The Restricted Boltzmann Machine (RBM) is one of the simplest generative neural networks capable of learning input distributions. Despite its simplicity, the analysis of its performance in learning from the training data is only well understood in cases that essentially reduce to singular value decomposition of the data. Here, we consider the limit of a large dimension of the input space and a constant number of hidden units. In this limit, we simplify the standard RBM training objective into a form that is equivalent to the multi-index model with non-separable regularization. This opens a path to analyze training of the RBM using methods that are established for multi-index models, such as Approximate Message Passing (AMP) and its state evolution, and the analysis of Gradient Descent (GD) via the dynamical mean-field theory. We then give rigorous asymptotics of the training dynamics of RBMs on data generated by the spiked covariance model as a prototype of a structure suitable for unsupervised learning. We show in particular that RBMs reach the optimal computational weak recovery threshold, aligning with the Baik-Ben Arous-Péché (BBP) transition, in the spiked covariance model.

Plus: The Pentagon says it used Grok in strikes on Iran. For decades, physicists have hunted for weakly interacting massive particles (WIMPs), a leading candidate for dark matter. But their search has run into a new problem: neutrinos. These tiny particles from the sun and other stars can create a "neutrino fog" that drowns out any signal of dark matter. Hitting the neutrino fog does not, however, mean an end to the search. Researchers just have to shift the focus of their hunt.

Model editing aims to efficiently revise incorrect or outdated knowledge within LLMs without incurring the high cost of full retraining and risking catastrophic forgetting. Currently, most LLM editing datasets are confined to narrow knowledge domains and cover a limited range of editing evaluation. They often overlook the broad scope of editing demands and the diversity of ripple effects resulting from edits. In this context, we introduce UNIEDIT, a unified benchmark for LLM editing grounded in open-domain knowledge. First, we construct editing samples by selecting entities from 25 common domains across five major categories, utilizing the extensive triple knowledge available in open-domain knowledge graphs to ensure comprehensive coverage of the knowledge domains. To address the issues of generality and locality in editing, we design an Neighborhood Multi-hop Chain Sampling (NMCS) algorithm to sample subgraphs based on a given knowledge piece to entail comprehensive ripple effects to evaluate. Finally, we employ proprietary LLMs to convert the sampled knowledge subgraphs into natural language text, guaranteeing grammatical accuracy and syntactical diversity. Extensive statistical analysis confirms the scale, comprehensiveness, and diversity of our UNIEDIT benchmark. We conduct comprehensive experiments across multiple LLMs and editors, analyzing their performance to highlight strengths and weaknesses in editing across open knowledge domains and various evaluation criteria, thereby offering valuable insights for future research endeavors.

WIRED goes on location--and on camera--with the cult hit. On March 16, 2026, at 5:45 pm in a leafy suburb of Atlanta called Sandy Springs, police pound on the door of a neglected French Country-style mansion, rifles at the ready, bodycams rolling. Minutes earlier, a distress call came from someone claiming to be hiding from a gunman in the mansion's downstairs bathroom. The dispatcher heard a gunshot ring out in the distance, then the line disconnected. "Open the door!" an officer yells. A calm young man with a mullet and woolly eyebrows steps out, hands raised. The police ask him who else is in the house. "Just my friends," he replies, as seven other young people, men and women, silently file out behind him, less evidently relaxed. They remain outside while two officers search the house. Inside the mansion there are no immediate signs of a massacre, but the decor alone arouses suspicion. All of the windows are frosted over, so only a chilly light leaks in. The place is a mess, and the walls are adorned with lurid, seemingly AI-generated art: a frowning baby holding an assault rifle, a rubber ducky bobbing in a mug of what looks like black coffee, a lidless and levitating eyeball crying into a martini glass. The rooms are painted primary colors, grass green and cherry red, like a kindergarten class. A vape dangles from a doorframe by a chain, suspended at mouth level. The pantry is practically empty. The bedroom is a dormitory featuring seven identical twin beds. No one is hiding in the bathroom. The call, it seems, was a prank. The police return to the driveway and ask, "What is it that you guys are doing here?" "We're just livestreaming," says a man in a camo hat named Matt. "You guys don't have any firearms or anything inside the house?" There are guns in the house, Matt says, for self-defense. Fans of their livestream can be obsessive, he explains, and tend to have perverse ideas about jokes. The officer asks to see their weapons, and they go downstairs. The room is cluttered with ergonomic swivel chairs, desks strewn with takeout containers and energy drinks, two flatscreen TVs, and a dozen computer monitors.

