Daily Papers

In this article, we consider a viscoelastic plate equation with a logarithmic nonlinearity in the presence of nonlinear frictional damping term. Using the the Faedo-Galerkin method we establish the global existence of the solution of the problem and we also prove few general decay rate results.

We study resonance expansions and localised long-time dynamics for three-dimensional semiclassical Dirac operators. For smooth Hermitian matrix-valued perturbations which are analytic outside a compact set, we first obtain exponential cut-off resolvent bounds away from the resonance set and polynomial bounds in thin resonance-free rectangles adjacent to the real axis. Combining these estimates with a local Oc(h^{-3}) upper bound on the number of resonances, a pigeonhole selection of admissible contours, almost-analytic functional calculus, and a Cauchy--Green deformation, we derive resonance expansions for spectrally localised propagators. Positive-energy resonances contribute for large positive times, whereas negative-energy resonances contribute for large negative times. We then specialise to mass-type perturbations mbfβV(x) in a nontrapping energy window. Using the logarithmic resonance-free region established in our earlier work together with a quantitative FBI-transform/escape-function argument, we obtain a polynomial bound for the continued cut-off resolvent and deduce rapid local-energy decay. We subsequently refine this polynomial estimate by a finite-time propagation argument in the undistorted region. Introducing the maximal positive-sheet connection time T_χ associated with the spatial cutoff, we prove a geometric continued-resolvent estimate and, for every fixed M below the resonance-free depth constant, derive the explicit local-energy decay threshold T_N>T_χ+(N+1)/M. The same analysis gives a rigorous microlocal obstruction to a uniform [hlog(1/h)]^{-1} bound for the full distorted resolvent and identifies a finite-flight-time amplification mechanism for the sandwiched continued resolvent at logarithmic depth.

In this paper, both the pointwise space-time structures of the solution for a three-dimensional model describing gas dynamics in thermal non-equilibrium and the corresponding background stabilities within the L^p framework are investigated under the small initial perturbation assumption and the irrotationality condition. Our main tools are the modified Green's function according to the irrotationality condition, a priori energy method and a refined decay estimates of products composed of the entropy function and high-order derivatives.

We study a one dimensional nonlinear Klein-Gordon equation with a potential, a localized quadratic nonlinearity, and a non-localized quartic nonlinearity. We assume that the linearized operator has a single discrete eigenvalue below the continuous spectrum, corresponding to an ''internal mode''. This eigenvalue generates localized, time-periodic solutions for the linear equation. Assuming the natural Fermi Golden Rule, we give a global description of the dynamics of the amplitude of the internal mode through the radiation damping mechanism, and prove scattering for the radiation. Our approach is based on the distorted Fourier transform and a collection of refined dispersive decay and smoothing estimates. The corresponding cubic problem is closely related to the question of global-in-space dispersive asymptotics for perturbations of kink solutions in the classical ϕ^4 model, which remains a challenging open question. From the perspective of nonlinear estimates, a quartic (non-localized) interaction is essentially sharp for our analysis, and closing the estimates with such a low degree nonlinear term requires a careful and delicate treatment. As a direct application of our analysis, we prove a result on the asymptotic stability of kinks for classes of scalar field models that can be seen as perturbations of the ϕ^4 model.

The perturbative QCD corrections to the hadronic decay width of the W boson are currently known up to next-to-next-to-next-to-next-to-leading order (N^4LO), whereas the exact N^5LO correction remains unavailable owing to its formidable computational complexity. In this work, we estimate the N^5LO contributions by adopting Bayesian analysis (BA). Before performing the estimation, the Principle of Maximum Conformality (PMC) is employed to improve the precision of the initial scale-dependent perturbative series. Through recursive application of the renormalization group equation, non-conformal terms are absorbed into the strong running coupling, yielding a scheme-independent, scale-invariant perturbative series with improved convergence. The PMC procedure determines an effective coupling α_s(Q_*), with the PMC scale fixed as Q_* = 100.102~GeV at next-to-next-to-leading logarithmic accuracy. Based on the improved and more precise series, the 95.5% BA credible interval yields an uncertainty of Δδ_QCD|_{PMC, BA}^{N^5LO} = pm 1.0times 10^{-5}. The resulting hadronic branching ratio is B(Wto hadrons)|_PMC = (65.84pm 1.54)%, which is consistent with experimental data within reasonable errors.

