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Mechanism-Aware Ensemble Conditioning for Data-Limited Emulation of Extreme Events

Isabella S. Thiel, Juan Bello-Rivas, Yannis G. Kevrekidis, Themistoklis P. Sapsis

arXiv:2609.30746v1cs.LGmath.DSphysics.ao-ph

TL;DR

Short trajectories make it difficult for surrogates to capture extremes driven by transient finite-time instability, and existing nudging does not exploit the local geometry of its ensemble. The paper uses ensemble covariance as an instability proxy and feeds compact summaries into FiLM conditioning. It reports improved rare-event diagnostics in low-dimensional and QG settings, with covariance directions aligning with OTD modes in the low-dimensional validation.

  • Problem

    Surrogates trained on limited data may reproduce bulk evolution while missing extremes generated by transient instability, and existing nudging does not exploit local ensemble geometry.

    Source: §1 · pp. 1–2

  • Method

    The method evolves a stochastic ensemble around a nudged coarse trajectory and uses its covariance-derived instability summaries to condition a temporal surrogate through FiLM.

    Source: §1 · pp. 2–3, §2.1 · p. 3

  • Results

    Ensemble conditioning improves tail-sensitive diagnostics and exceedance geometry over an unconditioned recurrent baseline in QG, while the low-dimensional validation finds covariance eigenspaces aligned with OTD modes.

    Source: §1 · pp. 2–3

  • Takeaways & Limitations

    The reported results support using local instability geometry as a conditioning signal for data-limited rare-event emulation in the tested low-dimensional and QG settings.

    Source: §1 · pp. 2–3

    The method offers limited improvement when coarse and reference statistics are already closely aligned, where the additional conditioning signal is weak.

    Source: §5 · p. 8

Abstract

from arXiv · show

Extreme events in chaotic systems are difficult to learn from short trajectories because they are controlled by transient finite-time instability rather than by frequently observed bulk dynamics. We propose a mechanism-aware conditioning plug-in framework that turns a nudged coarse ensemble into a non-intrusive sensor of local instability geometry. In the small-noise regime, the ensemble covariance aggregates the same finite-time deformation kernels that govern local instability, providing a Jacobian-free proxy for the local amplification structure around a synchronized coarse trajectory. A small FiLM module injects statistics of this ensemble geometry into an otherwise unchanged backbone while leaving the coarse simulator unchanged. We demonstrate this interface in two distinct pipelines: a Transformer-style residual-attention corrector for a controlled low-dimensional chaotic system and a probabilistic recurrent STORN corrector for topographic two-layer quasi-geostrophic (QG) flow. In the low-dimensional benchmark, ensemble covariance directions co-activate with OTD modes and FiLM conditioning improves 99th-percentile exceedance-frequency errors over an identical no-context Transformer baseline. In QG, a fixed ensemble-conditioned FiLM-STORN model trained on only \(50\) time units substantially improves long-horizon rare-event statistics in the data-limited regime, including density-tail errors, exceedance frequencies, and spatial exceedance-area distributions relative to an unconditioned STORN trained on the same data; on averaged high-threshold exceedance diagnostics, it also outperforms the baseline STORN trained with $20$ times more high-resolution data. These results show that local instability geometry is not merely interpretable post hoc, but an actionable conditioning signal for data-efficient rare-event emulation.

1 Introduction

Extreme events arise from transient instability that can be missed by surrogates trained on short trajectories, while existing nudging uses local alignment without exploiting ensemble geometry. The paper turns that geometry into a FiLM conditioning signal and reports improved data-limited rare-event emulation in two systems.

