Iran issues grim new order to citizens after US strikes'hit power plants' as conflict spirals Air passenger'invokes Sharia law' to avoid sitting next to a woman - before slapping stewardess who confronted him on flight from Turkey JFK Jr and Carolyn Bessette's REAL dying moments revealed in horrifying minute-by-minute detail: Her passenger seat terror... the graveyard spiral... violent moment of impact... and his last five words My husband seemed the perfect family man. But for years he was drugging me, raping me and filming it. Meghan would have felt'humiliated' as rows overshadowed UK trip, her friends tell People magazine What Ritalin really does to you: I took the ADHD drug for years but these were the terrifying and hidden side-effects that made me ditch the tablets. He was handsome, charming and so rich... but my extreme age-gap romance went nightmarishly wrong when I learned what he was REALLY into behind closed doors Experts reveal what ONE day of breathing America's toxic wildfire smoke does to your body as millions in 16 states are told to stay indoors Is George Clooney selling his $100M Lake Como party pad? Legendary holiday home has hosted the Obamas, Prince Harry and Meghan Markle and Emily Blunt's wedding The'Taylor Swift problem' hanging over the wedding of her'one that got away' ex Matty Healy, revealed by DOLLY BUSBY: 'He really did love her.

Follow this section to personalize your feed and get instant alerts. Follow Go to your personalized feed WHY FOLLOW? Smart Alerts: Get notified about major news as it happens. Follow this tag to personalize your feed and get instant alerts. Follow Go to your personalized feed WHY FOLLOW?

Follow this section to personalize your feed and get instant alerts. Follow Go to your personalized feed WHY FOLLOW? Smart Alerts: Get notified about major news as it happens. Follow this tag to personalize your feed and get instant alerts. Follow Go to your personalized feed WHY FOLLOW?

Despite positioning itself as an anti-hookup app, users tell WIRED that Goose has fake profiles, harsh acceptance standards, and problems with inclusivity. When Erick Hall heard that Goose, a new "anti-algorithm" dating app, was less focused on hookups, he was drawn to its mission. The New York City -based OnlyFans creator, who has over 800,000 followers on X, explains he has to hook up "all the time" for work. Because Goose was marketing itself as an alternative to that, he was curious what it had to offer. During the sign-up process he chose a few selfies where he was fully clothed; in one, wearing a black shirt, a baseball cap, and blue jeans, he pulled his shirt upward showing off his abs.

Taylor Swift marries Travis Kelce in'moving' ceremony where the bride wore Dior and walked down the aisle to one of her own songs... before partying the night away at Madison Square Garden Mississippi teen's'bad decision' cost him his life just days after graduation, mom says, as mourning family demands answers Lena Dunham leaves Taylor Swift wedding guests GASPING with shockingly rude dinner speech after taking microphone... as world famous celeb is dramatically turned away: Insiders leak outrageous MSG gossip Blake Lively's fury after Taylor Swift left her off wedding guest list as sources say it's the final straw Taylor Swift's celebrity wedding guests FLEE lavish MSG reception early... as Travis Kelce extravaganza runs into the early hours The WORST dressed guests at Taylor Swift and Travis Kelce's lavish wedding Does this photo capture Travis Kelce's last dose of Dutch courage before marriage? After all the wild lengths Taylor went to hide wedding... one image seems all too human Probe into fiery Missouri plane crash that killed 11 skydivers and pilot takes shocking twist... as investigators reveal head-scratching findings Trump takes swipe at Iranian leaders during America 250 speech revealing he gave them'a week off' for Ayatollah funeral Meghan's Taylor Swift wedding humiliation: KENNEDY's Montecito mole tells all as Prince William rubs salt in the wound! Bruised Tom Selleck feasts on McDonald's just after gym visit as fears grow about actor's grim new look All the BEST dressed guests at Taylor Swift and Travis Kelce's extravagant wedding Taylor Swift's wedding officiant is Adam Sandler! Twisted family secrets of postal worker mom, 35, slaughtered on delivery route just six months after husband's shock death: Horrifying new details of her final moments emerge The end of the America we know? Victoria Beckham risks Brooklyn's fury as she extends another olive branch in anniversary post for David - after'fuming' son said he'wished they'd stop posting about him' Taylor Swift's '40-page prenup': How $2BILLION in assets divide up... and the one major concession Travis is predicted to have written in as special clause Iconic Las Vegas casinos' years-long infestation with bed bugs exposed...as unearthed records reveal YEARS of disgusting stays that have sent mortified guests fleeing Elon Musk's next target could be your smartphone as SpaceX schemes to take on America's biggest mobile phone companies TV icon, 84, shares rare throwback photos ahead of Fourth of July holiday... can you guess who it is?

