Randomized controlled trials typically assume that prognostic covariates are known and available at no cost. In practice, obtaining high-dimensional pretreatment data is costly, forcing a trade-off between covariate-adaptive precision and a measurement budget. We introduce Dynamic Adaptive Rerandomization via Thompson Sampling (DARTS), which treats covariate acquisition as a sequential optimization problem embedded within a design-based causal inference task. A budgeted combinatorial Thompson sampler learns which covariates are most prognostic across successive batches; selected covariates then drive rerandomization and regression adjustment to reduce batch-level average treatment effect variance. Our primary theoretical contribution is a decoupling result: adaptive covariate selection based on past batches preserves batch-level randomization validity, and the cumulative inverse-variance weighted estimator achieves at least nominal asymptotic coverage. We further derive a Bayes risk bound for the acquisition layer that matches the minimax lower bound up to logarithmic factors. Empirically, DARTS systematically concentrates the budget on informative features, significantly closing the efficiency gap to oracle designs while maintaining strict inferential validity.

One widely recognized interpretation for their empirical success is their ability to perform in-context learning (ICL): pretrained transformers are capable of performing previously unseen tasks based on demonstrations and examples in the prompt, without requiring any additional task-specific fine-tuning (Brown et al., 2020). A line of recent works interpret the in-context learning (ICL) capability of transformers from an algorithmic perspective, viewing transformers as models that can implicitly execute certain learning algorithms on the context examples. Specifically, Garg et al. (2022) proposes a theoretical framework for ICL in terms of learning a hypothesis class, and empirically shows that transformers can in-context learn the linear function class. Motivated by this empirical finding, several recent works attempt to theoretically study how transformers perform in-context learning on linear regression tasks. Aky urek et al. (2022); Von Oswald et al. (2023) construct multi-layer transformers with linear attention that can execute gradient descent on the an "in-context loss" defined on the context data, thereby enabling in-context learning of linear regression.

Despite the prevalence of the attention sink phenomenon in Large Language Models (LLMs), where initial tokens disproportionately monopolize attention scores, its structural origins remain elusive. This work provides a \textit{mechanistic explanation} for this phenomenon. First, we trace its root to the value aggregation process inherent in self-attention, which induces a systematic variance discrepancy. We further demonstrate that this discrepancy is drastically amplified by the activation of super neurons within Feed-Forward Network (FFN) layers. Specifically, the channel-sparse down-projections trigger a dimension disparity of the first-token representation, necessitating the formation of attention sinks as a structural anchor. Then, we validate this causal chain through two controlled interventions: (i) isolating the aggregation effect via attention mask modifications and (ii) amplifying the variance of targeted token representations. Both interventions can replicate attention sinks at arbitrary positions. Our mechanistic understanding offers a foundation for the systematic control of sink formation. Finally, as a proof of concept, we propose \textit{head-wise RMSNorm}, an architectural modification that stabilizes value aggregation outputs during pre-training. Our experiments demonstrate that restoring statistical parity across positions significantly accelerates convergence.

Bayesian model calibration is central to digital twins and computer experiments, as it aligns model outputs with field observations by estimating calibration parameters and correcting systematic model bias. Classical Bayesian calibration introduces latent parameters and a discrepancy function to model bias, but suffers from parameter--discrepancy confounding and is typically formulated as an offline procedure under a stationary data-generating assumption. These limitations are restrictive in modern digital twin applications, where systems evolve over time and may exhibit gradual drift and abrupt regime shifts. While data assimilation methods enable sequential updates, they generally do not explicitly model systematic bias and are less effective under abrupt changes. We propose Bayesian Recursive Projected Calibration (BRPC), an online Bayesian calibration framework for streaming data under simulator mismatch and nonstationarity. BRPC extends projected calibration to the online setting by separating a discrepancy-free particle update for calibration parameters from a conditional Gaussian process update for discrepancy, preserving identifiability while enabling bias-aware adaptation under gradual system evolution. To handle abrupt changes, BRPC is integrated with restart mechanisms that detect regime shifts and reset the calibration process. We establish theoretical guarantees for both components, including tracking performance under gradual evolution and false-alarm and detection behavior for restart mechanisms. Empirical studies on synthetic and plant-simulation benchmarks show that BRPC improves calibration accuracy under gradual changes, while restart-augmented BRPC further improves robustness and predictive performance under abrupt regime shifts compared to sliding-window Bayesian calibration and data assimilation baselines.

Megan Rapinoe, in a shock to no one, backs Angel Reese skipping interviews as'taking power back' Here's why the coaches association's 24-team College Football Playoff could ruin the sport Boston Celtics star Jaylen Brown tells ESPN's Stephen A Smith to'be quiet and retire' President Trump on $1,000 World Cup ticket prices: 'I wouldn't pay it either, to be honest' Pirates vs. Diamondbacks betting preview targets the under as both offenses go cold in series Former LSU coach Brian Kelly uses AI to prepare for job interviews, proving he's just like the rest of us Newsom office source responds to planned protest against trans athlete at state playoff girls' track meet US waits for Iran's response on peace proposal Authorities try to'connect the dots' on hantavirus infections Jesse Watters: Spencer Pratt is a'charismatic, common-sense populist' Greg Gutfeld: Dana White laughs off the'toxic masculinity thing' Iranians are fearful of facing the regime's frustration and anger after the war, activist says OutKick White House calls out Newsom as California girls' track and field controversy reignites Spokeswoman called Newsom'a truly sick individual who has no regard for fairness, dignity, and respect' Jurupa Valley High School graduate Hadeel Hazameh responded to the news that the Trump administration has launched a Title IX investigation into her district over an incident involving trans volleyball teammate, which has resulted in her graduating early and leaving her sports career behind. President Donald Trump's White House has officially put California Gov. Gavin Newsom on notice as a controversial girls' track and field postseason is set to begin this weekend. A White House spokesperson called out Newsom in a statement to Fox News Digital as his state continues to allow biological male trans athletes to compete in girls' high school sports. Gavin Newscum is a truly sick individual who has no regard for fairness, dignity, and respect. If he did, he wouldn't allow men to compete in women's sports, limiting women's opportunities and jeopardizing their health and safety.