1 Introduction

  • Short-trajectory surrogates can learn bulk evolution yet miss rare extremes generated when transiently unstable regions amplify trajectories into the tails.Tail probabilities, return levels, and spatial organization of extremes are relevant diagnostics beyond short-horizon prediction error and low-order moments.Source: §1 · pp. 1–2
  • Existing nudging aligns coarse and reference states over finite windows but does not exploit the local ensemble geometry that contains information about directions of error and extreme-event amplification.The paper positions its correction as a fast, non-intrusive model using a cheap biased coarse simulator and limited high-resolution data.Source: §1 · p. 2
  • In the small-variance regime, ensemble covariance shares deformation operators with finite-time instability, providing a non-intrusive probe without tangent dynamics, Jacobians, or adjoint solvers.Covariance eigenspaces can approximate instability directions under additional spectral-gap and scale-separation assumptions.Source: §1 · pp. 2–3
  • Ensemble conditioning improves tail-sensitive diagnostics and exceedance geometry over an unconditioned recurrent baseline in QG, with a low-dimensional validation supporting the proposed mechanism.The covariance’s leading eigenspaces align with tangent-derived OTD modes, consistent with interpreting the ensemble as an instability proxy.Source: §1 · pp. 2–3
  • The paper distinguishes its ensemble’s role as a controlled geometric probe from prior ensembles used for state uncertainty, forecast spread, or assimilation corrections.Its covariance is used as a proxy for finite-time stretching directions quantified by OTD modes and Cauchy–Green geometry.Source: §1 · p. 2
  • A small FiLM module injects ensemble-derived instability features into temporal surrogates while leaving the backbone, simulator, and loss unchanged.The paper presents this as a plug-in interface rather than a replacement for the temporal model.Source: §1 · pp. 2–3

2 Method: Non-intrusive ensemble conditioning

The method nudges a coarse trajectory toward reference data and evolves a stochastic ensemble around it. In the small-noise regime, the ensemble covariance captures finite-time deformation geometry, which compact summaries feed to a FiLM module attached to an otherwise established surrogate.

2.1 Nudged coarse dynamics and ensemble stochastic differential equation

  • Nudging stabilizes the coarse trajectory around the reference over finite windows, and stochastic perturbations around that synchronized trajectory form a controlled probe of local amplification directions.The ensemble SDE is well posed with finite moments under standard global Lipschitz and linear-growth assumptions.Source: §2.1 · p. 3

2.2 Covariance–instability correspondence

  • In the small-noise regime, covariance evolves under the linearized deformation operator, so its dominant directions encode time-integrated finite-time stretching and can align with leading Cauchy–Green eigenspaces under additional assumptions.The covariance–instability correspondence is the method’s central theoretical object, distinguishing this ensemble from generic uncertainty quantification.Source: §2.2 · p. 4, Proof: see Appendix A.2 · p. 4

Proof: see Appendix A.2

Proof: see Appendix A.3

  • With moderate ensemble size, small noise, and finite time horizons, the covariance can identify the local unstable subspace of the nudged flow, with sampling error controlled by ensemble size.The covariance is treated as a dynamical descriptor of amplification, not epistemic uncertainty over model parameters.Source: Proof: see Appendix A.2 · p. 4, Proof: see Appendix A.3 · p. 5

2.3 Ensemble-conditioning module as a plug-in architecture

  • Compact ensemble statistics are transformed into FiLM parameters that modulate a temporal backbone’s hidden state, rather than propagating the full ensemble.In QG, the summary can use time-windowed means and standard deviations across ensemble members.Source: §2.3 · p. 5
  • The conditioning module is architecture-agnostic: it can attach to recurrent, probabilistic sequence, neural controlled differential equation, or transformer backbones that support feature-wise affine modulation.Its intended role is to condition the surrogate on local instability geometry, not replace the backbone or simulator.Source: §2.3 · pp. 5–6

3 Low-dimensional example

The low-dimensional example tests whether an ensemble covariance mode detects finite-time instability episodes and uses that signal in a controlled correction problem. The comparison focuses on matching the timing of instability bursts, not component-wise amplitudes.

3 Low-dimensional example

  • The three-dimensional autonomous system provides pronounced finite-time instabilities and well-defined OTD modes for validation.OTD modes can be computed independently from tangent dynamics, enabling comparison with ensemble-derived modes.Source: §3 · p. 6
  • The validation compares the leading eigenvector of centered ensemble-perturbation covariance with the leading OTD mode over time.The ensemble SDE is evolved around the same trajectory.Source: §3 · p. 6
  • The leading ensemble-covariance mode activates over the same finite-time burst window as the leading OTD mode, supporting its use as an instability detector.The comparison is intended to test temporal localization, not exact component-wise amplitude recovery.Source: Figure 3 · p. 6, §3 · p. 6
  • Table 1 reports sweep-selected z3 tail diagnostics as mean ± standard error over five runs, with training length 150 and test length 500.The table is a sensitivity summary, not the primary model-selection protocol.Source: Table 1 · p. 7

4 Experiments on high-dimensional chaotic PDE (QG)

In topographic two-layer QG, the experiments test whether nudged-ensemble conditioning improves rare-event emulation from limited high-resolution data. The conditioned model improves tail and exceedance diagnostics, while parameter sweeps and spatial comparisons examine robustness and event geometry.

