Arctic sea ice performs a vital role in global climate and has paramount impacts on both polar ecosystems and coastal communities. In the last few years, multiple deep learning based pan-Arctic sea ice concentration (SIC) forecasting methods have emerged and showcased superior performance over physics-based dynamical models. However, previous methods forecast SIC at a fixed temporal granularity, e.g.

Arctic sea ice performs a vital role in global climate and has paramount impacts on both polar ecosystems and coastal communities. In the last few years, multiple deep learning based pan-Arctic sea ice concentration (SIC) forecasting methods have emerged and showcased superior performance over physics-based dynamical models. However, previous methods forecast SIC at a fixed temporal granularity, e.g.

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We show that this worst-case influence can be efficiently computed, and though the optimization is NP-hard, a (1 1/e) approximation guarantee holds. We also analyze the structure to theadversary'schoiceofdiffusionprocess,andcontrastwithestablished models.

We propose the Sobolev Independence Criterion (SIC), an interpretable dependency measure between a high dimensional random variable X and a response variable Y. SIC decomposes to the sum of feature importance scores and hence can be used for nonlinear feature selection. SIC can be seen as a gradient regularized Integral Probability Metric (IPM) between the joint distribution of the two random variables and the product of their marginals. We use sparsity inducing gradient penalties to promote input sparsity of the critic of the IPM. In the kernel version we show that SIC can be cast as a convex optimization problem by introducing auxiliary variables that play an important role in feature selection as they are normalized feature importance scores. We then present a neural version of SIC where the critic is parameterized as a homogeneous neural network, improving its representation power as well as its interpretability. We conduct experiments validating SIC for feature selection in synthetic and real-world experiments. We show that SIC enables reliable and interpretable discoveries, when used in conjunction with the holdout randomization test and knockoffs to control the False Discovery Rate. Code is available at http://github.com/ibm/sic.

Graph Neural Networks (GNNs) excel on homophilous graphs but often fail under heterophily due to self-reinforcing and phase-inconsistent signals. We propose a Gauge-Equivariant Graph Network with Self-Interference Cancellation (GESC), which replaces additive aggregation with a projection-based interference mechanism. Unlike prior magnetic or gauge-equivariant GNNs that typically focus on phase handling in spectral filtering while largely relying on scalar weighting, GESC introduces a $\mathrm{U}(1)$ phase connection followed by a rank-1 projection that attenuates self-parallel components before attention. A sign- and phase-aware gate further regulates neighbor influence, attenuating components aligned with current node states and acting as a local notch on low-frequency modes. Across diverse graph benchmarks, our method consistently outperforms recent state-of-the-art models while offering a unified, interference-aware view of message passing. Our code is available at \href{here}{https://anonymous.4open.science/r/GESC-1B22}.

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