This paper builds a hierarchy of explicit, non-asymptotic tail bounds for the supremum of the Kostlan--Shub--Smale (KSS) random field on the sphere, and applies it to two problems: Spiked Tensor PCA and the landscape of the spherical $k$-spin model. For Tensor PCA, we study the non-asymptotic statistical limits of estimating a rank-$R$ symmetric signal tensor of order~$k\ge 3$ and dimension~$d\ge 3$ from a single Gaussian observation at signal-to-noise ratio~$λ$, through the \emph{profile maximum likelihood estimator}, the MLE restricted to normalized rank-$R$ tensors of coherence at least~$κ$. Our analysis uses a single reduction: a deterministic geometric inequality (the Tube Method) and a rank-reduction step bound the estimation error by the supremum of the canonical KSS field, which the Kac--Rice formula turns into a Gaussian integral against the expected absolute characteristic polynomial of a shifted Gaussian Orthogonal Ensemble, controlled in turn by the four explicit tail bounds of our hierarchy (three from a Mehta--Fyodorov representation, one from a Ben Arous--Dembo--Guionnet large deviation). The same reduction yields two results, each with explicit constants. For estimation, a finite-$(k,d)$ error bound recovers the asymptotically optimal rate~$\sqrt{d\log k}$ of Perry, Wein and Bandeira, with explicit dependence on the rank~$R$ and the coherence~$κ$. For the landscape, a two-sided non-asymptotic bracketing of the annealed complexity of the spherical $k$-spin Hamiltonian recovers the Auffinger--Ben Arous--Černý complexity function in the high-dimensional limit.

We study sparse semi-continuous tensor data with excess zeros, heavy right tails, and slice-specific dispersion. Such features arise naturally in monetary-valued multi-way data, such as international trade, where most exporter--importer--product--year cells are zero while positive values are continuous and highly variable. To model these data, we propose a Bayesian hierarchical tensor factorization model that places a low-rank CP structure on a latent Poisson rate tensor and couples it with a conditional Gamma model for positive outcomes, with rate parameters that can vary across slices within a mode. The model therefore separates the occurrence and magnitude of positive observations while borrowing strength across all tensor dimensions through a shared low-rank latent structure. To scale posterior inference to large arrays, we develop a hybrid variational--Monte Carlo algorithm that combines efficient coordinate ascent updates with a partially collapsed augmented-data sampler. Applied to approximately 60 million trade flows, the method surfaces multiway dependence across exporters, importers, products, and years that is difficult to recover from gravity-type or pairwise network analyses, which do not jointly model the product and temporal dimensions.

A botanist at Kew's Madagascar research site scans a plant for digitisation. A botanist at Kew's Madagascar research site scans a plant for digitisation. AI could help win'race against extinction' of vital plants, say botanists Tech is helping to identify and save new specimens and could open'genomic goldmine' of fungi data The rise of AI and digitisation could be a turning point in the "race against extinction" faced by botanists trying to identify and save vital plants before they vanish, according to a major report from Royal Botanic Gardens, Kew. New technology is enabling scientists to track how flowering times have shifted by weeks around the world, rapidly identify new specimens and even get crucial genetic data from 180-year-old fungus specimens, potentially opening a "genomic goldmine". Digitisation and online access to millions of specimens that were until now only accessible in archives is also producing new insights, especially in the global south.