4.1 Two-layer QG setup and nudged ensembles

  • The QG benchmark uses 128 × 128 reference dynamics and a 24 × 24 coarse model, with topography inducing localized exceedances.The nudged ensemble relaxes the coarse trajectory toward projected reference data and perturbs resolved modes.Source: §4.1 · p. 7

4.2 Baseline

  • The primary baseline is a probabilistic recurrent STORN correction trained on one nudged trajectory without ensemble inputs.The baseline choice follows prior controlled comparisons in which probabilistic recurrent formulations performed best.Source: §4.2 · p. 7

4.3 Results

  • KL divergence measures attractor misalignment, while log-L1 distance emphasizes tail discrepancies in corrected trajectories.Full metric details are provided in Appendix E.Source: §4.3 · p. 7

4.3.2 Ensemble parameter sweeps and robustness

  • The σ and M sweeps show an intermediate operating window: too-small σ collapses the ensemble, too-large σ loses local tracking, and gains from increasing M saturate.Figure 4 compares KL divergence and log-L1 errors across ensemble sizes and noise intensities, normalized to the T=1000 baseline.Source: §4.3.2 · p. 7, Figure 4 · p. 8

4.3.1 Data-limited learning of extremes

  • Ttrain=50 FiLM-STORN improves threshold-exceedance area and event-frequency errors over STORN trained on 20 times longer trajectory data.With short training windows, conditioning also improves tail distributions, exceedance probabilities, and long-horizon density statistics over the same-data single-trajectory baseline.Source: §4.3.1 · p. 7, Table 2 · p. 8

4.3.3 Extreme-event structure and exceedance geometry

  • The conditioned surrogate improves the localization, shape, and persistence of thresholded event regions over the single-trajectory baseline and pooled-ensemble control.In this QG benchmark, extreme events are localized and anisotropic, with dependence on bottom topography.Source: §4.3.3 · pp. 7–8

5 Limitations

The method’s benefits depend on dynamical regime, proxy assumptions, and available data and computation. Its evaluation demonstrates gains in specified systems and diagnostics, not uniform superiority.

5 Limitations

  • When coarse and reference statistics are already closely aligned, the conditioning signal is weak and improvement over standard coarse correction is limited.In severely data-limited cases, tail behavior can improve while bulk statistics remain under-corrected because too few samples are available to learn both.Source: §5 · pp. 8–9
  • At the highest thresholds, short-data STORN loses large exceedance regions while FiLM-STORN recovers the reference tail more accurately; Table 3 assesses area and frequency errors across c = 1.0, 1.5, and 1.75.Table 3 reports lower-layer ψ2 separately and includes a two-layer average.Source: Figure 5 · p. 9, Table 3 · p. 9
  • The covariance–instability proxy relies on small-variance fluctuations, local linearization, and a spectral gap; noise that is too weak or too strong can degrade alignment.Weak perturbations may fail to resolve anisotropy, while strong noise can mix dynamical and noise-induced variability.Source: §5 · p. 9
  • Ensemble evolution and summary-statistic computation cost more than a single coarse trajectory, so the overhead must be weighed against reduced high-resolution data needs.Small ensembles and low-order statistics suffice for substantial tail improvements in the QG experiments.Source: §5 · p. 9
  • The empirical evaluation covers a prototypical QG system with a probabilistic recurrent backbone and a low-dimensional system with tractable instability structure, not uniform superiority.The authors report consistent gains within the studied model–system regimes.Source: §5 · p. 9

6 Conclusion

The conclusion presents nudged coarse ensembles as a reusable source of local instability features, injected through FiLM into otherwise fixed temporal correctors. The appendix states the main proofs and establishes well-posedness and moment control for the nudged ensemble under stated assumptions.

