A t the world's biggest car fair, which opened in Beijing on Friday, there were hundreds of manufacturers, more than 1,000 vehicles, hundreds of thousands of enthusiasts - and hardly anyone behind a wheel. China's car companies have cornered the domestic electric vehicle market, and are increasingly visible on the global stage . Now they are turning their attention to what they are betting is the future of mobility: autonomous driving. At the Beijing Auto Fair, a huge industry event that covers 380,000 square metres on the outskirts of the capital, the country's carmakers showed off a range of intelligent driving technologies. In China's cut-throat domestic market, nearly every big carmaker is investing heavily in the software and computing power needed to make "hands-free" driving a reality as they compete to offer additional perks and find new ways to generate revenue.

Diffusion-based generative models have reformed generative AI, and have enabled new capabilities in the science domain, for example, generating 3D structures of molecules. Due to the intrinsic problem structure of certain tasks, there is often a symmetry in the system, which identifies objects that can be converted by a group action as equivalent, hence the target distribution is essentially defined on the quotient space with respect to the group. In this work, we establish a formal framework for diffusion modeling on a general quotient space, and apply it to molecular structure generation which follows the special Euclidean group $\text{SE}(3)$ symmetry. The framework reduces the necessity of learning the component corresponding to the group action, hence simplifies learning difficulty over conventional group-equivariant diffusion models, and the sampler guarantees recovering the target distribution, while heuristic alignment strategies lack proper samplers. The arguments are empirically validated on structure generation for small molecules and proteins, indicating that the principled quotient-space diffusion model provides a new framework that outperforms previous symmetry treatments.

To obtain more accurate model parameters and improve prediction accuracy, we proposed a regularized Kriging model that penalizes the hyperparameter theta in the Gaussian stochastic process, termed the Theta-regularized Kriging. We derived the optimization problem for this model from a maximum likelihood perspective. Additionally, we presented specific implementation details for the iterative process, including the regularized optimization algorithm and the geometric search cross-validation tuning algorithm. Three distinct penalty methods, Lasso, Ridge, and Elastic-net regularization, were meticulously considered. Meanwhile, the proposed Theta-regularized Kriging models were tested on nine common numerical functions and two practical engineering examples. The results demonstrate that, compared with other penalized Kriging models, the proposed model performs better in terms of accuracy and stability.

We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs. By heuristically extending the Convex Gaussian Min-Max Theorem (CGMT) to non-Gaussian settings, we derive an asymptotic min-max characterization of key statistics, enabling approximation of the mean $μ_{\hatθ}$ and covariance $C_{\hatθ}$ of the ERM estimator $\hatθ$. Specifically, under a concentration assumption on the data matrix and standard regularity conditions on the loss and regularizer, we show that for a test covariate $x$ independent of the training data, the projection $\hatθ^\top x$ approximately follows the convolution of the (generally non-Gaussian) distribution of $μ_{\hatθ}^\top x$ with an independent centered Gaussian variable of variance $\text{Tr}(C_{\hatθ}\mathbb{E}[xx^\top])$. This result clarifies the scope and limits of Gaussian universality for ERMs. Additionally, we prove that any $\mathcal{C}^2$ regularizer is asymptotically equivalent to a quadratic form determined solely by its Hessian at zero and gradient at $μ_{\hatθ}$. Numerical simulations across diverse losses and models are provided to validate our theoretical predictions and qualitative insights.

In federated healthcare systems, Federated Class-Incremental Learning (FCIL) has emerged as a key paradigm, enabling continuous adaptive model learning among distributed clients while safeguarding data privacy. However, in practical applications, data across agent nodes within the distributed framework often exhibits non-independent and identically distributed (non-IID) characteristics, rendering traditional continual learning methods inapplicable. To address these challenges, this paper covers more comprehensive incremental task scenarios and proposes a dynamic memory allocation strategy for exemplar storage based on the data replay mechanism. This strategy fully taps into the inherent potential of data heterogeneity, while taking into account the performance fairness of all participating clients, thereby establishing a balanced and adaptive solution to mitigate catastrophic forgetting. Unlike the fixed allocation of client exemplar memory, the proposed scheme emphasizes the rational allocation of limited storage resources among clients to improve model performance. Furthermore, extensive experiments are conducted on three medical image datasets, and the results demonstrate significant performance improvements compared to existing baseline models.

Efficient estimation of high-dimensional matrices--including covariance and precision matrices--is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators (e.g., consistency and sparsity), while largely overlooking the computational challenges inherent in high-dimensional settings. Theoretically, we first prove the convergence of LADMM, and then establish the convergence, convergence rate, and monotonicity of its reparameterized counterpart; importantly, we show that the reparameterized LADMM enjoys a faster convergence rate. Notably, the proposed reparameterization theory and methodology are applicable to the estimation of both high-dimensional covariance and precision matrices. Keywords: ADMM; High-dimensional; Learning-based optimization; Matrix estimation. 1. Introduction High-dimensional matrix estimation--covering both covariance and precision matrix estimation--constitutes a cornerstone of modern statistics and data science [1, 2, 3]. Accurate covariance estimation enables the characterization of dependence structures among a large number of variables [4, 5, 6], which is indispensable in diverse domains such as genomics [7, 8], neuroscience [9], finance [10, 11, 12], and climate science [13, 14]. Over the past two decades, substantial progress has been made in the statistical theory of high-dimensional matrix estimation, particularly with respect to the accuracy of estimators, including properties such as sparsistency and consistency [5, 15, 16]. However, in empirical studies, the dimensionality is often only on the order of tens to hundreds, and in many cases is comparable to the sample size [21, 22, 23, 24]. This observation highlights a notable gap between the statistical theory of estimators and the practical challenges of their computational implementation.

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.

Blind source separation (BSS) seeks to recover latent source signals from observed mixtures. Variational autoencoders (VAEs) offer a natural perspective for this problem: the latent variables can be interpreted as source components, the encoder can be viewed as a demixing mapping from observations to sources, and the decoder can be regarded as a remixing process from inferred sources back to observations. In this work, we propose AR-Flow VAE, a novel VAE-based framework for BSS in which each latent source is endowed with a parameter-adaptive autoregressive flow prior. This prior significantly enhances the flexibility of latent source modeling, enabling the framework to capture complex non-Gaussian behaviors and structured dependencies, such as temporal correlations, that are difficult to represent with conventional priors. In addition, the structured prior design assigns distinct priors to different latent dimensions, thereby encouraging the latent components to separate into different source signals under heterogeneous prior constraints. Experimental results validate the effectiveness of the proposed architecture for blind source separation. More importantly, this work provides a foundation for future investigations into the identifiability and interpretability of AR-Flow VAE.

This protocol is often regarded as a "golden compass" for navigating SoT A detectors. But can these stand-out "winners" be