Transformer-based large models have demonstrated remarkable generalization abilities across different tasks by leveraging a context-aware attention module for in-context learning. With richer context, transformers adapt more effectively to the current use case without any parameter updates. However, the quadratic computational and memory complexity with respect to context length significantly slows data processing in softmax transformers. Linear transformers were proposed to address this issue by reducing the complexity to linear dependence on context length, but the design and understanding of the feature mapping in linear attention, from a theoretical viewpoint, remain unclear. In this paper, we investigate the approximation and generalization abilities of linear transformers under a two-staged sampling process from domain generalization. We show that linear transformers perform in-context learning as learning a mapping from context distributions to response functions. A dimension-independent convergence rate is obtained for our generalization analysis, which also exhibits the tradeoff between the regularities of data distributions and latent features. Guided by our theoretical framework, we propose a new perspective on activation and loss design for linearizing pretrained softmax large language models.

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.

Autoencoders (AEs) have emerged as powerful tools for non-linear dimensionality reduction, often surpassing traditional linear methods such as Proper Orthogonal Decomposition (POD) in scenarios characterized by slowly decaying Kolmogorov $n$-widths. In the realm of Reduced-Order Modelling (ROM), these models are increasingly utilized to learn low-dimensional representations of solution manifolds associated with parametric Partial Differential Equations (PDEs). However, the high expressivity of AEs presents a challenge: although trained networks typically minimize reconstruction error, they often struggle to capture the essential properties necessary for building accurate and robust ROMs. Recent works by arXiv:2307.15288v2 and arXiv:2506.11641v1 have tackled this challenge in fully connected AEs by proposing representation-consistent architectures, which preserve some of the properties belonging to POD. This study builds upon that concept by extending representation consistency for convolutional layers. We introduce a novel class of symmetric Convolutional AutoEncoders (CAEs) designed to embody the primary properties of manifold parametrization mappings. When integrated into a ROM framework, this architecture demonstrates significantly improved predictive capabilities. Specifically, we compared the performance of the ROMs based on classical and symmetric CAEs on three one dimensional academic test cases, namely the Linear Advection, the Viscous Burger and the Kuramoto Sivashinsky equation. Numerical results demonstrate that our proposed symmetric approach consistently yields more accurate latent trajectories, lower reconstruction errors, and enhanced model robustness.

Travel, said users should'scroll past these summaries and look at guest reviews'. Travel, said users should'scroll past these summaries and look at guest reviews'. AI-generated overview found to gloss over allegations of sexual harassment and describes hotel being sued over hygiene as'spotless' A hotel being sued for mass food poisonings was described as "spotless" and a resort where guests complained of sexual harassment by staff was praised for "friendly" service by an AI intended to summarise millions of Tripadvisor reviews. The overviews of customer feedback downplayed serious complaints, ranging from the stench of mould to a lack of mains water, according to an investigation by the consumer campaign organisation Which? The AI-generated reviews appear on the travel website's hotel webpages to help holidaymakers decide where to book.

Penalty Shootouts: Is the Team That Kicks First More Likely to Win? Penalty kicks are already proving critical to big wins at this year's World Cup. But the advantage in penalty kicks has more to do with psychological effects than who kicks first. A penalty kick during the Netherlands' round of 32 match against Morocco. In a World Cup, some of the most important matches are decided by a penalty shootout. When that moment comes, the captains want to win the coin toss to decide the order of the kicks.

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'This story began in my childhood in rural Trinidad' Jamir Nazir. 'This story began in my childhood in rural Trinidad' Jamir Nazir. Jamir Nazir's The Serpent in the Grove, which critics allege has'obvious markers' of AI use, was described as'original, poetic and deeply moving' by the judging chair A story widely accused on social media of being written using AI has gone on to win the overall Commonwealth short story prize. Jamir Nazir's story The Serpent in the Grove went viral after being named as a regional winner in mid-May, with critics on X and Bluesky claiming it showed "obvious markers" of AI use. The literary magazine Granta subsequently pulled out of its long-running agreement to publish the Commonwealth winners.

I am on holiday later this month, so I'm pleased to find there's a really wide range of intriguing new science fiction to take with me. I'm particularly keen to get cracking on a tale by Sheila Armstrong about strange ancient things found in a bog, but I'm also excited to read a new book by one of my favourite authors, Paul Tremblay (even if it does sound very disturbing). And I'm looking forward to the high-concept thrillers and classic space-set sci-fi on offer, too - not forgetting the first new novel released in 30 years. This sounds a little -like and ideal summer reading for those of us who enjoy a good high-concept thriller. It's set in a near future where you can outsource your emotional pain thanks to a biotech company, Eudaimonia.