6 Conclusion

  • The interface couples a nudged ensemble’s local finite-time instability geometry with FiLM conditioning in fixed temporal correctors, demonstrated with QG FiLM-STORN and a low-dimensional residual-attention model.The conclusion frames the signal as reusable across surrogate architectures and reports improved QG rare-event statistics in the data-limited regime.Source: §6 · p. 10

A Proofs of main results

  • Appendix A provides proofs of the main results, including a well-posedness result for the controlled stochastic probe used over surrogate-training horizons.The passage describes the well-posedness result as standard for time-inhomogeneous SDEs with Lipschitz drift.Source: A Proofs of main results · p. 12, §A.1 · p. 12

A.1 Well-posedness and moment control for nudged ensemble

  • With globally Lipschitz, linear-growth f and bounded u and PF(u), the nudged SDE has a unique strong solution; Lp initial conditions yield moment bounds for fixed p ≥ 2.The stated moment-bound constant depends on p, n, K, τ, β, T, and the bounds on u and PF(u).Source: §A.1 · p. 12

A.2 Proof of Proposition 2.1 (Covariance-instability correspondence)

The proof links the nudged ensemble covariance to the linearized dynamics: it satisfies a perturbed Lyapunov equation and, to leading order, is generated by finite-time deformation kernels.

A.2 Proof of Proposition 2.1 (Covariance-instability correspondence)

  • The covariance dynamics satisfy a perturbed Lyapunov equation for centered ensemble fluctuations.The stochastic diffusion remains after centering and supplies the covariance source term.Source: §A.2 · pp. 13–14
  • At the O(β^-1) covariance scale, finite-time deformation kernels of the linearized nudged dynamics generate the leading covariance geometry.The kernel representation uses the fundamental solution Φ(t,s) generated by Lτ(t).Source: §A.2 · pp. 13–15
  • The ensemble mean follows the nudged coarse dynamics up to an O(β^-1) error uniformly on [0,T].The centered fluctuations have bounded second moment at the O(β^-1) scale.Source: §A.2 · p. 14

A.3 Proof of Theorem 2.2 (Finite-ensemble approximation of instability subspaces)

The appendix bounds how well a finite ensemble estimates leading covariance subspaces, then details the low-dimensional probe, corrector, training, and evaluation setup.

A.3 Proof of Theorem 2.2 (Finite-ensemble approximation of instability subspaces)

  • Under a spectral gap, the finite-sample theorem bounds leading-eigenspace projector error for iid centered fluctuations with a finite fourth moment.The sub-Gaussian remark gives exponential covariance and projector bounds; the fourth-moment result is the assumption-minimal statement used here.Source: §A.3 · p. 15

B.1 Dynamical system and coarse model.

  • The three-dimensional probe alternates non-normal transient growth and exponential growth or decay, while added z3 damping biases the coarse model.Its ensemble covariance leading eigenvector tracks the OTD unstable subspace without explicit tangent-dynamics integration or Jacobians.Source: §B.1 · p. 16

B.2 Training and test-time learning problem.

  • Models train on horizons of 5, 50, or 150 time units and are evaluated on an independent trajectory of length 500.At deployment, context is computed causally from the coarse trajectory alone, avoiding reference leakage.Source: §B.2 · p. 17

B.3 Residual-attention corrector.

  • The low-dimensional corrector keeps the attention backbone unchanged and applies FiLM modulation before the residual output heads.The no-context and conditioned models retain the same backbone, loss, optimizer, and output parameterization.Source: §B.3 · p. 17

B.4 Training loss.

  • Training combines path, residual, moment-matching, and tail losses, with smooth exceedance indicators defined at the 90th, 95th, and 99th percentiles.The loss also weights the third coordinate more strongly because the strongest extreme growth occurs in z3.Source: §B.4 · p. 18

B.5 Hardware and runtime.

  • The low-dimensional proof-of-concept completes in approximately 10 minutes on a single CPU core with negligible memory overhead.The runtime uses the same CPU-based setup as the high-dimensional experiments.Source: §B.5 · p. 19

B.6 Hyperparameters.

  • The appendix reports separate configuration tables for the controlled system and ensemble probe, and for the residual-attention corrector architecture.The no-FiLM and FiLM variants share the temporal backbone and output parameterization; FiLM adds the ensemble-derived context interface.Source: Table 4 · p. 19, Table 5 · p. 20

B.7 Evaluation metrics.

  • Because chaotic trajectories lose phase alignment over long horizons, pathwise RMSE is reported but is not the primary rare-event diagnostic.The evaluation also reports density discrepancies and percentile exceedance-frequency errors.Source: §B.7 · pp. 20–21

B.8 Low-dimensional results tables.

The low-dimensional results include a fixed-configuration repeated-run ablation and a separate sweep-based sensitivity summary.

