Trump declares deal with Iran is DEAD after'scum' opened fire on tankers: Oil prices surge Trump's pick for Florida governor accused of ambushing mom in gourmet grocery store: Watch him vow to'crush' her as aide screams Trump's inner circle have shown me the real UFO disclosure: The president has an imminent speech'written and ready'... what he'll explain about non-human life will make it all make sense Group chats of Travis Kelce's Chiefs teammates explode with's**t talk' about Taylor Swift wedding... as groom's snubbed friends vent their fury and players take sides: 'WTF?!' Actress who starred with Robert Redford and has famous daughter spotted out in LA... can you guess who she is? English King Alfred who massacred thousands of Vikings is'found buried' under Hampshire car park days before England play Norway in World Cup USA star at the heart of World Cup controversy offers groveling apology for team's failure: 'Not good enough' Bombshell first details about Taylor Swift's wedding dress: Stunning off-the-shoulder design revealed... incredible '25ft train'... and shock SECOND outfit Ford wrongly accused a worker of stealing a $1.95 cookie and fired him - then BEGGED him to return to work MTG brands Mitch McConnell's wife a'communist spy' as she flees to China during terrifying hospitalization Middle-aged man with America's WORST table manners sparks fury by chewing with his mouth open and hurling food on floor at bagel bakery Everyone's missed something so utterly humiliating about Taylor and Travis's wedding... I can't help but scream it: JANA HOCKING Sick twist in horrific case of youth pastor who pushed wife off cliff: Friends and family reveal chilling new details his final phone call hours before suicide... and insult from beyond the grave The humanoid robot designed'for a lifetime': China reveals creepy bots that look and feel like real humans - and they can even reproduce 90% of our movements China has revealed a new generation of creepy humanoid robots that are designed for a'lifetime' of companionship. At an event in the Chinese tech hub of Shenzhen, UBTech Robotics launched the world's first mass-produced ultra-realistic humanoid robots. These Uworld U1 androids are covered with'biomimetic skin' that looks and feels just like that of a real human.

The Chinese supercomputer LineShine was ranked as the fastest in the world, despite not using any GPUs. China now has the world's fastest supercomputer, overtaking the United States. The system, known as LineShine and installed at the National Supercomputing Center in Shenzhen, displaced the US system El Capitan from the top spot in the TOP500 ranking in terms of computing power. The breakthrough comes amid an intense competition between Beijing and Washington for technological supremacy, marked by high tariffs and restrictions on a wide range of hardware components and software. Since 1993, the TOP500 ranking has identified the world's most powerful supercomputers every six months through a series of standardized benchmarks that evaluate each system's performance, taking into account both its theoretical speed and its real-world performance, as well as its energy efficiency.

China beats U.S. with world's fastest supercomputer, but race not geared for AI work Workers at Elon Musk's xAI facility, which houses a large supercomputer known as Colossus, used for Artificial Intelligence (AI) data processing, in Memphis, Tennessee, on Sept. 11, 2025 | REUTERS SAN FRANCISCO - China has overtaken the U.S. to win the top spot on a list of the world's fastest supercomputers, but the results may say more about Beijing's desire to show self-sufficiency in computing systems than its standing in the global AI race, experts said. The LineShine system at the National Supercomputing Center in Shenzhen, China, uses domestically designed chips and won the top spot on the TOP500, a biannual global ranking of supercomputers, with the country's first listing in three years. The ranking comes as the U.S. and China are increasingly competing in advanced computing, with U.S. President Donald Trump on Monday signing an executive order that aims to put the U.S. ahead of China in the emerging field of quantum computing. In the June 2026 edition of TOP500, LineShine beat out the previous titleholder, El Capitan, a supercomputer housed at Lawrence Livermore National Laboratory that the U.S. government uses to develop and maintain its nuclear weapons stockpile. But technology and policy experts said the results do not mean that China has the world's fastest computer for AI work because of changes in the computing industry in recent years and the methods used to compile the list.

Physics-Informed Neural Networks (PINNs) often suffer from slow convergence, training instability, and reduced accuracy on challenging partial differential equations due to the anisotropic and rapidly varying geometry of their loss landscapes. We propose a lightweight curvature-aware optimization framework that augments existing first-order optimizers with an adaptive predictive correction based on secant information. Consecutive gradient differences are used as a cheap proxy for local geometric change, together with a step-normalized secant curvature indicator to control the correction strength. The framework is plug-and-play, computationally efficient, and broadly compatible with existing optimizers, without explicitly forming second-order matrices. Experiments on diverse PDE benchmarks show consistent improvements in convergence speed, training stability, and solution accuracy over standard optimizers and strong baselines, including on the high-dimensional heat equation, Gray--Scott system, Belousov--Zhabotinsky system, and 2D Kuramoto--Sivashinsky system.

