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Explanation of Dynamic Physical Field Predictions using WassersteinGrad: Application to Autoregressive Weather Forecasting

NeurIPS 2026 · Label-efficient and robust learning › Recognition and long-tail · approach: Prototype and concept dictionary models · 0 citations (OpenAlex)

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Shows that input-noise perturbations displace (rather than amplitude-perturb) gradient attributions in autoregressive weather forecasters and proposes WassersteinGrad, which aggregates perturbed attribution maps via an entropic Wasserstein barycenter instead of SmoothGrad's pointwise average.

Problem

Gradient-smoothing attribution methods like SmoothGrad average pointwise over noisy inputs, which blurs spatially misaligned attributions when explaining predictions of dynamic physical fields such as autoregressive weather forecasts.

Approach

Treat each perturbed attribution map as a spatial probability measure and aggregate them via an entropic (Sinkhorn) Wasserstein barycenter, which preserves geometric structure, optionally used as a spatial mask on the base gradient (WG-Bary x Grad).

Key results

• WG-Bary achieves best faithfulness (0.815 at t+1, 0.762 at t+5) and lowest LLE on both metrics at both lead times.
• WG-Bary x Grad reaches Gini sparsity 0.750 at t+5, best among methods there.
• Peak attribution displacement grows from about 32 km at t+1 to about 115 km at t+5 while relative prediction error stays under 1.5%.

Surprising findings

• Attribution centroids shift by 10-15 km under noise levels where prediction error changes by less than 1%, suggesting explanation fragility is not a model degradation.

Limitations

• Evaluated only on the UNetRPP forecaster and a single input-output channel pair (zonal wind 250 hPa to precipitation over Paris).
• Uses isotropic white Gaussian noise that is not physically informed.
• Wasserstein barycenter adds roughly 2x compute over SmoothGrad; WG-Bary loses sign information.

Experimental setup

Datasets: TITAN

Benchmarks: TITAN

Metrics: Gini sparsity ROAD faithfulness LLE l2 LLE cosine centroid displacement

Baselines: BaseGrad SmoothGrad VarGrad IntegratedGrad

Builds on: SmoothGrad Wasserstein barycenter Sinkhorn iterations ROAD UNetRPP

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