B.8 Low-dimensional results tables.

  • The sweep-selected z3 tail diagnostics in Table 6 are a sensitivity summary, not the primary model-selection protocol.The fixed-configuration Table 7 is identified as the main repeated-run ablation.Source: Table 6 · p. 21
  • At Ttrain = 50, σ = 10^-5, and M = 4, FiLM improves the residual-attention backbone across tail-density and exceedance diagnostics.Table 7 reports mean ± standard error over five independent training runs; E99 is absolute 99th-percentile exceedance-frequency error, with lower values better.Source: Table 7 · p. 21, §B.8 · p. 21

C QG model: governing equations and numerical implementation

The QG benchmark combines localized bottom topography with a coarse nudged ensemble and a probabilistic recurrent correction pipeline.

C.1 Full model definition

  • The two-layer QG benchmark adds seven Gaussian topographic bumps that break spatial homogeneity and generate localized extremes.The setup is described as more demanding than standard two-layer QG cases without bottom topography.Source: §C.1 · p. 22

C.2 Ensemble formulation

  • The ensemble uses independent stochastic perturbations around the nudged base trajectory, with tested sizes M ∈ {1, 2, 4, 8}.Members share the nudged trajectory but have no direct member-to-member coupling; M ≤ 4 is reported sufficient in the tested regime.Source: §C.2 · pp. 22–23

C.3 Numerical discretization

  • The reference and coarse simulations use 128 × 128 and 24 × 24 grids, respectively, with Fourier collocation and fourth-order Runge–Kutta time integration.The ensemble runs on the coarse grid, and its added wall-clock cost is reported negligible relative to reference-data generation.Source: §C.3 · p. 23

C.4 QG solver pipeline

  • The pipeline projects the high-resolution reference to the coarse grid, generates free-running and nudged coarse trajectories, and evolves a nudged ensemble for conditioning.The model input is the nudged coarse trajectory with ensemble summaries; the target is the projected reference.Source: §C.4 · pp. 23–24

C.5 Parameter table

  • The parameter table describes a doubly periodic QG model with seven localized Gaussian topographic features and parameters chosen to approximate atmospheric circulation under imposed shear.The implementation uses Fourier spectral discretization and fourth-order Runge–Kutta time stepping.Source: Table 8 · p. 24

D.1 Problem formulation and model summary

  • The learning task is probabilistic sequence-to-sequence correction from nudged coarse trajectories to projected high-resolution fields, using a recurrent STORN with optional ensemble-driven FiLM.Evaluation uses long-horizon corrected coarse trajectories beyond the training horizon.Source: §D.1 · pp. 24–25

D.2 Model architecture

The QG correction pipeline adds low-dimensional ensemble context to a probabilistic recurrent backbone, then evaluates long-horizon statistics using free-running coarse trajectories. FiLM conditioning improves tail-sensitive diagnostics in data-limited settings, while larger ensembles and pooled inputs involve trade-offs.

D.2 Model architecture

  • STORN encodes each input, samples a Gaussian latent, processes it through an LSTM, and decodes the corrected field.The FiLM-STORN adds a small conditioning network that maps ensemble context to modulation parameters for the recurrent hidden state.Source: §D.2 · p. 25

D.3 Training objective

  • Training minimizes a semi-physics-informed objective combining reconstruction accuracy, mass conservation, and KL regularization.The mass-conservation term enforces zero domain-integrated height disturbance.Source: §D.3 · p. 27

D.4 Implementation details: data, batching, and optimization

  • Training windows come from a single post-spin-up reference realization, use a chronological 90%/10% train-validation split, and models train for 2,000 epochs with Adam.Runtime and peak memory increase with additional ensemble members, although FiLM-STORN input dimension remains independent of their number.Source: §D.4 · p. 27, Figure 8 · p. 28

D.5 Evaluation protocol

  • Long-horizon evaluation uses an independent free-running coarse trajectory, with FiLM context computed from coarse fields alone to avoid reference leakage despite a deliberate distribution shift.Shared offline routines compare corrected trajectories using PDFs, log-PDF error, autocorrelations, spectra, and exceedance statistics.Source: §D.5 · pp. 27–28

FiLM conditioning

  • FiLM-STORN yields the largest data-limited improvements on tail-sensitive metrics, while short-horizon unconditioned STORN systematically underestimates extremes.The reported tail-sensitive metrics include log-PDF error and exceedance area.Source: FiLM conditioning · p. 28

