This paper presents a unified framework that allows high-quality dynamic Gaussian Splatting from both defocused and motion-blurred monocular videos. Due to the significant difference between the formation processes of defocus blur and motion blur, existing methods are tailored for either one of them, lacking the ability to simultaneously deal with both of them. Although the two can be jointly modeled as blur kernel-based convolution, the inherent difficulty in estimating accurate blur kernels greatly limits the progress in this direction. In this work, we go a step further towards this direction. Particularly, we propose to estimate per-pixel reliable blur kernels using a blur prediction network that exploits blur-related scene and camera information and is subject to a blur-aware sparsity constraint. Besides, we introduce a dynamic Gaussian densification strategy to mitigate the lack of Gaussians for incomplete regions, and boost the performance of novel view synthesis by incorporating unseen view information to constrain scene optimization. Extensive experiments show that our method outperforms the state-of-the-art methods in generating photorealistic novel view synthesis from defocused and motion-blurred monocular videos.

Fine-tuning pre-trained models with custom data leads to numerous expert models on specific tasks. Merging models into one universal model to empower multi-task ability refraining from data leakage has gained popularity. With the expansion in data and model size, parameter-efficient tuning becomes the common practice for obtaining task-specific models efficiently. However, few methods are dedicated to efficient merging, and existing methods designed for full fine-tuning merging fail under efficient merging. To address the issue, we analyze from low-rank decomposition and reveal that direction robustness during merging is crucial for merging efficient modules. We furthermore uncover that compensating for the gap between stark singular values contributes to direction robustness. Therefore, we propose RobustMerge, a training-free parameter-efficient merging method with complementary parameter adaptation to maintain direction robustness. Specifically, we (1) prune parameters and scale coefficients from inter-parameter relations for singular values to maintain direction stability away from task interference, and (2) perform cross-task normalization to enhance unseen task generalization. We establish a benchmark consisting of diverse multimodal tasks, on which we conduct experiments to certify the outstanding performance and generalizability of our method.

Trump turns on the charm after extended'alpha' handshake with Macron and kisses for Brigitte at Palace of Versailles Sensational REAL reason Jelly Roll is divorcing Bunnie XO: Insiders reveal'preacher's wife' bombshell that's the talk of Nashville... truth about legendary rocker cuckolding rumor... and G-string mishap LIZ JONES: The cracks in Harry and Meghan's perfect facade have started to show. It's so obvious he's tiring of her tone-deaf approach... and I predict there's serious trouble in store Taylor Swift's bottomless thirst for attention, her greed and sheer tackiness are now truly unbearable... this latest stunt has shown her true colors: MAUREEN CALLAHAN NBA star's fiancee breaks her silence after friend, 26, mysteriously dropped dead at her luxury bachelorette party in St Barts Luxury fashion tycoon beloved by the stars hangs her head in shame as she's indicted for allegedly exploiting her workers and stealing $50k from their wages Jeff Bezos mercilessly mocked for taking'fake phone calls' when out with wife Lauren Sanchez Anguished family members flee court over sick details of Gilgo Beach murderer's kill room: Live updates'She has not been transparent... the damage has been done': How influencer Elle Darby'betrayed' thousands of young female fans...as insiders tell MOLLY CLAYTON how she cashed in As a divorced mother-of-three, cocaine was my little treat while my fellow middle-class friends had a few wines. What happened next was every family's worst nightmare... this is my warning to mums who'dabble' Desperate search for mom-of-three who hasn't been seen in three days as husband pleads for her return The shocking betrayal behind Jelly Roll's divorce from Bunnie XO is so utterly cruel... but have you yet spotted her revenge: JACQUELYNN POWERS Devastating supply crunch forces Apple to raise prices on iPhones and other devices, calling the move'unavoidable' Jeff's Dream Team: Bezos recruits world's top architects to build most expensive mega mansion on Billionaire Bunker island The Ring star Daveigh Chase's friends searched for her on LA's Skid Row in months before her shock death at 35 Watch horrifying drone video that follows woman's plunge to death after bungee team threw her from bridge without rope Stonehenge's secret SISTER: Archaeologists discover an ancient monument just three miles away that may have served as a'prototype' for the famous stones Archaeologists have discovered a secret sister monument to Stonehenge that might have served as a'prototype' for the famous stones. This ancient site is just three miles away from Stonehenge itself, located in the village of Bulford, Wiltshire. Consisting of two wooden poles placed 400 feet (120 metres) apart, this long-lost monument might appear rather basic at first glance.

