You're viewing the US edition You can switch to the UK or AU homepage at any time using this menu. His penis grew by a THIRD in minutes after game-changing new enlargement method... now thrilled patient bares all and declares: 'My phone's already buzzing' Hoover Dam's horror threat to 40 million Americans: As'tipping point' is reached... expert warns residents in THREE states to brace Supreme Court clears path for Trump's mail-in voting crackdown ahead of make-or-break midterms No one will dare say it out loud... but there's only one bombshell way Harry and Meghan's'half-in, half-out' new life in Britain can work: ROBERT JOBSON Enes Kanter Freedom hits back at'terrified' WNBA as he learns draft fate after ex-NBA star was ejected from game over explosive courtside clash The 10-cent supplement that turbocharges your Mounjaro AND reduces your cholesterol: Most patients won't have heard of it, but now experts reveal why anyone on jabs must take it - and how it can stop you putting weight back on James Blunt breaks silence on claims he was'famous British singer' who Hayden Panettiere was put into bed with when she was 18 Glamorous Duke University influencer accused of astonishingly sly plot... as students reveal blistering evidence Brian Hickerson's dark family secrets outed by his own sister... who reveals moment his'demons' took over... and real reason Hayden Panettiere kept going back Mother of three young boys who vanished on Thanksgiving 2010 while being cared for by their dad admits she is a PEDOPHILE at ex's murder trial Veteran actor who quit Hollywood for extreme career change steps out at 86... can you guess who? Truth about the $10 fast food challenge: From McDonald's to Raising Cane's and Chipotle, I hit every major spot to get the biggest bang for my buck... the winner stunned me Dodgers star's wife shares stunning vacation photos... three weeks after being hospitalized in terrifying health scare Entitled Oregon woman had huge tantrum after being told to get her dog's paws off coffee shop counter... then she got a taste of her own medicine Sea level rise could be even worse than previously thought for some unlucky coastal communities, as scientists uncover a massive difference in local tides. Satellite images have revealed that tides can vary by almost a metre across the length of a single bay. This means that some parts of the coast are at far greater risk of coastal flooding, saltwater intrusion, and pollution spills than their nearby neighbours.

Normalizing Flows excel at modeling a single fixed density, yet many problems across the sciences, such as high energy physics, instead require modeling how that density deforms as a function of continuous parameters: the strength of a physical effect, a calibration constant, or a source of systematic uncertainty. Learning a separate flow for every parameter configuration quickly becomes intractable, since the number of joint settings grows exponentially with the number of parameters. We introduce Factorizable Normalizing Flows (FNFs), which represent the parameter-dependent density as a fixed, high-fidelity flow for a reference configuration composed with a learnable transformation that is polynomial in the parameters and factorized over them. This structure has a practical consequence: each parameter's effect is learned in isolation, from samples in which that parameter alone is varied. The combined response of many parameters is then recovered by summation at inference, without ever sampling their combinatorially large joint space. On a controlled problem with two interpretable deformations applied jointly to the data, the learned transformation reproduces the true deformations and matches the optimal likelihood, while optional interaction terms capture residual correlations when several parameters vary strongly at once. The resulting model is interpretable, scales linearly with the number of parameters, and keeps the likelihood tractable. This provides a general tool for any inference workflow requiring continuous density morphing, and directly enables the next generation of unbinned likelihood fits in high energy physics.

Textual data are often collected alongside structured response variables, but prediction and interpretation are commonly treated as separate tasks. This paper studies rating prediction as an initial case of interpretable text-response modelling, where the aim is to learn textual representations that are both semantically meaningful and aligned with an external response. We propose a joint non-negative matrix factorisation and binomial regression model, in which the document-topic representation is learned from both text reconstruction and rating prediction. Simulation experiments and a real-world review dataset show that the model can recover stable response-relevant textual signals and achieve competitive performance against linear and ridge regression baselines. The framework provides a practical step towards interpretable modelling of text-linked outcomes, with potential extensions to other response types beyond bounded ratings.

Diffusion Transformers (DiTs) achieve state-of-the-art results in text-to-image, text-to-video generation, and editing. However, their large model size and the quadratic cost of spatial-temporal attention over multiple denoising steps make video generation computationally expensive. Static caching mitigates this by reusing features across fixed steps but fails to adapt to generation dynamics, leading to suboptimal trade-offs between speed and quality. We propose Foresight, an adaptive layer-reuse technique that reduces computational redundancy across denoising steps while preserving baseline performance. Foresight dynamically identifies and reuses DiT block outputs for all layers across steps, adapting to generation parameters such as resolution and denoising schedules to optimize efficiency. Applied to OpenSora, Latte, and CogVideoX, Foresight achieves up to 1.63 end-to-end speedup, while maintaining video quality.

