Taylor, your album should be'Life of a Callgirl'. KENNEDY's appalled take on Swift's new record... and its ultra-vivid sex shout outs for Travis the Sasquatch The truth about Keith Urban's guitarist'other woman' Maggie Baugh revealed amid Nicole Kidman divorce How I look like this at 62. I've lost 5 stone fast, 20 years off my biological age and wear size 8... without weight-loss jabs. My war with Harry & Meghan, by PIERS MORGAN: What really happened, their absurd accusations, the brutal truth about post-royal life... and how I believe their royal racism lies helped kill off woke Shroud of Turin mystery deepens as surgeon spots hidden detail that points to Jesus' resurrection I'm no longer sleeping with my husband - and never will again, says MOLLY RYDDELL. I love him, but counted down the moments until he climaxed. Then I couldn't bear it any more and the truth spilled out... so many women feel the same Fans erupt at Taylor Swift's'dig' at Travis Kelce's ex Kayla Nicole in wild The Life of a Showgirl track Trump dollar coin design released by Treasury... and it's inspired by an iconic political photo The THREE singers Keith Urban's been cosying up to revealed - now Nicole Kidman's on the warpath and has done the thing every estranged husband fears most: ALISON BOSHOFF Lori Loughlin's husband Mossimo Giannulli seen with mystery brunette in tiny skirt day after shock split Trump appears alongside Melania at dinner hosted by JD Vance and Usha after'disappearance' rumors Top plastic surgeons reveal secrets behind Taylor Swift's'changing' face: 'It is looking very full' I'm a woman with autism... here are the signs you might be masking, even from yourself Cake-faced 90s sitcom star looks unrecognizable as she ditches the heavy eyeshadow for an LA errand run can you guess who?

An entire family - a married couple and their two young sons - have been killed in an overnight Russian drone attack in Ukraine's north-eastern Sumy region, local officials have said. Regional head Oleh Hryhorov said a residential building was hit in the village of Chernechchyna. The bodies of the two children, aged four and six, and their parents were later recovered from the wreckage. Ukraine's air force said its units shot down 46 out of 65 Russian drones across the country - but there were 19 direct hits in six locations. Russia's military has not commented.

Electroencephalography (EEG) recordings of rhythm perception might contain enough information to distinguish different rhythm types/genres or even identify the rhythms themselves. We apply convolutional neural networks (CNNs) to analyze and classify EEG data recorded within a rhythm perception study in Kigali, Rwanda which comprises 12 East African and 12 Western rhythmic stimuli - each presented in a loop for 32 seconds to 13 participants. We investigate the impact of the data representation and the pre-processing steps for this classification tasks and compare different network structures. Using CNNs, we are able to recognize individual rhythms from the EEG with a mean classification accuracy of 24.4% (chance level 4.17%) over all subjects by looking at less than three seconds from a single channel. Aggregating predictions for multiple channels, a mean accuracy of up to 50% can be achieved for individual subjects.

Can Ukraine restore its pre-war borders? Why are Tomahawk missiles for Ukraine a'red line' for Russia? Is Russia testing NATO with aerial incursions in Europe? At least 4 killed in major Russian drone, missile attack on Ukraine's Kyiv Russia's President Vladimir Putin said his forces are prevailing in what he described as a "righteous battle" in Ukraine . "Our fighters and commanders go on the attack, and the entire country, all of Russia, is waging this righteous battle and working hard," he said.

With the widespread adoption of Large Language Models (LLMs) across various applications, it is empirical to ensure their fairness across all user communities. However, most LLMs are trained and evaluated on Western centric data, with little attention paid to low-resource languages and regional contexts. To address this gap, we introduce PakBBQ, a culturally and regionally adapted extension of the original Bias Benchmark for Question Answering (BBQ) dataset. PakBBQ comprises over 214 templates, 17180 QA pairs across 8 categories in both English and Urdu, covering eight bias dimensions including age, disability, appearance, gender, socio-economic status, religious, regional affiliation, and language formality that are relevant in Pakistan. We evaluate multiple multilingual LLMs under both ambiguous and explicitly disambiguated contexts, as well as negative versus non negative question framings. Our experiments reveal (i) an average accuracy gain of 12\% with disambiguation, (ii) consistently stronger counter bias behaviors in Urdu than in English, and (iii) marked framing effects that reduce stereotypical responses when questions are posed negatively. These findings highlight the importance of contextualized benchmarks and simple prompt engineering strategies for bias mitigation in low resource settings.