Knowing which training examples drive outputs is fundamental to auditing, correcting, and understanding language models, yet for modern LLMs this remains expensive, approximate, and largely post-hoc. Standard language models generate tokens through a dense network pathway, causing training data's influence to be distributed across parameters rather than organized along explicit, traceable components. We introduce a prototype language model architecture, Prototypes for Interpretable Sequence Modeling (PRISM), that forms each prediction via a sparse, non-negative mixture of learned prototypes, trained with clustering objectives that anchor each prototype to coherent neighborhoods of training examples. Across architectures from 130M to 1.6B parameters trained on up to 50B tokens, prototype language models either surpass or remain within 2.5 percentage points on average downstream accuracy of matched dense baselines. We show that sparse prototype structure localizes curvature in the loss landscape, yielding a more tractable Hessian and enabling training data attribution that is ~500x faster than post hoc baselines when consuming equivalent memory. Calibrating linear prototype controllers can improve downstream accuracy by roughly 3 points while tracing those corrections back to training neighborhoods, and targeted prototype suppression can remove model behaviors without finetuning or measurable loss in generation quality.

Conformal prediction guarantees marginal coverage, but pooled calibration averages over heterogeneous regions and can mask regional undercoverage in safety-critical subgroups. We introduce Self-Organized Conformal Prediction (SOCP), a calibration scheme that discovers input-space groups with a Self-Organizing Map (SOM) and, at test time, draws a local calibration buffer from the query's best-matching unit (BMU) cell or a fixed grid neighborhood. The same retrieval rule applies to regression and classification tasks across tabular features and image embeddings, leaving the predictor and nonconformity score untouched. SOCP gives exact validity for BMU-cell retrieval and fixed retrieved-set validity for neighborhood buffers; central-cell validity for neighborhood retrieval holds up to a Kolmogorov-Smirnov (KS) bias term. A split-routed extension recovers fixed retrieved-set validity conditional on the routing split. On eight regression and classification benchmarks, SO-SCP reduces the weighted regional coverage gap on $7/8$ datasets (mean paired change $-7.1\%$) for a mean prediction-set size increase of $6.2\%$, with negligible overhead on the largest six datasets; SO-CQR yields smaller gains, since quantile regression already absorbs much of the heterogeneity. By learning groups directly from the input geometry, SOCP provides group-local calibration with exact fixed-group guarantees and approximate central-cell guarantees, without supervised partitions or predictor retraining.

We prove a single algebraic mixed coincidence identity that unifies a broad swath of information-theoretic variational results. For any family of priors $\{π_i\}$ and real exponents $\{ α_i \}$, the log of the mixed count $E_{x\simν}\!\left[\prod_{i=1}^W π_i^{α_i}(x)\right]$ is simultaneously a Boltzmann coincidence weight, an exponential-family normalizer, a maximum-entropy value, and a KL-barycenter optimum. The identity yields a unified derivation of classical cornerstones of information theory: concentration of empirical distributions (Sanov-type decompositions and Gibbs conditioning), hypothesis-testing error exponents (Chernoff information and its multi-way analogue), change-of-measure inequalities (Donsker-Varadhan and PAC-Bayes), and laws governing rare-pattern coincidences (Erdos-Renyi run-length, iterative guesswork, rate-distortion, and birthday thresholds). Each is recovered as a specialization of the same algebraic equality. It strictly generalizes the classical Renyi entropy and divergence variational formulas (one and two priors respectively) to a $W$-prior simplex, and holds for unnormalized and continuum-indexed priors. Among its consequences are an exact multi-prior PAC-Bayes penalty that subtracts an explicit "coincidence bonus" from the usual single-prior posterior penalty, and the asymptotic MAP error exponent for $W$-ary hypothesis testing as an edge-restricted simplex optimum. We demonstrate the calculus at scale on two large alphabets encoding richly modeled sequential languages: on language-model next-token predictives where we recover contrastive decoding, and on human genomic regulatory sequence where it separates correlated from diverse prior families along a sliding-window trace.

Graphon models provide a flexible nonparametric framework for estimating latent connectivity probabilities in networks, enabling a range of downstream applications such as link prediction and data augmentation. However, accurate graphon estimation typically requires a large graph, whereas in practice, one often only observes a small-sized network. One approach to addressing this issue is to adopt a transfer learning framework, which aims to improve estimation in a small target graph by leveraging structural information from a larger, related source graph. In this paper, we propose a novel method, namely GTRANS, a transfer learning framework that integrates neighborhood smoothing and Gromov-Wasserstein optimal transport to align and transfer structural patterns between graphs. To prevent negative transfer, GTRANS includes an adaptive debiasing mechanism that identifies and corrects for target-specific deviations via residual smoothing. We provide theoretical guarantees on the stability of the estimated alignment matrix and demonstrate the effectiveness of GTRANS in improving the accuracy of target graph estimation through extensive synthetic and real data experiments. These improvements translate directly to enhanced performance in downstream applications, such as the graph classification task and the link prediction task.

We study the problem of sampling from a distribution under local differential privacy (LDP). Given a private distribution P P, the goal is to generate a single sample from a distribution that remains close to P in f-divergence while satisfying the constraints of LDP.