February 2026

We present a novel property-preserving kernel-based operator learning method for incompressible flows governed by the incompressible Navier-Stokes equations. Traditional numerical solvers incur significant computational costs to respect incompressibility. Operator learning offers efficient surrogate models, but current neural operators fail to exactly enforce physical properties such as incompressibility, periodicity, and turbulence. Our method maps input functions to expansion coefficients of output functions in a property-preserving kernel basis, ensuring that predicted velocity fields analytically and simultaneously preserve the aforementioned physical […]

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When there’s authority, it’s easy to come to an agreement. Players can simply have a referee blow the whistle to signal the start of the game, and a bank can confirm balances in transactions. In crypto networks, though, there are no bank intermediaries. Players can join from anywhere in the world, bring their own computers, and join without permission. Some of the players might know one another; most of them don’t. They’re not expected to trust each other. […]

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Federated learning (FL) allows remote clients to train a global model collaboratively while protecting client privacy. Despite its privacy-preserving benefits, FL has significant drawbacks, including slow convergence, high communication cost, and non-independent-and-identically-distributed (non-IID) data. In this work, we present a novel FedAvg variation called Fractional-Order Federated Averaging (FOFedAvg), which incorporates Fractional-Order Stochastic Gradient Descent (FOSGD) to capture long-range relationships and deeper historical information. By introducing memory-aware fractional-order updates, FOFedAvg improves communication efficiency and accelerates convergence while mitigating instability […]

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Generative models have made it possible to synthesize highly realistic images, potentially providing an abundant data source for training machine learning models. Despite the advantages of these synthesizable data sources, the indiscriminate use of generated images as real images for training can even cause mode collapse due to modality discrepancies between real and synthetic domains. In this paper, we propose a novel framework for discriminative use of generated images, coined GMAIL, that explicitly treats generated images as a […]

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Reinforcement learning (RL) has achieved notable performance in high-dimensional sequential decision-making tasks, yet remains limited by low sample efficiency, sensitivity to noise, and weak generalization under partial observability. Most existing approaches address these issues primarily through optimization strategies, while the role of architectural priors in shaping representation learning and decision dynamics is less explored. Inspired by structural principles of the cerebellum, we propose a biologically grounded RL architecture that incorporate large expansion, sparse connectivity, sparse activation, and dendritic-level […]

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arXiv:2512.13228v2 Announce Type: replace-cross Abstract: Semi-supervised classification leverages both labeled and unlabeled data to improve predictive performance, but existing software support remains fragmented across methods, learning settings, and data modalities. We introduce ModSSC, an open source Python framework for inductive and transductive semi-supervised classification designed to support reproducible and controlled experimentation. ModSSC provides a modular and extensible software architecture centered on reusable semi-supervised learning components, stable abstractions, and fully declarative experiment specification. Experiments are defined through configuration files, […]

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arXiv:2512.00499v2 Announce Type: replace-cross Abstract: Reinforcement learning (RL) has become a central component of post-training for large language models (LLMs), particularly for complex reasoning tasks that require stable optimization over long generation horizons. However, achieving performance at scale often introduces a fundamental trade-off between training stability and training efficiency. Token-level optimization applies fine-grained updates at the individual units, but is prone to high variance in gradient estimation, which can result in unstable training dynamics. In contrast, Sequence-level optimization […]

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arXiv:2510.25154v2 Announce Type: replace-cross Abstract: Bayesian inference provides principled uncertainty quantification but is often limited by challenges of prior and likelihood elicitation. The martingale posterior (MGP) (Fong et al., 2023) offers an alternative by replacing these requirements with a predictive rule. Additionally MGP focuses inference on parameters defined through a loss function. This framework is especially resonant in the era of foundation transformers; practitioners increasingly leverage models like TabPFN for their state-of-the-art capabilities, yet often require epistemic uncertainty […]

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