Ensemble context size and construction

  • A four-dimensional context of layer-wise means and standard deviations is reported sufficient, while adding members beyond a small number such as four yields diminishing accuracy returns and higher runtime.At QG deployment, the context is a rolling coarse-field proxy, not an instantaneous ensemble covariance or recovered spatial covariance eigenspace.Source: §D.2 · p. 26, Ensemble context size and construction · p. 28

Pooled-ensemble baseline behavior

  • The pooled-ensemble baseline is competitive with abundant data but less data-efficient and robust in low-data settings; its input dimension grows with ensemble size and can worsen tail statistics.The short-horizon mapping is described as underconstrained.Source: Pooled-ensemble baseline behavior · pp. 28–29

Training horizon sensitivity and failure modes

Training horizon affects rare-event fidelity: FiLM-STORN gains saturate at intermediate horizons, while very short training leaves residual errors.

Training horizon sensitivity and failure modes

E.1 Evaluation metrics

The evaluation uses complementary diagnostics for attractor consistency, tail probabilities, event frequency, and the spatial organization of extremes.

E.1 Evaluation metrics

  • KL divergence measures global mismatch relative to the reference distribution and emphasizes bulk attractor consistency, but can be insensitive to far-tail discrepancies.Source: §E.1 · pp. 29–30
  • The log-density L1 discrepancy emphasizes tail fidelity because logarithmic scaling makes multiplicative probability errors visible, including errors in low-mass tails.Source: §E.1 · p. 30
  • Exceedance-area distributions measure the spatial fraction occupied by extremes, capturing their extent, localization, and persistence beyond one-point marginal densities.Wasserstein-1 remains well-defined when the distributions have substantial mass at zero, as can occur at high thresholds.Source: §E.1 · p. 30
  • Event-frequency error and exceedance-area error distinguish producing threshold events at the wrong rate from producing events with the wrong spatial extent.The lower-layer statistic is reported separately because topography acts directly there, alongside a two-layer average.Source: §E.1 · p. 30
  • The metric set covers global attractor consistency, tail-probability accuracy, and spatial organization rather than relying only on trajectory loss or a single density discrepancy.Source: §E.1 · p. 30

E.2 Detailed results

This section presents detailed QG diagnostics of distributional fidelity, tail accuracy, spatial rare-event geometry, ensemble-construction sensitivity, and regional tail behavior. It also records checklist disclosures about human subjects, crowdsourcing, and the role of LLMs.

E.2 Detailed results

  • Tables 10–11 report global density diagnostics across training lengths, ensemble noise levels, and added ensemble members, with unconditioned STORN as the baseline.The main short-data comparison fixes σ = 0.01 and Nadd = 2; Table 11 reports global log(L1), averaged over five runs, with lower values better.Source: §E.2 · p. 31, Table 11 · p. 32
  • The (σ, Nadd) sweep shows that very large perturbations such as σ = 0.2 can degrade global metrics, consistent with probing local deformation geometry rather than generic stochastic simulation.Table 13 summarizes sweep-selected best configurations, not the primary fixed-configuration comparison.Source: §E.2 · p. 31, Table 13 · p. 33
  • Log-PDF and regional PDF visualizations assess tail discrepancies and spatially heterogeneous behavior for the fixed short-data configuration, including in the topography-influenced lower layer.Figures 9–11 cover global log-PDFs and nine-region comparisons for upper ψ1 and lower ψ2 against projected reference, coarse, and STORN trajectories.Source: §E.2 · pp. 31–32, Figure 9 · p. 33, Figure 10 · p. 34
  • Threshold-resolved exceedance-area diagnostics compare spatial event-area distributions and event-frequency errors for the fixed Ttrain = 50, σ = 0.01, Nadd = 2 FiLM-STORN model.EAOT(c) is the Wasserstein-1 distance between reference and model distributions of Ac(t)/A; Efreq(c) is the absolute error in P(Ac(t) > 0).Source: §E.2 · p. 31, Table 12 · p. 32

2. Limitations

  • The paper states that it does not involve crowdsourcing or research with human subjects.Source: §2 · p. 41
  • The paper marks LLM usage as not applicable because LLMs are not an important, original, or non-standard component of core method development.Source: §2 · p. 42

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