The Half-Trek Criterion (HTC) is the primary graphical tool for determining generic identifiability of causal effect coefficients in linear structural equation models (SEMs) with latent confounders. However, HTC is inherently node-wise: it simultaneously resolves all incoming edges of a node, leaving a gap of "inconclusive" causal effects (15-23% in moderate graphs). We introduce Iterative Identification Closure (IIC), a general framework that decouples causal identification into two phases: (1) a seed function S_0 that identifies an initial set of edges from any external source of information (instrumental variables, interventions, non-Gaussianity, prior knowledge, etc.); and (2) Reduced HTC propagation that iteratively substitutes known coefficients to reduce system dimension, enabling identification of edges that standard HTC cannot resolve. The core novelty is iterative identification propagation: newly identified edges feed back to unlock further identification -- a mechanism absent from all existing graphical criteria, which treat each edge (or node) in isolation. This propagation is non-trivial: coefficient substitution alters the covariance structure, and soundness requires proving that the modified Jacobian retains generic full rank -- a new theoretical result (Reduced HTC Theorem). We prove that IIC is sound, monotone, converges in O(|E|) iterations (empirically <=2), and strictly subsumes both HTC and ancestor decomposition. Exhaustive verification on all graphs with n<=5 (134,144 edges) confirms 100% precision (zero false positives); with combined seeds, IIC reduces the HTC gap by over 80%. The propagation gain is gamma~4x (2 seeds identifying ~3% of edges to 97.5% total identification), far exceeding gamma<=1.2x of prior methods that incorporate side information without iterative feedback.

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.

Electroencephalography (EEG)-based emotion recognition suffers from severe performance degradation when models are transferred across heterogeneous datasets due to physiological variability, experimental paradigm differences, and device inconsistencies. Existing domain adversarial methods primarily enforce global marginal alignment and often overlook class-conditional mismatch and decision boundary distortion, limiting cross-corpus generalization. In this work, we propose a unified Prototype-driven Adversarial Alignment (PAA) framework for cross-corpus EEG emotion recognition. The framework is progressively instantiated in three configurations: PAA-L, which performs prototype-guided local class-conditional alignment; PAA-C, which further incorporates contrastive semantic regularization to enhance intra-class compactness and inter-class separability; and PAA-M, the full boundary-aware configuration that integrates dual relation-aware classifiers within a three-stage adversarial optimization scheme to explicitly refine controversial samples near decision boundaries. By combining prototype-guided subdomain alignment, contrastive discriminative enhancement, and boundary-aware aggregation within a coherent adversarial architecture, the proposed framework reformulates emotion recognition as a relation-driven representation learning problem, reducing sensitivity to label noise and improving cross-domain stability. Extensive experiments on SEED, SEED-IV, and SEED-V demonstrate state-of-the-art performance under four cross-corpus evaluation protocols, with average improvements of 6.72\%, 5.59\%, 6.69\%, and 4.83\%, respectively. Furthermore, the proposed framework generalizes effectively to clinical depression identification scenarios, validating its robustness in real-world heterogeneous settings. The source code is available at \textit{https://github.com/WuCB-BCI/PAA}

Quantifying predictive uncertainty is essential for real world machine learning applications, especially in scenarios requiring reliable and interpretable predictions. Many common parametric approaches rely on neural networks to estimate distribution parameters by optimizing the negative log likelihood. However, these methods often encounter challenges like training instability and mode collapse, leading to poor estimates of the mean and variance of the target output distribution. In this work, we propose the Neural Energy Gaussian Mixture Model (NE-GMM), a novel framework that integrates Gaussian Mixture Model (GMM) with Energy Score (ES) to enhance predictive uncertainty quantification. NE-GMM leverages the flexibility of GMM to capture complex multimodal distributions and leverages the robustness of ES to ensure well calibrated predictions in diverse scenarios. We theoretically prove that the hybrid loss function satisfies the properties of a strictly proper scoring rule, ensuring alignment with the true data distribution, and establish generalization error bounds, demonstrating that the model's empirical performance closely aligns with its expected performance on unseen data. Extensive experiments on both synthetic and real world datasets demonstrate the superiority of NE-GMM in terms of both predictive accuracy and uncertainty quantification.

As a representative continuous-depth neural network approach, stochastic differential equation (SDE)-based Bayesian neural networks (BNNs) have attracted considerable attention due to their solid theoretical foundations and strong potential for real-world applications. However, their reliance on numerical SDE solvers inevitably incurs a large number of function evaluations (NFEs), resulting in high computational cost and occasional convergence instability. To address these challenges, we propose a Nesterov-accelerated gradient (NAG) enhanced SDE-BNN model. By integrating NAG into the SDE-BNN framework along with an NFE-dependent residual skip connection, our method accelerates convergence and substantially reduces NFEs during both training and testing. Extensive empirical results show that our model consistently outperforms conventional SDE-BNNs across various tasks, including image classification and sequence modeling, achieving lower NFEs and improved predictive accuracy.

In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower bound on the critical sample complexity required for reliable model selection. More specifically, we show that distinguishing a $k$-component mixture from a simpler model necessitates a sample size scaling of $Ω(Δ^{-(4k-4)})$. We then propose a thresholding-based estimation algorithm that evaluates the spectral gap of an empirical covariance matrix constructed from random Fourier measurement vectors. This parameter-free estimator operates with an efficient time complexity of $\mathcal{O}(k^2 n)$, scaling linearly with the sample size. We demonstrate that the sample complexity of our method matches the established lower bound, confirming its minimax optimality with respect to the component separation distance $Δ$. Conditioned on the estimated model order, we subsequently introduce a gradient-based minimization method for parameter estimation. To effectively navigate the non-convex objective landscape, we employ a data-driven, score-based initialization strategy that guarantees rapid convergence. We prove that this method achieves the optimal parametric convergence rate of $\mathcal{O}_p(n^{-1/2})$ for estimating the component means. To enhance the algorithm's efficiency in high-dimensional regimes where the ambient dimension exceeds the number of mixture components (i.e., \(d > k\)), we integrate principal component analysis (PCA) for dimension reduction. Numerical experiments demonstrate that our Fourier-based algorithmic framework outperforms conventional Expectation-Maximization (EM) methods in both estimation accuracy and computational time.