Trump's unprecedented $347MILLION'mountain of cash' plan gives Republicans a glimmer of hope for midterm elections... as GOP aims to take down Democrats with blunt'gridlock' message As dozens of potential rat virus cases are monitored, lessons can be learned from forgotten outbreak that ravaged an American icon... and left a trail of death in its wake Top ISIS commander is killed by American forces as Trump says world's'most active terrorist' has been'eliminated' You CAN lose weight and keep it off after age 60: I was running daily but still piling on the pounds. Now I'm in the best shape of my life... and my secret is so simple anyone can do it Cheerful Christian mom is pillar of Florida community and loves going on TV... but she has a childhood secret so evil that she stuttered with shock when confronted with it Mortifying moment Bruce Springsteen leaves fawning Chris Christie hanging in brutal'snub' at concert HGTV star reveals fatal slip up that led to her being brutally removed from her own show... and catastrophic single word that turned network against her Kendall Jenner fuels Jacob Elordi dating rumors as they're'spotted TOGETHER in Hawaii' after her sister Kylie'set them up' Husband of doomed dive group leader says'something must have happened down there' as mystery surrounds why the five attempted to explore'cave so deep even divers with best equipment don't try' Jennifer Lopez mocked for diva antics as she waits for fans to clear out of the way for a'staged' paparazzi walk Reese Witherspoon and Ryan Phillippe reunite for son's NYU graduation... as Kate Hudson cheers on her boy at same ceremony with Goldie Hawn and Kurt Russell Washington's Democrat ex-governor says she's disgusted at millionaires' tax brought in by her gleeful woke successors'How do you live with that?' Disgraced Eric Swalwell's'blindsided' wife dresses for revenge... as friends reveal brutal toll sex assault scandal has had on young mom Diet inspired by the Bible touted as helpful for depression, bad skin and processed food'poison' Brutal moment MLB pitcher's leg is broken by 111mph liner with team set to lose star man for'a long time' It's a debate as old as time: can single men and women truly be just friends? Now, scientists have revealed a tell-tale sign your male pal actually wants to date you - and it all comes down to the bill. Experts have discovered that men who are romantically or sexually interested in their female friends are more likely to regularly pay for things when hanging out. And rather than singling out a girl they like the most, they're more likely to simply pay for all their girl mates, the study found.

"I've got one hand on the keyboard, one hand down below," an artist who role-plays with their chatbot tells WIRED. But some asexual advocates aren't thrilled about the association. Kor "got really addicted" to their NSFW role-playing AI chatbot last year. The 35-year-old artist from the Midwest recalls a two-month period spending "eight to 10 hours a day" creating elaborate fantasies with SpicyChat, a relationship role-playing platform . Sometimes inputting 3,000-word mini essays into the program, Kor and the AI spun narratives featuring a rotating cast of suitors often based on characters from the Marvel comic book universe.

More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. There's more to airplane toilets than meets the eye. Breakthroughs, discoveries, and DIY tips sent six days a week. But that incredibly loud sucking sound is actually something of an engineering marvel. In this episode of Ask Us Anything by, we get into all the smelly details of how airplane toilets actually work. Ask Us Anything answers your most outlandish, mind-burning questions--from the everyday things you've always wondered to the bizarre things you never thought to ask. So, yes, there's a reason we can't remember being babies and no, not all cats hate water .

Science Archaeology 1.3 million people share DNA with Maryland's earliest colonists Some are even related to the former colony's first governor. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. The exterior of the reconstructed Catholic chapel at Historic St.Mary's City in St. Mary's City, Maryland. Breakthroughs, discoveries, and DIY tips sent six days a week. In 1634, English settlers established St. Mary's City as the first permanent outpost in the colony of Maryland.

Passive sensors and high resolution cameras help this robot find signs of coral reef. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Breakthroughs, discoveries, and DIY tips sent six days a week. Coral reefs may soon have new swimming visitors observing their life-rich aquatic metropolises. Developed by the Woods Hole Oceanographic Institution (WHOI) Reef Solutions Initiative, this new underwater surveyor uses a combination of hydrophones, high-resolution cameras, and an onboard computer to find signs of marine life hotspots.

Environment Animals Wildlife'Two-headed snake' confuses predators More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. The reed snake is only about eight inches long. Breakthroughs, discoveries, and DIY tips sent six days a week. Only around 600 of the nearly 4,000 known snake species are venomous. The recently discovered Guangxi reed snake () in China is not one of those species, but its alternative defense mechanism is strange enough to keep most predators at bay.