We derive rates of exponential relative-entropy decay for a broad class of infinite-dimensional quantum Gibbs samplers. A key technical ingredient is a perturbative stability theory for hypercontractive estimates and logarithmic Sobolev inequalities. For suitably chosen dissipative couplings, we obtain exponential entropy decay for full multimode Bose-Hubbard samplers with arbitrary hopping and repulsive density interactions. For harmonically confined quantum Coulomb gases and molecular systems, we prove exponential entropy decay for every fixed finite-rank low-energy truncation of the interaction. Finally, we exhibit a periodic charging model with a positive spectral gap but no finite-time L^2-to-L^p bound for any p>2.

In this paper, we establish a quantitative finite-time approximation of scattering fields for nonlinear Alfvén waves in three-dimensional ideal incompressible magnetohydrodynamics near a strong constant magnetic background. Using the global weighted estimates, we prove that truncating the scattering profiles at time T introduces an error in both the L^infty norm and the H^{N_*+1} norm of order $ Obigl(varepsilon^2(R+T)^{-δ}bigr), where \varepsilon\in (0,1) measures the size of the initial perturbation, R\ge100 is the scale parameter in the weighted energy, δ\in(0,2/3) is the exponent related to weights, and N_*+1$ is the Sobolev regularity order assumed for the initial data. The pointwise estimate follows from the decay of the nonlocal pressure along nonlinear characteristics, while the Sobolev estimate combines higher-order weighted pressure bounds with estimates for derivatives of the characteristic flows. Numerical experiments measure pointwise and Sobolev pressure-integral tails to verify the quadratic dependence of the initial perturbation amplitude.

In this work we estimate the first unknown QCD correction to the decay of the Higgs boson into gluons, Hto gg, in the heavy-top limit using Padé approximants built to the perturbative series and to its Borel transform. In the process, we also obtain estimates for the first unknown coefficients of the QCD β function, of the QCD decoupling relation, and of the gluonium correlator. We also provide an updated prediction for the first unknown coefficient of Γ(Hto bb). We determine the polynomial dependence of the perturbative coefficients on the number of quark flavors, n_f. We point out that the large-n_f result for Hto gg can be obtained from results for the gluonium correlator already available in the literature. The coefficient of the highest power of n_f is then imposed as a constraint and is also used as a new test to discard unreliable approximants. The method is validated through the postdiction of the last known coefficient of the series. Our model-independent estimate for the yet unknown coefficient of order α_s^7 of Γ(Hto gg) is -312pm 15 (in the mathrm{MS} scheme with μ=m_H, where m_H is the Higgs mass). With our estimate the residual renormalization-scale dependence of Γ(Hto gg) is reduced by a factor of almost 1.5.

The standard Monte Carlo estimator I_N^{MC} of int fdω relies on independent samples from ω and has variance of order 1/N. Replacing the samples with a determinantal point process (DPP), a repulsive distribution, makes the estimator consistent, with variance rates that depend on how the DPP is adapted to f and ω. We examine two existing DPP-based estimators: one by Bardenet & Hardy (2020) with a rate of O(N^{-(1+1/d)}) for smooth f, but relying on a fixed DPP. The other, by Ermakov & Zolotukhin (1960), is unbiased with rate of order 1/N, like Monte Carlo, but its DPP is tailored to f. We revisit these estimators, generalize them to continuous settings, and provide sampling algorithms.

We study the problem of estimating the time delay between two signals representing delayed, irregularly sampled and noisy versions of the same underlying pattern. We propose and demonstrate an evolutionary algorithm for the (hyper)parameter estimation of a kernel-based technique in the context of an astronomical problem, namely estimating the time delay between two gravitationally lensed signals from a distant quasar. Mixed types (integer and real) are used to represent variables within the evolutionary algorithm. We test the algorithm on several artificial data sets, and also on real astronomical observations of quasar Q0957+561. By carrying out a statistical analysis of the results we present a detailed comparison of our method with the most popular methods for time delay estimation in astrophysics. Our method yields more accurate and more stable time delay estimates: for Q0957+561, we obtain 419.6 days for the time delay between images A and B. Our methodology can be readily applied to current state-of-the-art optical monitoring data in astronomy, but can also be applied in other disciplines involving similar time series data.

