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

Apr 24, 2026

Existing gradient-based attribution methods suffer from blurred attribution maps in dynamic physical fields—such as numerical weather prediction—due to geometric displacements, undermining their reliability for interpretation. This work proposes WassersteinGrad, an attribution aggregation framework grounded in entropy-regularized Wasserstein barycenters, which aligns attribution maps generated from multiple perturbations via optimal transport, thereby overcoming the limitations of conventional pointwise averaging. WassersteinGrad reveals, for the first time, that attribution discrepancies primarily stem from geometric shifts rather than amplitude noise, enabling the construction of geometrically consistent attribution consensus. Evaluated on regional meteorological data using an autoregressive neural weather forecasting model validated by meteorologists, WassersteinGrad consistently outperforms existing gradient-based baselines in both single-step and multi-step forecasts, yielding significantly sharper and more stable explanations.

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Wasserstein distance based semi-supervised manifold learning and application to GNSS multi-path detection

Dec 05, 2025

To address the scarcity of labeled images in GNSS multipath interference detection, this paper proposes a semi-supervised manifold learning method based on the Wasserstein distance. The method leverages optimal transport theory to construct an implicit graph structure, embedding the Wasserstein distance—as a geometrically meaningful similarity metric between samples—into a label propagation mechanism within a deep convolutional neural network framework, enabling robust classification under low-labeling-rate regimes. Compared with fully supervised baselines, the proposed approach achieves significant improvements in classification accuracy across diverse signal conditions, especially when the labeling rate falls below 20%. Its core contribution lies in the first integration of the Wasserstein distance into semi-supervised graph-based learning, effectively capturing both geometric structure and distributional discrepancies in high-dimensional feature spaces. This enhances model sensitivity to sparse annotations and improves generalization capability.

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Non-asymptotic confidence regions on RKHS. The Paley-Wiener and standard Sobolev space cases

Jul 09, 2025

This paper addresses the problem of constructing global, probabilistic, non-asymptotic confidence regions for an unknown function residing in a reproducing kernel Hilbert space (RKHS) under random design. Focusing on two canonical RKHSs—the Paley–Wiener and standard Sobolev spaces—the proposed method leverages exact estimation of the RKHS norm: it recasts confidence region construction as deriving a tight upper bound on the function’s RKHS norm, integrating residual analysis of kernel ridge regression under random design with functional inequalities. The resulting framework delivers rigorous, finite-sample probabilistic guarantees—free from asymptotic assumptions or pointwise inference constraints. It yields the first computationally tractable, globally uniform, and non-asymptotically valid confidence bands for these fundamental function classes. This advance substantially enhances both the practical applicability and theoretical rigor of uncertainty quantification in nonparametric regression.

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Latest Papers

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

Apr 24, 2026

Existing gradient-based attribution methods suffer from blurred attribution maps in dynamic physical fields—such as numerical weather prediction—due to geometric displacements, undermining their reliability for interpretation. This work proposes WassersteinGrad, an attribution aggregation framework grounded in entropy-regularized Wasserstein barycenters, which aligns attribution maps generated from multiple perturbations via optimal transport, thereby overcoming the limitations of conventional pointwise averaging. WassersteinGrad reveals, for the first time, that attribution discrepancies primarily stem from geometric shifts rather than amplitude noise, enabling the construction of geometrically consistent attribution consensus. Evaluated on regional meteorological data using an autoregressive neural weather forecasting model validated by meteorologists, WassersteinGrad consistently outperforms existing gradient-based baselines in both single-step and multi-step forecasts, yielding significantly sharper and more stable explanations.

0 citationsRead paper

Wasserstein distance based semi-supervised manifold learning and application to GNSS multi-path detection

Dec 05, 2025

To address the scarcity of labeled images in GNSS multipath interference detection, this paper proposes a semi-supervised manifold learning method based on the Wasserstein distance. The method leverages optimal transport theory to construct an implicit graph structure, embedding the Wasserstein distance—as a geometrically meaningful similarity metric between samples—into a label propagation mechanism within a deep convolutional neural network framework, enabling robust classification under low-labeling-rate regimes. Compared with fully supervised baselines, the proposed approach achieves significant improvements in classification accuracy across diverse signal conditions, especially when the labeling rate falls below 20%. Its core contribution lies in the first integration of the Wasserstein distance into semi-supervised graph-based learning, effectively capturing both geometric structure and distributional discrepancies in high-dimensional feature spaces. This enhances model sensitivity to sparse annotations and improves generalization capability.

0 citationsRead paper

Non-asymptotic confidence regions on RKHS. The Paley-Wiener and standard Sobolev space cases

Jul 09, 2025

This paper addresses the problem of constructing global, probabilistic, non-asymptotic confidence regions for an unknown function residing in a reproducing kernel Hilbert space (RKHS) under random design. Focusing on two canonical RKHSs—the Paley–Wiener and standard Sobolev spaces—the proposed method leverages exact estimation of the RKHS norm: it recasts confidence region construction as deriving a tight upper bound on the function’s RKHS norm, integrating residual analysis of kernel ridge regression under random design with functional inequalities. The resulting framework delivers rigorous, finite-sample probabilistic guarantees—free from asymptotic assumptions or pointwise inference constraints. It yields the first computationally tractable, globally uniform, and non-asymptotically valid confidence bands for these fundamental function classes. This advance substantially enhances both the practical applicability and theoretical rigor of uncertainty quantification in nonparametric regression.

0 citationsRead paper