63 with no chemistry and -1.47 with raw geochemistry; all three converged near -2.50 at the full set.The authors conclude that chemical inputs benefit presence prediction, while abundance predictions depend primarily on the measured mineral list and benefit from chemistry mainly when labels are scarce.Source: D Comparing simulated and measured… · p. 25
  • 1.38 nats at 26 rocks and 0.70 nats at the full fitting set: the latent-input head had lower joint NLL than recalibration, but recalibration had lower absolute error from 210 rocks onward.The authors attribute weaker recalibrated confidence to the broad sampled formation-condition distribution, whose spread the recalibration layer can only partly absorb.Source: D Comparing simulated and measured… · p. 25

F Supplementary Figures

  • Figures D1–D3 compare recalibration tiers, measured-abundance heads, and their most performant configurations; F3 decomposes joint NLL into presence and abundance factors.The D figures use median joint NLL and mean per-category abundance MAE on a fixed 111-rock validation set; F3 reports medians and interquartile ranges over 10 replicates.Source: Figure D1 · p. 26, Figure D2 · p. 26, Figure D3 · p. 27

E Supplementary Tables

  • Supplementary Tables E1–E4 define the reported scopes: held-out element-imputation R2, per-category zero-shot presence AUROC, abundance Spearman correlation, and abundance-bias measures.Table E1 scores log-space R2 over 157,544 held-out compositions; Table E4 includes the fraction overpredicted, median predicted-to-measured ratio, and category sample count.Source: Table E1 · p. 28, Table E2 · p. 28, Table E3 · p. 28

F Supplementary Figures

  • Supplementary figures also show encoder pretraining loss, per-head training losses, and amphibole occurrence and abundance across simulated validation compositions.The claims checklist scopes the model’s stated capabilities to equilibrium crystallization of volcanic rocks.Source: Figure F1 · p. 29, Figure F2 · p. 30, Figure F4 · p. 32

2. Limitations

The paper identifies constraints on simulator fidelity and the model’s scope, and reports documentation for reproducing its experiments, accessing assets, and understanding its settings.

2. Limitations

  • The work is limited by simulator omissions of kinetics, transport, and measured formation conditions, its scope to equilibrium crystallization of volcanic rocks, and systematic abundance bias from simulated labels.Assumptions about formation conditions also affect the spread of predicted distributions.Source: §2 · p. 33

3. Theory assumptions and proofs

  • The paper reports no theoretical results or proofs, so the theory-assumptions checklist is marked not applicable.The authors characterize the work as empirical.Source: §3 · p. 34

4. Experimental result reproducibility

  • The reproducibility checklist says experimental setups, data splits, hyperparameter procedures, and evaluation protocols are detailed in the paper and appendices.The description includes tokenization, encoder configuration, corpus generation, head architectures, training, and recalibration fitting.Source: §4 · p. 34

5. Open access to data and code

  • Code, configuration files, a version-pinned environment, trained checkpoints, benchmark tables, and the figure pipeline are reported as available in the repository.The checklist asks for open access and sufficient instructions to reproduce results.Source: §5 · p. 35

6. Experimental setting/details

  • The paper reports that optimizer, learning rate, schedule, hyperparameter search spaces, selection criteria, data splits, and evaluation protocols are specified.The checklist marks training and test details as provided.Source: §6 · p. 35

7. Experiment statistical significance

The paper describes uncertainty reporting and experimental resources alongside its ethics, impact, asset, and disclosure statements. It reports spread for distributional predictions and additional uncertainty sources across the experiments.

7. Experiment statistical significance

  • The paper reports spread for its distribution predictions and describes benchmark variability through bootstrap resampling and training variability from random training-rock selection.Its checklist identifies interquartile-range whiskers as an example of uncertainty display.Source: §7 · pp. 35–36

8. Experiments compute resources

  • The authors report that Appendix B details hardware and execution time for corpus generation, pretraining, hyperparameter searches, head training, and recalibration.Approximate compute time is also given for unreported preliminary iterations.Source: §8 · p. 36

9. Code of ethics; 14. Crowdsourcing and research with human subjects

  • The ethics checklist is marked yes because the work uses public scientific data and involves no human subjects or personal data; the paper also reports no crowdsourcing or human-subject research.The authors state that the data are physical rock measurements from published sources.Source: §9 · p. 36, §14 · p. 39

10. Broader impacts

  • The paper discusses higher-throughput mineral characterization as a positive impact and notes that inaccurate zero-shot predictions could affect downstream decisions, recommending recalibration on measured rocks.The broader-impacts checklist marks discussion of positive and negative impacts as present.Source: §10 · p. 37

11. Safeguards

  • The safeguards checklist is marked not applicable because the authors say neither the rock-mineralogy model nor its published-source data carries high misuse risk.The checklist concerns releases of assets with high misuse risk.Source: §11 · p. 37

12. Licenses for existing assets

  • The authors report that used datasets and software are cited and that their licenses permit use, including CC BY 4.0, public domain, GPL-3.0, and MIT licenses.MAGEMin is described as an unmodified solver.Source: §12 · p. 38

13. New assets

  • New assets include trained encoder and head weights, benchmark tables, and the simulated label corpus; the repository provides an excerpt and links to the full corpus.Appendix B.4 gives the full corpus-generation procedure.Source: §13 · p. 38

16. Declaration of LLM usage

  • The authors state that LLM tools assisted with writing and code implementation but were not part of the core methodology or scientific reasoning.The checklist marks declaration of LLM usage as not applicable to core methods.Source: §16 · p. 39
Loading 2610.36429v1…