Ensemble Kalman Inversion (EKI) is a derivative-free, ensemble-based method for inverse and optimization problems. Its continuous-time formulation can be interpreted as an interacting particle system driven by a Kalman-type preconditioned descent direction. A well-known limitation of this dynamics is the possible premature collapse of the covariance of the ensemble, which makes the method sensitive to the initial ensemble. We introduce a second-order particle system in which the particles evolve according to an inertial dynamics. The model combines a Kalman-type relaxation force with damping, attraction towards the ensemble mean, and a short-range repulsive interaction designed to counteract ensemble collapse. The resulting dynamics can be interpreted as a heavy-ball reformulation of continuous-time EKI enriched by competing attractive and repulsive mechanisms. For linear inverse problems, we analyze the induced mean and fluctuation dynamics and identify a parameter regime in which fully collapsed configurations are linearly unstable. We further characterize asymptotic equilibria through a constrained optimality condition on the subspace retained by the limiting ensemble covariance and derive an exponential decay estimate. Numerical experiments illustrate the effect of inertia and repulsion on the ensemble dynamics and compare the proposed second-order method with first-order EKI-type

We present anyakrakusuma, an open-source Python library that solves the discrete static Schrödinger bridge problem, the entropically regularized counterpart of optimal transport, through a log-domain Sinkhorn--Knopp iteration and reconstructs the entropic interpolation between two empirical point clouds. The solver is paired with a diagnostic pipeline that characterizes the optimal coupling and the intermediate distributions through information-theoretic and geometric measures. We exercise the library on four idealized planar cases spanning a circle-to-circle dilation, a spiral-to-mixture fragmentation, a rigid reorientation of two moons, and a Lissajous-to-trefoil deformation. The log-domain formulation is necessary rather than merely convenient at the parameters studied, where the cost-to-regularization ratio reaches four hundred and the Gibbs kernel underflows double precision across most of its range; the iteration nonetheless attains a marginal residual of 10^{-9} and unit marginal fidelity in every case. Residual histories decay geometrically over approximately eight decades at per-iteration contraction factors between 0.966 and 0.976, which are local rates near the fixed point that lie many orders of magnitude below the worst-case Hilbert-metric bound. The covariance analysis recovers an imposed ninety-degree reorientation to within 0.07^circ, roughly forty times smaller than its uncertainty, across a masked interval of near-isotropy on which the principal axis is unobservable. The diagnostics are reported with explicit attention to the regimes in which each is well defined, including the differential entropy, which is meaningful only on the open interpolation interval. The presented cases are constructed rather than measured; quantitative application to empirical point clouds requires further study.

Although deep learning has produced dazzling successes for applications of image, speech, and video processing in the past few years, most trainings are with suboptimal hyper-parameters, requiring unnecessarily long training times. Setting the hyper-parameters remains a black art that requires years of experience to acquire. This report proposes several efficient ways to set the hyper-parameters that significantly reduce training time and improves performance. Specifically, this report shows how to examine the training validation/test loss function for subtle clues of underfitting and overfitting and suggests guidelines for moving toward the optimal balance point. Then it discusses how to increase/decrease the learning rate/momentum to speed up training. Our experiments show that it is crucial to balance every manner of regularization for each dataset and architecture. Weight decay is used as a sample regularizer to show how its optimal value is tightly coupled with the learning rates and momentums. Files to help replicate the results reported here are available.

Recent advances in learning rate (LR) scheduling have demonstrated the effectiveness of decay-free approaches that eliminate the traditional decay phase while maintaining competitive performance. Model merging techniques have emerged as particularly promising solutions in this domain. We present Warmup-Stable and Merge (WSM), a general framework that establishes a formal connection between learning rate decay and model merging. WSM provides a unified theoretical foundation for emulating various decay strategies-including cosine decay, linear decay and inverse square root decay-as principled model averaging schemes, while remaining fully compatible with diverse optimization methods. Through extensive experiments, we identify merge duration-the training window for checkpoint aggregation-as the most critical factor influencing model performance, surpassing the importance of both checkpoint interval and merge quantity. Our framework consistently outperforms the widely-adopted Warmup-Stable-Decay (WSD) approach across multiple benchmarks, achieving significant improvements of +3.5% on MATH, +2.9% on HumanEval, and +5.5% on MMLU-Pro. The performance advantages extend to supervised fine-tuning scenarios, highlighting WSM's potential for long-term model refinement.

