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Evaluating Explainable AI Methods for Geoscientific Regression: Insights from Applications and the Lorenz-63 System

T0 review · 0 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper argues that most explainable-AI methods, developed for classification, carry technical limitations in the regression problems that dominate Earth system science, and illustrates these failure modes on a Lorenz-63 forecast…

desk verdict A useful, honest review with a nice L63 teaching demo, but the paper's headline claim—that these XAI methods fail for regression-specific reasons—is asserted rather than demonstrated, because no classification control is run. read the letter →

arxiv 2608.07406 v1 pith:RNBVJSCB submitted 2026-08-07 physics.ao-ph

Ieuan Higgs , Todd Jones , Kieran Hunt , Anna-Louise Ellis This is my paper · ORCID
classification physics.ao-ph
keywords explainableAIregressionLorenz-63chaoticdynamicsattributionmethodsSHAPlayer-wiserelevancepropagationEarthsystemscience
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper is a review with a demonstration. It argues that most widely used explainable-AI (XAI) methods were built for classification tasks—they assume a decision boundary, a probabilistic output, and a meaningful 'null' class—and that those anchors are absent in the regression problems that dominate Earth system science. To make the argument concrete, the authors train a small neural network to emulate the Lorenz-63 chaotic system and apply five families of attribution methods: saliency, Input $\times$ Gradient, Integrated Gradients, SHAP, and layer-wise relevance propagation. The result is a catalogue of failure modes: attributions depend strongly on baseline choice, off-manifold inputs degrade reliability, sign and aggregation choices obscure meaning, and explanations vary rapidly in chaotic regimes. If correct, the paper implies that practitioners should treat classification-era XAI methods as diagnostic tools to be adapted deliberately, not as readymade explanations, and that gradient-based sensitivity methods deserve special attention because they connect to established adjoint sensitivity analysis in numerical weather prediction.

What carries the argument

The central object is a fully-connected feed-forward ReLU neural network (three hidden layers of widths 128, 64, 64) trained to forecast the Lorenz-63 state 25 integration steps ahead, with a test error near 0.62% NRMSE. The Lorenz-63 system—a three-variable chaotic model of Rayleigh–Bénard convection—provides an implicit physical benchmark: known attractor sensitivities (weak on a lobe, strong near the divergence region between lobes) serve as the reference against which each explanation is judged. The analysis machinery is the comparison protocol itself: attributions are computed separately for each output variable and aggregated as the sum of absolute values, and the same protocol is run under different baseline choices for Integrated Gradients and SHAP and different propagation rules for layer-wise relevance propagation. This protocol isolates the effect of methodological choices—baseline, sign, aggregation—from the behaviour of the underlying dynamical system.

What would settle it

A single quantitative experiment could settle the generalisation claim: apply the same five attribution methods to an operational-scale regression model (for example, a graph-based weather emulator) and compare their outputs against a ground-truth sensitivity field computed from a physics-based adjoint model. If mean-baseline SHAP or Integrated Gradients turned out to be more faithful than saliency at that scale, the paper's conclusion that classification-era methods systematically mislead in geoscience regression would be weakened; if the baseline and off-manifold failures reappear, its central claim is supported.

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Extended reading notes

Core claim

On its own terms, the paper establishes that routine XAI methods are not neutral instruments for explaining regression models in Earth science. Using the Lorenz-63 system as a physically meaningful testbed, it shows that saliency (the gradient of output with respect to input) reproduces known attractor sensitivities—strong importance near the divergence region between lobes, dominated by $x$ and $y$ rather than $z$—while methods that multiply gradients by input magnitude or integrate from a baseline suppress or rescale importance in ways that depend on the reference state. Integrated Gradients and SHAP produce substantially different explanations when the baseline is the mean state versus nearby training states, and SHAP's marginalization over feature subsets produces off-manifold states for a dynamical system. Layer-wise relevance propagation's choice of propagation rule changes the spatial pattern of attributions, with asymmetric rules such as $\alpha=1,\beta=0$ and $\gamma$ discarding or amplifying negative contributions in ways that distort the signed balance of physical tendencies. The paper's central claim is that these are systematic limitations of the methods, not artefacts of the testbed, and it generalizes them to high-dimensional operational settings.

Load-bearing premise

The load-bearing premise is that failure modes observed in one small neural network emulating the Lorenz-63 system at a fixed lead time generalize to high-dimensional operational Earth-system models, with visual agreement against known Lorenz-63 sensitivities used as the implicit ground truth for explanation quality rather than any formal XAI fidelity metric.