A man has been charged after allegedly threatening Andrew Mountbatten-Windsor during an incident near his home on the Sandringham Estate in Norfolk. Norfolk Police earlier said a man was arrested shortly after 19:30 BST on Wednesday after officers received a report of a man a behaving in an intimidating manner in Wolferton. The Daily Telegraph reported Mountbatten-Windsor was threatened by a balaclava-clad man while out walking his dogs and fled to his car along with his security. Alex Jenkinson, 39, of Stowmarket, Suffolk, has been remanded in custody and is due to appear at Norwich Magistrates' Court on Friday. Police said he has been charged with two counts of using threatening, abusive or insulting words or behaviour to harass someone or cause alarm or distress and failing to provide a specimen of blood in custody.

Here's why the coaches association's 24-team College Football Playoff could ruin the sport Boston Celtics star Jaylen Brown tells ESPN's Stephen A Smith to'be quiet and retire' President Trump on $1,000 World Cup ticket prices: 'I wouldn't pay it either, to be honest' Pirates vs. Diamondbacks betting preview targets the under as both offenses go cold in series Former LSU coach Brian Kelly uses AI to prepare for job interviews, proving he's just like the rest of us Newsom office source responds to planned protest against trans athlete at state playoff girls' track meet'This can touch anyone': Gorman family speaks following loss of Sheridan'Project Freedom' could soon resume: Report Iranian people are not citizens, but'subjects' of the regime: Middle East expert Vice Admiral Robert Harward weighs in on restarting'Project Freedom' in Strait of Hormuz Largest teachers' union accused of antisemitism in federal civil rights complaint McEnany's URGENT plea: 'Be Spencer Pratt!' WHO doesn't expect large Hantavirus outbreak US blockade keeps stranglehold on Iran's economy What And Who Is Next In The Russini Saga? | OutKick Hot Mic TMZ Sports obtained documents this week showing that New England Patriots coach Mike Vrabel and former NFL reporter Dianna Russini signed a waiver for a private boating trip during her pregnancy in 2021. The report adds that Vrabel and Russini were the only two people on board for the two-to-three-hour excursion. On Thursday, the outlet obtained video and photos of the two on a dock in Putnam County, TN. See TMZ Sports' video below: ARE WE SURE MIKE VRABEL WILL SURVIVE RUSSINI SCANDAL AND COACH PATRIOTS THIS SEASON? According to the report, Russini gave birth to her first child with her husband, Kevin, later that summer. She was about six to seven months pregnant during the boating trip with Vrabel.

We're seeing coding be one of the leading applications of artificial intelligence tools, and OpenAI is continuing to expand on its offerings in that space. The company has launched a Chrome extension for its Codex platform. The new browser-based capabilities of the plugin include testing web apps, collecting context from across open tabs and using Chrome DevTools in parallel while the user performs other tasks. This extension could also help Codex be more appealing to casual users and additional professions beyond developers since so many computing tasks happen in browsers. Codex can now take on more of your browser dev work.

Meta's AI agent plans reportedly include an OpenClaw competitor that can shop on Instagram Meta's AI agent plans reportedly include an OpenClaw competitor that can shop on Instagram Last week during Meta's earnings, Mark Zuckerberg said that the company is working on new AI agents for people and businesses on the company's platform. Now, we know a bit more about what those plans entail, thanks to a new report from . The publication reports that Meta is working on an OpenClaw-inspired agent currently dubbed Hatch. It sounds like the company intends for Hatch to work within its own apps, including agentic shopping on Instagram, as well as with outside services. The company has tested Hatch on simulated versions of third-party services like DoorDash, Reddit and Outlook, according to .

Boston Celtics star Jaylen Brown tells ESPN's Stephen A Smith to'be quiet and retire' President Trump on $1,000 World Cup ticket prices: 'I wouldn't pay it either, to be honest' Pirates vs. Diamondbacks betting preview targets the under as both offenses go cold in series Former LSU coach Brian Kelly uses AI to prepare for job interviews, proving he's just like the rest of us Newsom office source responds to planned protest against trans athlete at state playoff girls' track meet'This can touch anyone': Gorman family speaks following loss of Sheridan'Project Freedom' could soon resume: Report Iranian people are not citizens, but'subjects' of the regime: Middle East expert Vice Admiral Robert Harward weighs in on restarting'Project Freedom' in Strait of Hormuz Largest teachers' union accused of antisemitism in federal civil rights complaint McEnany's URGENT plea: 'Be Spencer Pratt!' WHO doesn't expect large Hantavirus outbreak US blockade keeps stranglehold on Iran's economy OutKick Here's why the coaches association's 24-team College Football Playoff could ruin the sport College Football Playoff Eying 24 Team Expansion: Is Bigger Better? The college football playoff could expand to 24 teams -- and a lot of people aren't happy about it. After just moving to 12, this feels like overkill. Is the sport trying to fix something that wasn't broken? When college football first moved to a playoff format, there were just four teams included.