We study quantum state tomography when the unknown state lies in a trace-distance ball of radius R around a known reference state ρ. For arbitrary collective measurements, we determine the minimax expected risk and confidence radius up to universal constants, uniformly over the dimension, center spectrum, radius, and sample size. Write Γ=d(Trsqrtρ)^2+d^2R. For dge2, 0<Rle1, and nge1 copies, the expected risk is Θ(min{R,Γ/n}). At failure probability 0<δle1/3, the minimax confidence radius is \[ Θ\!\left(\min\left\{R,\frac{Γ+\log(1/δ){n}}\right\}\right). \] For varepsilonle c_0R with a universal c_0>0, the copy complexity is Θ((Γ+log(1/δ))/varepsilon^2). For the lower bound we use a weighted trace-norm witness to retain all spectral scales in a square-root perturbation family. For the upper bound, we give a direct spectral and concentration analysis of a modified existing purification-based procedure.

A longitudinal web crawl is a sequence of partial samples of an evolving URL population. Pairwise containment between two crawls is the standard probe; under a simple urn model of the crawl -- each round samples a fraction of the URLs and replaces a fraction -- it recovers two interpretable rates, per-round survival α and coverage c, but treats the population as uniform and consumes one pair at a time. In this work, we define a formal language for talking about a crawl. We extend this analysis with the discovery curve U(s, T), the cumulative URL footprint over a sliding window of T crawls starting at s, which under the same urn model is also a closed-form function of (α, c). Containment and the discovery curve are then two projections of one process: independent fits agree on (α, c) when the urn is homogeneous, so any disagreement is itself a measurement. Applied to Common Crawl (2020--2025, domain granularity) and to the German Academic Web (GAW, URL granularity), the two projections disagree on both archives, and a two-component urn with a persistent core fraction κ alongside shell parameters (α_partial, c_partial) reconciles the disagreement. A residual on c_partial remains, signaling that the shell itself is not homogeneous; κ is recorded as the scalar entry point to a rank-resolved generalization, which is left to follow-up work. web archive \and crawl coverage \and discovery curve \and urn model \and two-component model \and URL lifetime

In this paper, we suggest a novel method for detecting mortality deceleration. We focus on the gamma-Gompertz frailty model and suggest the subtraction of a penalty in the log-likelihood function as an alternative to traditional likelihood inference and hypothesis testing. Over existing methods, our method offers advantages, such as avoiding the use of a p-value, hypothesis testing, and asymptotic distributions. We evaluate the performance of our approach by comparing it with traditional likelihood inference on both simulated and real mortality data. Results have shown that our approach is more accurate in detecting mortality deceleration and provides more reliable estimates of the underlying parameters. The proposed method is a significant contribution to the literature as it offers a powerful tool for analyzing mortality patterns.

Tau leptons serve as an important tool for studying the production of Higgs and electroweak bosons, both within and beyond the Standard Model of particle physics. Accurate reconstruction and identification of hadronically decaying tau leptons is a crucial task for current and future high energy physics experiments. Given the advances in jet tagging, we demonstrate how tau lepton reconstruction can be decomposed into tau identification, kinematic reconstruction, and decay mode classification in a multi-task machine learning setup. Based on an electron-positron collision dataset with full detector simulation and reconstruction, we show that common jet tagging architectures can be effectively used for these sub-tasks. We achieve comparable momentum resolutions of 2-3% with all the tested models, while the precision of reconstructing individual decay modes is between 80-95%. We find ParticleTransformer to be the best-performing approach, significantly outperforming the heuristic baseline. This paper also serves as an introduction to a new publicly available Fuτure dataset for the development of tau reconstruction algorithms. This allows to further study the resilience of ML models to domain shifts and the efficient use of foundation models for such tasks.