Tensors, as higher-order generalizations of matrices, have emerged as powerful tools for representing and analyzing multi-dimensional data. They naturally arise in diverse applications such as multi-relational networks, spatiotemporal measurements, neuroimaging, and latent variable models. Unlike matrices, which capture only pairwise relationships, tensors encode multi-way interactions, offering richer structural insights. Among the various tensor models, orthogonally decomposable (odeco) tensors play a special role. Their decomposition structure parallels the eigendecomposi-tion of matrices, but with important advantages in both statistical robustness and computational tractability. In particular, odeco tensors arise in the method of moments for latent variable models.

We study empirical risk minimization in a single-head tied-attention layer trained on synthetic high-dimensional sequence tasks, given by the recently introduced attention-indexed model. Using tools from random matrix theory, spin-glass physics, and approximate message passing, we derive sharp asymptotics for training and test errors, locate interpolation and recovery thresholds, and characterize the limiting spectral distribution of the learned weights. Weight decay induces an implicit nuclear-norm regularization, favoring low-rank query and key matrices. Leveraging this, we compare the standard factorized training of query and key matrices with a direct parameterization in which their product is trained element-wise, revealing the inductive bias introduced by the factorized form. Remarkably, the predicted spectral distribution echoes empirical trends reported in large-scale transformers, offering a theoretical perspective consistent with these phenomena.

Neural scaling laws underlie many of the recent advances in deep learning, yet their theoretical understanding remains largely confined to linear models. In this work, we present a systematic analysis of scaling laws for quadratic and diagonal neural networks in the feature learning regime. Leveraging connections with matrix compressed sensing and LASSO, we derive a detailed phase diagram for the scaling exponents of the excess risk as a function of sample complexity and weight decay. This analysis uncovers crossovers between distinct scaling regimes and plateau behaviors, mirroring phenomena widely reported in the empirical neural scaling literature. Furthermore, we establish a precise link between these regimes and the spectral properties of the trained network weights, which we characterize in detail. As a consequence, we provide a theoretical validation of recent empirical observations connecting the emergence of power-law tails in the weight spectrum with network generalization performance, yielding an interpretation from first principles.

Neighborhood sampling is an important ingredient in the training of large-scale graph neural networks. It suppresses the exponential growth of the neighborhood size across network layers and maintains feasible memory consumption and time costs. While it becomes a standard implementation in practice, its systemic behaviors are less understood. We conduct a theoretical analysis by using the tool of neural tangent kernels, which characterize the (analogous) training dynamics of neural networks based on their infinitely wide counterparts -- Gaussian processes (GPs). We study several established neighborhood sampling approaches and the corresponding posterior GP. With limited samples, the posteriors are all different, although they converge to the same one as the sample size increases. Moreover, the posterior covariance, which lower-bounds the mean squared prediction error, is uncomparable, aligning with observations that no sampling approach dominates.

We develop a physics-informed neural network (PINN) framework for parameter estimation in fractional-order SEIRD epidemic models. By embedding the Caputo fractional derivative into the network residuals via the L1 discretization scheme, our method simultaneously reconstructs epidemic trajectories and infers both epidemiological parameters and the fractional memory order $α$. The fractional formulation extends classical integer-order models by capturing long-range memory effects in disease progression, incubation, and recovery. Our framework learns the fractional memory order $α$ as a trainable parameter while simultaneously estimating the epidemiological rates $(β, σ, γ, μ)$. A composite loss combining data misfit, physics residuals, and initial conditions, with constraints on positivity and population conservation, ensures both accuracy and biological consistency. Tests on synthetic Mpox data confirm reliable recovery of $α$ and parameters under noise, while applications to COVID-19 show that optimal $α\in (0, 1]$ captures memory effects and improves predictive performance over the classical SEIRD model. This work establishes PINNs as a robust tool for learning memory effects in epidemic dynamics, with implications for forecasting, control strategies, and the analysis of non-Markovian epidemic processes.