Physics-informed neural networks (PINNs) provide a mesh-free framework for solving PDE-constrained inverse problems, but their extension to Bayesian inversion still faces a fundamental difficulty: prior distributions are typically defined in the weight space of neural networks, whereas physically meaningful prior assumptions are more naturally expressed in function space. In this study, we introduce a unified framework, termed functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks (fpBPINN), to incorporate functional priors into Bayesian PINN-based inversion. We consider two complementary approaches. The first is a functional-prior-informed Bayesian PINN (FPI-BPINN), in which a neural network weight prior is learned to be consistent with a prescribed functional prior, and Bayesian inference is subsequently performed in weight space. The second is function-space particle-based variational inference for PINNs (fParVI-PINN), which performs Bayesian estimation using ParVI directly in function space. We also show that random Fourier features (RFF) play an important role in representing Gaussian functional priors with neural networks and in improving posterior approximation. We applied the proposed approaches to one-dimensional seismic traveltime tomography and two-dimensional Darcy-flow permeability inversion. These numerical experiments showed that both approaches accurately estimated posterior distributions, highlighting the significance of introducing physically interpretable functional priors into Bayesian PINN-based inverse problems. We also identified the contrasting advantages of FPI-BPINN and fParVI-PINN, namely flexibility and accuracy, respectively.

Offline-to-online learning aims to improve online decision-making by leveraging offline logged data. A central challenge in this setting is the distribution shift between offline and online environments. While some existing works attempt to leverage shifted offline data, they largely rely on UCB-type algorithms. Thompson sampling (TS) represents another canonical class of bandit algorithms, well known for its strong empirical performance and naturally suited to offline-to-online learning through its Bayesian formulation. However, unlike UCB indices, posterior samples in TS are not guaranteed to be optimistic with respect to the true arm means. This makes indices constructed from purely online and hybrid data difficult to compare and complicates their use. To address this issue, we propose sample-mean anchored TS (Anchor-TS), which introduces a novel median-based anchoring rule that defines the arm index as the median of an online posterior sample, a hybrid posterior sample, and the online sample mean. The median anchoring systematically corrects bias induced by distribution shift by mitigating over-estimation for suboptimal arms and under-estimation for optimal arms, while exploiting offline information to obtain more accurate estimates when the shift is small. We establish theoretical guarantees showing that the proposed algorithm safely leverages offline data to accelerate online learning, and quantifying how the degree of distribution shift and the size of offline data affect the resulting regret reduction. Extensive experiments demonstrate consistent improvements of our algorithm over baselines.

Reinforcement learning (RL) for large language models (LLMs) is dominated by the cost of rollout generation, which has motivated the use of low-precision rollouts (e.g., FP8) paired with a BF16 trainer to improve throughput and reduce memory pressure. This introduces a rollout-training mismatch that biases the policy gradient and can cause training to collapse outright on reasoning benchmarks. We show that the mismatch is non-stationary and acts as a double-edged sword: early in training it provides a stochastic exploration bonus, exposing the gradient to trajectories the trainer would otherwise under-sample, but the same perturbation transitions into a destabilizing source of bias as the policy concentrates. To solve this, we propose Adaptive Importance Sampling (AIS), a correction framework that adjusts the strength of its intervention on a per-batch basis. AIS combines three real-time diagnostics, namely weight reliability, divergence severity, and variance amplification, into a single mixing coefficient that interpolates between the uncorrected and fully importance-weighted gradients, suppressing the destabilizing component of the mismatch while preserving its exploratory benefit. We integrate AIS into GRPO and evaluate it on the diffusion-based LLaDA-8B-Instruct and the autoregressive Qwen3-8B and Qwen3.5-9B across mathematical reasoning and planning benchmarks. AIS matches the BF16 baseline on most tasks while retaining the 1.5 to 2.76x rollout speedup of FP8.

We present a covariance-aware sampler that improves the quality of pixel-space Diffusion Model (DM) sampling in the few-step regime. We hypothesize that in the few-step regime samplers fail because they rely solely on the predicted mean of the reverse distribution, while our solution explicitly models the reverse-process covariance. Our method combines Tweedie's formula to estimate the covariance with an efficient, structured Fourier-space decomposition of the covariance matrix. Implemented as an extension of DDIM, our method requires only a minimal overhead: one extra Jacobian-Vector Product (JVP) per step. We demonstrate that for pixel-based DMs, our method consistently produces superior samples compared to state-of-the-art second order samplers (Heun, DPM-Solver++) and the recent aDDIM sampler, at an identical number of function evaluations (NFE).