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}.

We present a decentralized algorithm that achieves the same performance as a centralized one, contradicting the existing lower bounds for that problem. This is possible by "hacking" the standard model by constructing a communication protocol between players that deliberately enforces collisions, allowing them to share their information at a negligible cost.

We use sparsity inducing gradient penalties to promote input sparsity of the critic of the IPM.

Thanks, typos will be corrected.

Neural Information Processing Systems http://nips.cc/

Although high-resolution mapping of Pan-Arctic sea ice with reliable corresponding uncertainty is essential for operational sea ice concentration (SIC) charting, it is a difficult task due to some key challenges, e.g., the subtle nature of ice signature features, model uncertainty, and data heterogeneity. This letter presents a novel Bayesian Transformer approach for Pan-Arctic SIC mapping and uncertainty quantification using Sentinel-1, RADARSAT Constellation Mission (RCM), and Advanced Microwave Scanning Radiometer 2 (AMSR2) data. First, to improve feature extraction, we design a novel high-resolution Transformer model with both global and local modules that can better discern the subtle differences in sea ice patterns. Second, to improve uncertainty quantification, we design a Bayesian extension of the proposed Transformer model, treating its parameters as random variables to more effectively capture uncertainties. Third, to address data heterogeneity, we fuse three different data types (Sentinel-1, RCM, and AMSR2) at decision-level to improve both SIC mapping and uncertainty quantification. The proposed approach is tested on Pan-Arctic datasets from September 2021, and the results demonstrate that the proposed model can achieve both high-resolution SIC maps and robust uncertainty maps compared to other uncertainty quantification approaches.

Serious illness conversations (SICs), discussions between clinical care teams and patients with serious, life-limiting illnesses about their values, goals, and care preferences, are critical for patient-centered care. Without these conversations, patients often receive aggressive interventions that may not align with their goals. Clinical care teams face significant barriers when conducting serious illness conversations with older adult patients in Emergency Department (ED) settings, where most older adult patients lack documented treatment goals. To understand current practices and identify AI support opportunities, we conducted interviews with two domain experts and nine ED clinical care team members. Through thematic analysis, we characterized a four-phase serious illness conversation workflow (identification, preparation, conduction, documentation) and identified key needs and challenges at each stage. Clinical care teams struggle with fragmented EHR data access, time constraints, emotional preparation demands, and documentation burdens. While participants expressed interest in AI tools for information synthesis, conversational support, and automated documentation, they emphasized preserving human connection and clinical autonomy. We present design guidelines for AI tools supporting SIC workflows that fit within existing clinical practices. This work contributes empirical understanding of ED-based serious illness conversations and provides design considerations for AI in high-stakes clinical environments.