In this paper, it is shown, for the first time, that centralized performance is achievable in decentralized learning without sharing the local datasets. Specifically, when clients adopt an empirical risk minimization with relative-entropy regularization (ERM-RER) learning framework and a forward-backward communication between clients is established, it suffices to share the locally obtained Gibbs measures to achieve the same performance as that of a centralized ERM-RER with access to all the datasets. The core idea is that the Gibbs measure produced by client~$k$ is used, as reference measure, by client~$k+1$. This effectively establishes a principled way to encode prior information through a reference measure. In particular, achieving centralized performance in the decentralized setting requires a specific scaling of the regularization factors with the local sample sizes. Overall, this result opens the door to novel decentralized learning paradigms that shift the collaboration strategy from sharing data to sharing the local inductive bias via the reference measures over the set of models.

Attendees at the Canton Fair in Guangzhou, China, take pictures of various service robots on display. At the world's largest trade show, it's not just the clientele that had a different look this year. Despite the near absence of buyers wearing a traditional Arab headdress and robe at the Canton Fair, a vast showcase that started last week in China's southern metropolis of Guangzhou, a brash new generation of tech companies stood out just as much. Few wanted to dwell on the war. Even as the conflict in the Middle East once more fractures global commerce, interviews with more than a dozen exporters at the fair found many were already eager to look beyond the hostilities blamed for the worst energy disruption in generations.

Density ratio estimation (DRE) is a useful tool for quantifying discrepancies between probability distributions, but existing approaches often involve a trade-off between estimation quality and computational efficiency. Classical direct DRE methods are usually efficient at inference time, yet their performance can seriously deteriorate when the discrepancy between distributions is large. In contrast, score-based DRE methods often yield more accurate estimates in such settings, but they typically require considerable repeated function evaluations and numerical integration. We propose One-step Score-based Density Ratio Estimation (OS-DRE), a partly analytic and solver-free framework designed to combine these complementary advantages. OS-DRE decomposes the time score into spatial and temporal components, representing the latter with an analytic radial basis function (RBF) frame. This formulation converts the otherwise intractable temporal integral into a closed-form weighted sum, thereby removing the need for numerical solvers and enabling DRE with only one function evaluation. We further analyze approximation conditions for the analytic frame, and establish approximation error bounds for both finitely and infinitely smooth temporal kernels, grounding the framework in existing approximation theory. Experiments across density estimation, continual Kullback-Leibler and mutual information estimation, and near out-of-distribution detection demonstrate that OS-DRE offers a favorable balance between estimation quality and inference efficiency.

Physics-informed neural networks (PINNs) offer a unified framework for solving both forward and inverse problems of differential equations, yet their performance and physical consistency strongly depend on how governing laws are incorporated. In this work, we present a systematic comparison of different thermodynamic structure-informed neural networks by incorporating various thermodynamics formulations, including Newtonian, Lagrangian, and Hamiltonian mechanics for conservative systems, as well as the Onsager variational principle and extended irreversible thermodynamics for dissipative systems. Through comprehensive numerical experiments on representative ordinary and partial differential equations, we quantitatively evaluate the impact of these formulations on accuracy, physical consistency, noise robustness, and interpretability. The results show that Newtonian-residual-based PINNs can reconstruct system states but fail to reliably recover key physical and thermodynamic quantities, whereas structure-preserving formulation significantly enhances parameter identification, thermodynamic consistency, and robustness. These findings provide practical guidance for principled design of thermodynamics-consistency model, and lay the groundwork for integrating more general nonequilibrium thermodynamic structures into physics-informed machine learning.

An engineer at the AgiBot factory in Shanghai, China, where the 5,000th mass-produced humanoid robot had rolled off the production line. An engineer at the AgiBot factory in Shanghai, China, where the 5,000th mass-produced humanoid robot had rolled off the production line. How close are we to the sci-fi vision of autonomous humanoid robots? C hen Liang, the founder of Guchi Robotics, an automation company headquartered in Shanghai, is a tall, heavy-set man in his mid-40s with square-rimmed glasses. His everyday manner is calm and understated, but when he is in his element - up close with the technology he builds, or in business meetings discussing the imminent replacement of human workers by robots - he wears an exuberant smile that brings to mind an intern on his first day at his dream job. Guchi makes the machines that install wheels, dashboards and windows for many of the top Chinese car brands, including BYD and Nio. He took the name from the Chinese word, "steadfast intelligence", though the fact that it sounded like an Italian luxury brand was not entirely unwelcome. For the better part of two decades, Chen has tried to solve what, to him, is an engineering problem: how to eliminate - or, in his view, liberate - as many workers in car factories as technologically possible. Late last year, I visited him at Guchi headquarters on the western outskirts of Shanghai. Next to the head office are several warehouses where Guchi's engineers tinker with robots to fit the specifications of their customers. Chen, an engineer by training, founded Guchi in 2019 with the aim of tackling the hardest automation task in the car factory: "final assembly", the last leg of production, when all the composite pieces - the dashboard, windows, wheels and seat cushions - come together. At present, his robots can mount wheels, dashboards and windows on to a car without any human intervention, but 80% of the final assembly, he estimates, has yet to be automated. That is what Chen has set his sights on. As in much of the world, AI has become part of everyday life in China . But what most excites Chinese politicians and industrialists are the strides being made in the field of robotics, which, when combined with advances in AI, could revolutionise the world of work.

Deploying trustworthy AI systems requires principled uncertainty quantification. Conformal prediction (CP) is a widely used framework for constructing prediction sets with distribution-free coverage guarantees. In many practical settings, including healthcare, finance, and mobile sensing, the calibration data required for CP are distributed across multiple clients, each with its own local data distribution. In this federated setting, data can often be partitioned into, potentially overlapping, groups, which may reflect client-specific strata or cross-cutting attributes such as demographic or semantic categories. We propose group-conditional federated conformal prediction (GC-FCP), a novel protocol that provides group-conditional coverage guarantees. GC-FCP constructs mergeable, group-stratified coresets from local calibration scores, enabling clients to communicate compact weighted summaries that support efficient aggregation and calibration at the server. Experiments on synthetic and real-world datasets validate the performance of GC-FCP compared to centralized calibration baselines.

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