This paper examines the performance of ridge regression in reproducing kernel Hilbert spaces in the presence of noise that exhibits a finite number of higher moments. We establish excess risk bounds consisting of subgaussian and polynomial terms based on the well known integral operator framework. The dominant subgaussian component allows to achieve convergence rates that have previously only been derived under subexponential noise--a prevalent assumption in related work from the last two decades. These rates are optimal under standard eigenvalue decay conditions, demonstrating the asymptotic robustness of regularized least squares against heavy-tailed noise. Our derivations are based on a Fuk-Nagaev inequality for Hilbert-space valued random variables.

Do esports students do more than play games? Playing video games in college may seem unusual, but for many teenagers across the country, it could lead to professional careers. Students at Central Bedfordshire College have just finished their first year of the Level 3 Pearson BTEC in esports, the first time the college has offered such a course. While gaming is a key part of the learning, students also study a broad range of modules designed to prepare them for work both inside and outside competitive gaming. These can include psychology to understand how the brain reacts under pressure, alongside nutrition and fitness to ensure they have the energy to compete effectively.

We propose a novel diffusion-based framework for automatic colorization of Animestyle facial sketches, which preserves the structural fidelity of the input sketch while effectively transferring stylistic attributes from a reference image. Our approach builds upon recent continuous-time diffusion models, but departs from traditional methods that rely on predefined noise schedules, which often fail to maintain perceptual consistency across the generative trajectory. To address this, we introduce SSIMBaD (Sigma Scaling with SSIM-Guided Balanced Diffusion), a sigma-space transformation that ensures linear alignment of perceptual degradation, as measured by structural similarity. This perceptual scaling enforces uniform visual difficulty across timesteps, enabling more balanced and faithful reconstructions.

Speculative decoding accelerates inference in large language models (LLMs) by generating multiple draft tokens simultaneously.

Recent advances in Structure-based Drug Design (SBDD) have leveraged generative models for 3D molecular generation, predominantly evaluating model performance by binding affinity to target proteins. However, practical drug discovery necessitates high binding affinity along with synthetic feasibility and selectivity, critical properties that were largely neglected in previous evaluations. To address this gap, we identify fundamental limitations of conventional diffusion-based generative models in effectively guiding molecule generation toward these diverse pharmacological properties. We propose CBYG, a novel framework extending Bayesian Flow Network into a gradient-based conditional generative model that robustly integrates property-specific guidance. Additionally, we introduce a comprehensive evaluation scheme incorporating practical benchmarks for binding affinity, synthetic feasibility, and selectivity, overcoming the limitations of conventional evaluation methods. Extensive experiments demonstrate that our proposed CBYG framework significantly outperforms baseline models across multiple essential evaluation criteria, highlighting its effectiveness and practicality for real-world drug discovery applications.

Synthetic data generation in histopathology faces unique challenges: preserving tissue heterogeneity, capturing subtle morphological features, and scaling to unannotated datasets. We present a latent diffusion model that generates realistic heterogeneous histopathology images through a novel dual-conditioning approach combining semantic segmentation maps with tissue-specific visual crops. Unlike existing methods that rely on text prompts or abstract visual embeddings, our approach preserves critical morphological details by directly incorporating raw tissue crops from corresponding semantic regions. For annotated datasets (i.e., Camelyon16, Panda), we extract patches ensuring 20 80%tissue heterogeneity. For unannotated data (i.e., TCGA), we introduce a self-supervised extension that clusters whole-slide images into 100 tissue types using foundation model embeddings, automatically generating pseudo-semantic maps for training.

Reconstructing dynamic 3D scenes from monocular videos remains a fundamental challenge in 3D vision. While 3DGaussian Splatting (3DGS) achieves real-time rendering in static settings, extending it to dynamic scenes is challenging due to the difficulty of learning structured and temporally consistent motion representations.

Discrete diffusion has emerged as a powerful framework for generative modeling in discrete domains, yet efficiently sampling from these models remains challenging. Existing sampling strategies often struggle to balance computation and sample quality when the number of sampling steps is reduced, even when the model has learned the data distribution well. To address these limitations, we propose a predictor-corrector sampling scheme where the corrector is informed by the diffusion model to more reliably counter the accumulating approximation errors. To further enhance the effectiveness of our informed corrector, we introduce complementary architectural modifications based on hollow transformers and a simple tailored training objective that leverages more training signal. We use a synthetic example to illustrate the failure modes of existing samplers and show how informed correctors alleviate these problems. On the text8 and tokenized ImageNet 256 256datasets, our informed corrector consistently produces superior samples with fewer errors or improved FID scores for discrete diffusion models. These results underscore the potential of informed correctors for fast and high-fidelity generation using discrete diffusion. Our code is available at https://github.

We consider the following question: given a submodular/supermodular set function f: 2V R, how should one minimize/maximize its average value f(S)/|S| over non-empty subsets S V? This problem generalizes several well-known objectives, including Densest Subgraph (DSG), Densest Supermodular Set (DSS), and Submodular Function Minimization (SFM). Motivated by recent applications [42, 34], we formalize two new broad problems: the Unrestricted Sparsest Submodular Set (USSS) and Unrestricted Densest Supermodular Set (UDSS), both of which allow negative and non-monotone functions. Using classical results, we show that DSS, SFM, USSS, UDSS, and Minimum Norm Point (MNP) are all equivalent under strongly polynomial-time reductions. This equivalence enables algorithmic cross-over: methods designed for one problem can be repurposed to solve others efficiently. In particular, we use the perspective of the minimum norm point in the base polyhedron of a sub/supermodular function, which, via Fujishige's results, yields the dense decomposition as a byproduct.

Modern single-image super-resolution (SISR) models deliver photo-realistic results at the scale factors on which they are trained, but collapse when asked to magnify far beyond that regime. We address this scalability bottleneck with Chain-of-Zoom (CoZ), a model-agnostic framework that factorizes SISR into an autoregressive chain of intermediate scale-states with multi-scale-aware prompts. CoZ repeatedly re-uses a backbone SR model, decomposing the conditional probability into tractable sub-problems to achieve extreme resolutions without additional training. Because visual cues diminish at high magnifications, we augment each zoom step with multi-scale-aware text prompts generated by a vision-language model (VLM). The prompt extractor itself is fine-tuned using Generalized Reward Policy Optimization (GRPO) with a critic VLM, aligning text guidance towards human preference. Experiments show that a standard 4 diffusion SR model wrapped in CoZ attains beyond 256 enlargement with high perceptual quality and fidelity.