Editorial extensions

If this is right

  • Do not assume classification-era XAI methods transfer directly to regression: without a decision boundary or probabilistic output, explanations must be interpreted over a continuous output space where sign, magnitude, and variation carry meaning.
  • Baseline or reference states must be chosen deliberately and grounded in a physically meaningful quantity; an arbitrary baseline produces attributions that can be misleading and hard to interpret.
  • Attributions from off-manifold inputs may describe the model's limitations rather than the phenomenon of interest, so they should be flagged as such rather than presented as physical explanations.
  • Aggregation of explanation metrics (for example, summing absolute attributions across outputs) is a consequential choice that can hide sign information and interaction effects; it should be justified rather than applied by default.
  • Gradient-based sensitivity methods have a direct analogue to adjoint sensitivity in numerical weather prediction, giving them a principled foundation for regression before extensions such as Input $\times$ Gradient or Integrated Gradients are layered on.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable extension of the paper's comparison is to run a quantitative faithfulness or robustness metric on the same Lorenz-63 emulator, using perturbations restricted to the data manifold; the paper's qualitative ranking would predict that saliency scores highest and mean-baseline Input $\times$ Gradient or SHAP score lower.
  • The rapid variation of explanations in chaotic regimes suggests that operational XAI should report explanation variance or ensemble spread alongside point attributions, since a single local explanation may be unstable over short forecast lead times.
  • The stakeholder-lifecycle framing implies that XAI should be specified during problem definition—choosing the baseline, the aggregation, and the output target before training—rather than applied post-hoc; operational forecasting centres could adopt such 'explanation specifications' as part of model handover.
  • The adjacency between saliency and adjoint sensitivity raises a promising direction: treat the ML model's backpropagated gradients as a free adjoint, validated against physics-based adjoints, to diagnose reanalysis biases and target observations—an idea the paper leaves implicit but its cited applications point toward.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

0 major / 6 minor

Summary. This paper argues that many XAI methods, developed primarily for classification, carry structural assumptions that do not transfer cleanly to the regression problems that dominate Earth system science. It presents a taxonomy of XAI methods, illustrates five families (saliency, Input×Gradient, Integrated Gradients, SHAP, and LRP variants) on a neural-network emulator of the Lorenz-63 system, surveys regression-focused XAI applications in the geosciences, and situates XAI within a model-development lifecycle with distinct stakeholder needs. The paper closes with practical recommendations emphasizing baseline intentionality, on-manifold inputs, sign and aggregation choices, and stakeholder-specific explanation design.

Significance. This is a timely and useful synthesis for the AI for Earth Systems community. Its strengths include a clear conceptual framework, an explicit connection between gradient-based XAI and established adjoint sensitivity methods, an honest statement that no formal quantitative XAI evaluation is included (Section 4g), and a reproducible L63 codebase. The L63 illustrations are valuable for building intuition, though they are qualitative. The classification-versus-regression contrast is advanced through structural arguments rather than a controlled experiment; this is a limitation, but the paper's own hedged framing in Sections 4g and 7a makes it acceptable rather than a blocking flaw.

minor comments (6)
  1. [4f.2, Fig. 9] The caption of Fig. 9 states that the α0β1 rule was used in the penultimate layer, while the surrounding text describes the α1β0 rule as a positive-only propagation rule and interprets Fig. 9 on that basis. These two rules have opposite sign selectivity, so the caption and the text cannot both be correct. Please correct the caption, or update the implementation and interpretation to match the rule actually used.
  2. [4g and abstract] The paper explicitly disclaims a formal quantitative evaluation, and the L63 demonstrations are visual comparisons. Because no classification analog is included, the abstract's claim that classification-developed methods 'raise questions about their suitability' for regression is best read as a structural argument (Section 2) rather than an empirically demonstrated regression-specific effect. I suggest adding one sentence in Section 7a or the abstract clarifying that the L63 examples illustrate how these failure modes manifest in a regression setting, without claiming uniqueness to regression.
  3. [Section 3] The ANN emulator is described with a single reported test NRMSE of 0.62%, but no random seed, number of training runs, or run-to-run variability is given. Please state whether this is a single training realization, and note that the qualitative conclusions are drawn from that one realization.
  4. [4e, Eq. (7)] The local-accuracy property is written as f(x)=f(x')+Σ_i A_i. This is correct for a single baseline state, but when the reference is a distribution of background states, the additive constant should be the expectation of the model output over that distribution. Please clarify this to avoid a formally incorrect reading.
  5. [4d and 4e] The comparisons between baseline choices (e.g., Figs. 4 vs. 5 and 6 vs. 7) are presented visually. A simple quantitative agreement measure, such as a rank correlation between the aggregated importance maps, would strengthen the claim that baseline choice changes the explanation; if this is deliberately deferred, please state so explicitly in Section 4g.
  6. [5b] The statement that SHAP is 'by far the most popular explanation method' in the Earth science literature would benefit from a supporting citation or a count from the papers reviewed in Section 5.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the L63 illustrations and review claims are self-contained, with peripheral non-load-bearing self-citations only.

