February 2026

Geometric deep learning (GDL) deals with supervised learning on data domains that go beyond Euclidean structure, such as data with graph or manifold structure. Due to the demand that arises from application-related data, there is a need to identify further topological and geometric structures with which these use cases can be made accessible to machine learning. There are various techniques, such as spectral convolution, that form the basic building blocks for some convolutional neural network-like architectures on non-Euclidean […]

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Multimodal learning seeks to integrate information from heterogeneous sources, where signals may be shared across modalities, specific to individual modalities, or emerge only through their interaction. While self-supervised multimodal contrastive learning has achieved remarkable progress, most existing methods predominantly capture redundant cross-modal signals, often neglecting modality-specific (unique) and interaction-driven (synergistic) information. Recent extensions broaden this perspective, yet they either fail to explicitly model synergistic interactions or learn different information components in an entangled manner, leading to incomplete representations […]

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We consider the general problem of learning a predictor that satisfies multiple objectives of interest simultaneously, a broad framework that captures a range of specific learning goals including calibration, regret, and multiaccuracy. We work in an online setting where the data distribution can change arbitrarily over time. Existing approaches to this problem aim to minimize the set of objectives over the entire time horizon in a worst-case sense, and in practice they do not necessarily adapt to distribution […]

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This paper presents a physics-informed neural network approach for dynamic modeling of saturable synchronous machines, including cases with spatial harmonics. We introduce an architecture that incorporates gradient networks directly into the fundamental machine equations, enabling accurate modeling of the nonlinear and coupled electromagnetic constitutive relationship. By learning the gradient of the magnetic field energy, the model inherently satisfies energy balance (reciprocity conditions). The proposed architecture can universally approximate any physically feasible magnetic behavior and offers several advantages over […]

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Hypergraph Neural Networks (HyGNNs) have demonstrated remarkable success in modeling higher-order relationships among entities. However, their performance often degrades on heterophilic hypergraphs, where nodes connected by the same hyperedge tend to have dissimilar semantic representations or belong to different classes. While several HyGNNs, including our prior work BHyGNN, have been proposed to address heterophily, their reliance on labeled data significantly limits their applicability in real-world scenarios where annotations are scarce or costly. To overcome this limitation, we introduce […]

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Adjoint-based shape optimization of ship hulls is a powerful tool for addressing high-dimensional design problems in naval architecture, particularly in minimizing the ship resistance. However, its application to vessels that employ complex propulsion systems introduces significant challenges. They arise from the need for transient simulations extending over long periods of time with small time steps and from the reverse temporal propagation of the primal and adjoint solutions. These challenges place considerable demands on the required storage and computing […]

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I’m a very heavy user of Claude Code on the web, Anthropic’s excellent but poorly named cloud version of Claude Code where everything runs in a container environment managed by them, greatly reducing the risk of anything bad happening to a computer I care about. I don’t use the web interface at all (hence my dislike of the name) – I access it exclusively through their native iPhone and Mac desktop apps. Something I particularly appreciate about the […]

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Reinforcement learning with verifiable rewards (RLVR) has been a main driver of recent breakthroughs in large reasoning models. Yet it remains a mystery how rewards based solely on final outcomes can help overcome the long-horizon barrier to extended reasoning. To understand this, we develop a theory of the training dynamics of RL for transformers on compositional reasoning tasks. Our theory characterizes how the effectiveness of RLVR is governed by the smoothness of the difficulty spectrum. When data contains […]

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