The modeling of samples of distributions is a major challenge since distributions do not form a vector space. While various approaches exist for univariate distributions, including transformations to a Hilbert space, far less is known about the multivariate case. We utilize a transformation approach to map multivariate distributions to a Hilbert space via a Wasserstein slicing method that is invertible. This approach combines functional data analysis tools, such as functional principal component analysis and modes of variation, with the facility to map back to interpretable distributions. We also provide convergence guarantees for the Hilbert space representations under a broad class of such transforms. The method is illustrated using joint systolic and diastolic blood pressure data.

Two narratives about machine learning ecosystems grew out of the recent algorithmic fairness discourse. In one, dubbed monoculture, algorithmic ecosystems tend toward homogeneity akin to a single model making all decisions. Individuals then face the risk of systematic exclusion with no recourse. In the other, model multiplicity, many models solve the same task with similar accuracy, causing excessive variation in individual outcomes. Both narratives are compelling, yet, seemingly at odds: model multiplicity can't materialize in a strict monoculture.

We introduce FAEclust, a novel functional autoencoder framework for cluster analysis of multi-dimensional functional data, data that are random realizations of vector-valued random functions. Our framework features a universal-approximator encoder that captures complex nonlinear interdependencies among component functions, and a universal-approximator decoder capable of accurately reconstructing both Euclidean and manifold-valued functional data. Stability and robustness are enhanced through innovative regularization strategies applied to functional weights and biases. Additionally, we incorporate a clustering loss into the network's training objective, promoting the learning of latent representations that are conducive to effective clustering. A key innovation is our shape-informed clustering objective, ensuring that the clustering results are resistant to phase variations in the functions. We establish the universal approximation property of our non-linear decoder and validate the effectiveness of our model through extensive experiments.

Lithography orchestrates a symphony of light, mask and photochemicals to transfer the integrated circuit patterns onto the wafer. Lithography simulation serves as the critical nexus between circuit design and manufacturing, where its speed and accuracy fundamentally govern the optimization quality of downstream resolution enhancement techniques (RETs). While machine learning promises to circumvent computational limitations of lithography process through data-driven or physics-informed approximations of computational lithography, existing simulators suffer from inadequate lithographic awareness due to insufficient training data capturing essential process variations and mask correction rules.

Each split is entirely unique, and no labyrinth appears more than once in4 the entire dataset, regardless of its split. Each entry consists of five pieces of information:5 obs: the path to the image representation for that state;6 actions: the integer action performed for that solution in that state;7 rewards: the float reward received for that action in that state;8 episode_starts: the boolean status that states if it is the first state in an episode; and9 info: the textual information required to load the same labyrinth structure if needed.10 We provide images in each dataset since we believe that visual information is more useful to the11 imitation learning agent, and if a vector representation is needed, the info parameter allows researchers12 to load the same structure and the actions enables the recreation of the dataset in its vector format.13 Each observation is an image of size 600 600 3. Although each baseline trained in this work14 uses a 64 64 3input, we thought that providing a bigger image would benefit models requiring15 downsizing (e.g., the walls will not disappear during resizing).

Private Evolution (PE) is a promising training-free method for differentially private (DP) synthetic data generation. While it achieves strong performance in some domains (e.g., images and text), its behavior in others (e.g., tabular data) is less consistent. To date, the only theoretical analysis of the convergence of PE depends on unrealistic assumptions about both the algorithm's behavior and the structure of the sensitive dataset. In this work, we develop a new theoretical framework to understand PE's practical behavior and identify sufficient conditions for its convergence. For d-dimensional sensitive datasets with n data points from a convex and compact domain, we prove that under the right hyperparameter settings and given access to the Gaussian variation API proposed in [33], PE produces an (ε,δ)-DP synthetic dataset with expected 1-Wasserstein distance O(d(nε) 1/d) from the original; this establishes worst-case convergence of the algorithm as n . Our analysis extends to general Banach spaces as well. We also connect PE to the Private Signed Measure Mechanism, a method for DP synthetic data generation that has thus far not seen much practical adoption. We demonstrate the practical relevance of our theoretical findings in experiments.