full rationale

The paper contains no derivation that reduces to its own input. The ANN is fitted to Lorenz-63 data, but the paper's claims concern properties of the XAI methods themselves—baseline dependence, off-manifold interpolation, sign/aggregation loss, and chaotic sensitivity—which are analytic consequences of Eqs. (4)-(7) or of the chaotic system, not predictions derived from the fitted emulator. Section 4g explicitly disclaims a formal quantitative evaluation, so the illustrations are presented as demonstrations rather than validated empirical findings. The 'known sensitivities' of the L63 attractor (Section 3) serve as an external visual benchmark for interpreting the explanation maps, not as an input that determines the computed attributions, and no explanation value is fitted to match that benchmark. The regression-versus-classification contrast is anchored in external references such as Letzgus et al. (2022) and in the mathematical structure of classifiers and regressors, not in the authors' own prior results. The self-citations present—Higgs et al. 2026, Hunt and Harrison 2025, and Hunt and Turner 2024—are literature-review examples of SHAP applications and are not load-bearing for the paper's central methodological claims. The absence of a classification control is an evidentiary gap concerning generalization, not a circularity. Overall, the derivation chain is self-contained; no fitted parameter is renamed as a prediction, no uniqueness claim is imported from the authors' prior work, and no equation is equivalent to its input by construction.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The paper contributes no new equations or entities; its arguments depend on the standard mathematics of Lorenz-63 and XAI, plus domain assumptions that the small emulator and visual comparison to known dynamics are adequate proxies for geoscientific regression practice.

free parameters (4)
  • LRP epsilon (epsilon-rule) = 0.1
    Chosen by hand for the LRP-epsilon and mixed-rule illustrations (Section 4f.1); affects how strongly small pre-activations are damped and thereby changes attribution patterns.
  • Forecast lead time = 25 integration steps (t=0.25)
    Chosen as loosely analogous to a 6-hour weather forecast (Section 3); sensitivity and attribution patterns depend on this horizon, but no justification beyond analogy is given.
  • IntG/SHAP baselines = mean state vs. nearby sampled training states
    Baselines are chosen by hand to demonstrate sensitivity (Sections 4d and 4e); the paper's central point is that this choice changes results, but the specific choices are ad hoc for the illustration.
  • ANN architecture and hyperparameters = 3 hidden layers (128,64,64), ReLU, lr=0.001, early stopping patience 10
    Chosen without systematic tuning; the paper states emulator optimality is not the aim (Section 3). The trained weights are fitted to data and influence all subsequent attributions.
assumptions (4)
  • standard math Lorenz-63 equations (sigma=10, rho=28, beta=8/3) and RK4 integration describe the reference dynamics.
    Section 3; used to generate training data and as the implicit benchmark for judging XAI outputs.
  • domain assumption The trained ANN is a representative proxy for geoscientific regression models.
    Section 3; the paper extrapolates XAI limitations from this small ReLU network to high-dimensional operational systems, with no quantitative bridge (Section 7, Theme 2).
  • domain assumption Known sensitivity properties of the L63 attractor constitute ground truth for explanation correctness.
    Section 4b: importance patterns are judged against known sensitivities of the attractor (Sparrow 2012) without a quantitative metric, as admitted in Section 4g.
  • ad hoc to paper XAI methods are evaluated on a scalar output target derived from the state vector via the Eq. (3) aggregation.
    Section 4a defines the absolute-value sum aggregation across outputs; the paper acknowledges this choice can obscure sign and structure (Section 7a).

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Pith. "Pith review of Evaluating Explainable AI Methods for Geoscientific Regression: Insights from Applications and the Lorenz-63 System." pith.science (2026). https://pith.science/paper/RNBVJSCB

@misc{pith2026260807406,
  author       = {Pith},
  title        = {Pith review of: Evaluating Explainable AI Methods for Geoscientific Regression: Insights from Applications and the Lorenz-63 System},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RNBVJSCB}},
  note         = {Machine review of arXiv:2608.07406}
}
read the original abstract

As artificial intelligence (AI) systems transition from research prototypes to operational tools in Earth system science and forecasting, establishing trust in their predictions becomes increasingly important. Although model inputs and outputs are observable, the internal decision-making of modern AI models remains complex and hard to interpret, earning them the label ``black boxes.'' Explainable artificial intelligence (XAI) offers techniques to provide insight into these processes. However, most XAI methods were developed for classification tasks, raising questions about their suitability for the regression problems that dominate geoscientific applications. We review XAI approaches through this lens, organising them into a structured framework and examining both their theoretical foundations and practical behaviour. To ground this discussion, we apply a selection of methods to a machine learning emulator of the Lorenz 1963 system, an archetypal chaotic model that provides a tractable, physically meaningful setting for exposing the limitations and failure modes of general-purpose XAI in regression contexts. We then survey how these and related methods have been applied across a variety of Earth system sciences. We further situate XAI within the model development lifecycle, linking methodological choices to the needs of different stakeholder groups across operational Earth system science. We close by identifying gaps in existing methodologies and outlining a forward-looking research agenda, with practical recommendations for the responsible, effective use of XAI in regression applications of geoscientific modelling and forecasting.

Figures

Figures reproduced from arXiv: 2608.07406 by the authors.

Figure 4
Figure 4. [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗

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