Binary data factorization is common, but real-valued methods ignore discreteness and yield hard-to-interpret factors. Boolean Matrix Factorization (BooMF) instead decomposes a binary matrix into two lower-rank binary matrices via logical AND and OR, expressing the data as a Boolean disjunction of interpretable patterns. In cancer genomics, BooMF can reveal coordinated feature changes that may drive tumor evolution, unlike rotational or additive decompositions. Most existing BooMF methods are heuristic, greedy, sensitive to initialization, prone to local optima, and do not support principled model selection or uncertainty quantification. We introduce Bayesian Boolean Matrix Factorization (BBMF), a fully conjugate generative model with sparsity-inducing priors. It enforces Boolean constraints, yields interpretable latent factors with coherent uncertainty quantification, and admits Gibbs sampling with closed-form full conditionals. Because cancer evolution often involves widespread, near-simultaneous chromosome-number changes (e.g., whole-genome duplication followed by instability and selection), Boolean factorizations capture these patterns more naturally than additive models. Applied to arm-level copy-number alteration data in multiple myeloma, where entries indicate presence/absence of chromosomal-arm amplifications, BBMF finds a small set of interpretable bicliques linking patient subsets to recurrently co-altered chromosomal arms, providing a compact, biologically meaningful summary of tumor heterogeneity and demonstrating BBMF's utility for uncovering discrete latent structure in complex binary data.

We develop a framework for conformal prediction in dyadic regression problems under complex missingness mechanisms. At the theoretical level, we develop general technical tools for establishing finite-sample validity of conformal prediction under distributional invariance conditions weaker than exchangeability. A key result handles the case where the sample itself is a random subset of the index set, a setting not covered by existing theory, via a novel bijection argument that constructs an explicit measure-preserving correspondence between events. In addition, we propose conformal prediction procedures for jointly exchangeable arrays, including full conformal, split conformal, a row-column approach exploiting similarities within rows and columns, and a selective conformal procedure achieving mask-conditional validity. For missing elements, we establish asymptotic validity of a weighted conformal procedure under a nonparametric graphon model for the missingness mechanism. We further establish conditional validity results for both continuous and discrete responses; to the best of our knowledge, this is the first formal proof of asymptotic conditional validity for weighted conformal prediction under a missing-not-at-random assumption. The proposed methods are illustrated on synthetic and real network data.

A variety of widely used optimization methods like SignSGD and Muon can be interpreted as instances of steepest descent under different norm-induced geometries. In this work, we study the implicit bias of mini-batch stochastic steepest descent in multi-class classification, characterizing how batch size, momentum, and variance reduction shape the limiting max-margin behavior and convergence rates under general entry-wise and Schatten-$p$ norms. We show that, without momentum, worst-case convergence and successful classification can only be guaranteed with full-batch gradient. In contrast, momentum enables small-batch convergence to an approximate max-margin solution through a batch-momentum trade-off, though it slows convergence. This approach provides fully explicit, dimension-free rates that improve upon prior results. Moreover, we prove that variance reduction can recover the exact full-batch implicit bias for any batch size, albeit at a slower convergence rate. Finally, we further investigate the batch-size-one steepest descent without momentum, and reveal its convergence to a fundamentally different bias via a concrete data example, which reveals a key limitation of purely stochastic updates. Overall, our unified analysis clarifies when stochastic optimization aligns with full-batch behavior, and paves the way for perform deeper explorations of the training behavior of stochastic gradient steepest descent algorithms.

Testing conditional independence is fundamental yet intrinsically difficult: without additional assumptions, Type I error control is impossible in general. The "Model-X'' paradigm addresses this difficulty by assuming exact knowledge of a relevant conditional distribution. While small deviations from this assumption can sometimes be tolerated in classical one-shot testing, existing sequential conditional independence tests typically require the Model-X conditional to be known exactly, making them fragile when it must instead be estimated. We propose a new approach that is substantially more robust to such estimation error. Our method applies testing-by-betting to an adaptively optimized Kernel Conditional Independence statistic, together with a normalization scheme and a truncate-and-shift calibration strategy. These modifications greatly reduce Type I error inflation while preserving high power across high-dimensional synthetic benchmarks and real-world fairness tasks, outperforming existing sequential Model-X approaches. Code is available at https://github.com/he-zh/SKCI.