We propose a Koopman-enhanced physics-informed neural network (K--PINN) framework for parameter inference and forecasting in nonlinear epidemic models. This method combines Koopman operator theory and physics-informed learning. It maps epidemic states into a latent observable space where the dynamics evolve approximately linearly while satisfying the governing epidemic equations through automatic differentiation. This integration improves interpretability, parameter identifiability, and long-term predictive stability. We apply the proposed framework to a normalized SEIRSD epidemic model and evaluate it using synthetic monkeypox (Mpox) data and real-world datasets from Germany, Morocco, and Sweden for the SARS-CoV-2 virus. Synthetic trajectories are generated using a structure-preserving, nonstandard finite difference scheme to ensure reliable training data. Numerical results demonstrate that K--PINN achieves more accurate parameter estimation, trajectory reconstruction, and long-term forecasting than classical PINNs and Koopman-EDMD approaches. These results suggest that K--PINN is an effective machine learning framework for epidemic modeling that can be extended to more complex systems.

Large Language Models (LLMs) require significant GPU memory when processing long texts, with the key value (KV) cache consuming up to 70% of total memory during inference. Although existing compression methods reduce memory by evaluating the importance of individual tokens, they overlook critical semantic relationships between tokens, resulting in fragmented context and degraded performance. We introduce ChunkKV, which fundamentally reimagines KV cache compression by treating semantic chunks - rather than isolated tokens - as basic compression units. This approach preserves complete linguistic structures and contextual integrity, ensuring that essential meaning is retained even under aggressive compression. Our innovation includes a novel layer-wise index reuse technique that exploits the higher cross-layer similarity of preserved indices in ChunkKV, reducing computational overhead and improving throughput by 26.5%. Comprehensive evaluations on challenging benchmarks: LongBench, Needle-InA-HayStack, GSM8K, and JailbreakV demonstrate that ChunkKV outperforms state-of-the-art methods by up to 8.7% in precision while maintaining the same compression ratio. These results confirm that semantic-aware compression significantly enhances both efficiency and performance for long-context LLM inference, providing a simple yet effective solution to the memory bottleneck problem. The code is available at link.

Former Olympian is arrested for allegedly vandalizing Reflecting Pool... but he claims he merely touched it Call me cynical, but the real reason Gruesome Twosome Harry and Meghan are returning to the UK is just so obvious... and highly humiliating: MAUREEN CALLAHAN Three more arrested over bungee jumper's death after she was hurled from bridge without a rope I lost 50lb without jabs using this easy but overlooked method. But I still felt dowdy - until I discovered these expert anti-ageing fashion and beauty tips. Inside America's new fattest town: Burgers are the size of your head, gyms lie empty and custom mobility scooters carry 800lb loads... as we investigate why Ozempic just DOESN'T work Blake Lively runs errands in frumpy outfit after reconciling with ex-BFF Taylor Swift... miles away from reported'bachelorette party' I've spoken to thousands of children who claim they can recall a past life ... these chilling stories have convinced me they're telling the truth Stingy fast food giant named America's favorite restaurant AGAIN... and experts think they know why Ex-partner of dad who was berated for taking his daughters into women's bathroom claims he'exploited' girls and accuses him of failing to pay child support... before he hits back The'marry me' sex move that'll make even the most commitment-phobic of men beg to see you again... and it worked for THREE of my friends America's next real estate time bomb detonates the sun-kissed southern housing dream: 'New condo crisis' sparks chilling warning as it snakes across the nation Furious Trump hits back at Italian Prime Minister Meloni and gives her unusual'nickname' as their photo feud ramps up TV star mom, 46, who appeared on'quitting everything to change your life' show died in fire at luxury Caribbean beach resort that sent 1,700 tourists running for their lives Grace Kelly's lookalike granddaughter, 27, wows in bikini snaps...as she packs on the PDA during beach getaway The four mistakes that led to bungee tragedy on Skeleton Bridge: FRED KELLY saw the scene for himself, now he retraces the prelude to disaster. So was it really an accident? Famous TV mansion left standing after Malibu's harshest wildfires struggled to find a buyer for 14 years but finally sells for an eye-watering price Swedish actress, 81, was in TWO James Bond movies and also worked with Charlton Heston, who is she?