On biomedical tabular data, flexible models such as deep networks, gradient-boosted trees, and kernel methods are repeatedly matched or beaten by linear and logistic regression given the same features. The usual reaction is to treat this as a model-side shortfall, to be fixed with more data, a better architecture, or tuning, on the assumption that the nonlinear structure is there and the model has failed to capture it. We argue that these fixes cannot help when the binding limit is the measurement rather than the model, as it frequently is in biomedicine. Additive noise blurs the population-optimal predictor, and because blurring removes a function's fine, rapidly varying detail before its broad shape, it erases nonlinear structure faster than linear structure. A degree-$k$ interaction is attenuated by the $k$-th power of feature reliability, while the linear part is attenuated only once. At the reliabilities typical of biomedical measurement, the nonlinear advantage can vanish even when the underlying biology is strongly nonlinear, and what the noise removes cannot be recovered by a larger cohort or a more flexible model, only by better measurement. The nonlinearity is hidden, not absent, and a tie between linear and flexible models is not by itself a verdict on the biology. These pieces are classical, drawn from measurement-error statistics, psychometrics, and Gaussian analysis, and we assemble them into an exact excess-risk identity. Measurement reliability is one of three conditions, alongside sample size and feature representation, that must align for a flexible model to help, and together they leave only a narrow window that most biomedical tasks fall outside. Across 140 UK Biobank tasks, the gap between flexible and linear models, where it exists, carries the predicted noise signature, and the three conditions can be separated by intervention but not by a benchmark alone.

Recent empirical work shows that semantically equivalent paraphrases can fool financial sentiment classifiers: although a paraphrase remains close to the original under a strong reference embedding, it may shift the target model's representation enough to change the predicted class. Existing robustness theory either assumes a single-model threat model or focuses mainly on empirical attack algorithms. We develop a continuous local model of semantic paraphrase perturbations that captures this two-model structure. We show that the worst-case local displacement of the target representation, subject to a proxy-model budget, is governed by the largest generalised eigenvalue of a matrix pencil $(A,B)$ constructed from the Jacobians of the two embedding maps. The resulting attackability index $λ^*(x)$ is intrinsic to the local paraphrase geometry and the chosen embedders, yields a closed-form prediction-flip condition for affine readouts, and supports conservative population and finite-sample attackability certificates. For uniform control over classes of affine readouts, we derive a distribution-free VC bound for binary attackability indicators and a scale-sensitive margin bound based on an attackability-adjusted margin that subtracts a local geometric penalty from the standard classifier margin. We also connect the continuous theory to discrete paraphrase search, identify an asymmetry between successful and unsuccessful finite searches, and give a covering condition under which the discrete and continuous settings agree. Finally, we propose an empirical verification framework using soft-token relaxations and generated paraphrase sets to assess the local eigenvalue geometry, prediction-flip condition, and finite-search approximation on a deployed financial-text classifier.

Gaussian width is a central geometric complexity measure in high-dimensional probability, compressed sensing, convex optimization, and learning theory. It quantifies the average extent of a set along random directions, thereby capturing the effective dimension of constraint sets, hypothesis classes, and descent cones. However, this notion is intrinsically Euclidean. Statistical models instead carry a natural Riemannian geometry induced by the Fisher information metric, where directions are scaled according to statistical distinguishability rather than ambient Euclidean length. We introduce Fisher width, a Fisher-geometric analogue of Gaussian width for statistical manifolds. At a parameter point $θ$, Fisher width replaces the Euclidean identity by the local metric tensor $G(θ)^{1/2}$, measuring the Gaussian width of the Fisher-rescaled set. This makes the resulting quantity sensitive to local statistical curvature and invariant under smooth reparameterizations. We develop the basic theory of Fisher width, showing that it retains key structural features of Gaussian width, including concentration, metric perturbation stability, and spectral comparison bounds with the Euclidean baseline, while also capturing anisotropic geometric effects invisible to Euclidean measures. As an application, we prove a generalization bound for Fisher-Lipschitz hypothesis classes and propose computable estimators, which we evaluate empirically on MNIST across three model classes. Fisher width is to statistical manifolds what Gaussian width is to Euclidean convex bodies. This work lays the foundation for studying complexity and learning on curved statistical manifolds.