Precision beta decay experiments serve as powerful probes of physics beyond the Standard Model, enabling stringent tests of fundamental symmetries of nature. In particular, these experiments primarily focus on precise determinations of the Cabibbo-Kobayashi-Maskawa matrix element Vud and the search for exotic weak currents, both of which depend critically on theoretical calculations of radiative, recoil-order, and isospin-breaking corrections with quantified uncertainties. In recent years, ab initio nuclear many-body methods--grounded in realistic nucleon-nucleon interactions and systematically improvable approximations--have advanced considerably in their ability to compute these higher-order corrections for various nuclei. This review provides a comprehensive overview of state-of-the-art ab initio calculations of beta-decay corrections, encompassing both radiative corrections and recoil-order terms, and examines their significance for precision tests of the Standard Model. We discuss the theoretical formalisms employed, including the integration of effective field theory frameworks with many-body approaches. Particular attention is given to recent results for superallowed Fermi decays (e.g., 10C -> 10B and 14O -> 14C) and allowed Gamow-Teller transitions (e.g., 6He -> 6Li, 8Li -> 8Be, 8B -> 8Be), where ab initio calculations have achieved unprecedented precision. We also highlight emerging calculations for unique forbidden decays, which offer complementary sensitivity to BSM physics. Finally, we outline future directions aimed at extending the reach of ab initio calculations to heavier nuclei and additional decay modes, thereby strengthening the synergy between theory and experiment in the ongoing search for new physics.

Open quantum systems lose energy and phase coherence through different dissipative processes, but these processes can produce overlapping dynamical signatures. The Liouvillian spectrum summarizes how such a system relaxes, yet it is not obvious how much of that spectrum is needed to distinguish the underlying dissipation rates. We study this question for amplitude damping and dephasing in a six-qubit Lindblad model whose spectrum can be derived analytically. We retain only the slowest non-steady spectral modes and ask how many are required before each dissipative rate becomes recoverable. We show that population modes contain no dephasing information, which creates a lower bound of D = 2^n retained modes for uniform dephasing identifiability in the relevant rate regime. The measured recovery threshold reaches this bound at n = 4,5,6, while n = 3 remains above it. At n = 6, least squares achieves a mean joint absolute error of order 10^-9, compared with 4.355 x 10^-4 for four tabular learning methods. Robustness tests show that this advantage weakens when the spectra are perturbed and when a transverse field breaks the commuting structure. These results show that the amount and structure of retained spectral information can determine whether dissipative parameters are recoverable, independently of the estimator used. The present conclusions apply to noise-free simulator spectra rather than measurement-derived spectra.

Benchmark contamination is diagnosed with n-gram overlap, likelihood-based membership inference, or canary strings, and each needs something usually unavailable: the training corpus, a well-chosen test statistic, or foresight at release. A recent alternative reads it off a linear probe on internal activations. We show the natural way to do this does not work, specify one that survives measurement, then find that the correction making it work carries more variance than the null it is tested against. The protocol reports a zero-sum contrast on the depth profile of probe accuracy, recentred on a level-matched placebo baseline, tested against a label-permutation null, with the reference set twice the size of the suspect set. Each choice replaces a simpler alternative we rejected on measurement. Reporting the level of excess separability rather than its shape makes the false positive rate track the size of the analyst's own control set, 0.03 to 0.99 under a true null. Contrasting against a flat depth profile rejects a true null 0.72 of the time when surface decodability rises with depth, and loses all power when it falls. On real transformers the protocol fails a test the simulations did not pose. The recentring subtracts an estimate, and the permutation null holds it fixed. Re-estimated across split seeds on four audits of contaminated checkpoints, its standard deviation is 1.30 to 1.56 times the null's own in every arm: what is subtracted to remove a bias is more variable than what it corrects. The one nominally significant result, p = 0.0075, becomes 0.0745 once that variance is propagated, and no verdict is issued. The simulations missed this because their surface key is the covariate driving item variation; on real text it is a proxy, and degrading key quality in simulation reproduces it. We add a companion measurement and a widened null. No arm shows contamination.

Weight decay is a broadly used technique for training state-of-the-art deep networks from image classification to large language models. Despite its widespread usage and being extensively studied in the classical literature, its role remains poorly understood for deep learning. In this work, we highlight that the role of weight decay in modern deep learning is different from its regularization effect studied in classical learning theory. For deep networks on vision tasks trained with multipass SGD, we show how weight decay modifies the optimization dynamics enhancing the ever-present implicit regularization of SGD via the loss stabilization mechanism. In contrast, for large language models trained with nearly one-epoch training, we describe how weight decay balances the bias-variance tradeoff in stochastic optimization leading to lower training loss and improved training stability. Overall, we present a unifying perspective from ResNets on vision tasks to LLMs: weight decay is never useful as an explicit regularizer but instead changes the training dynamics in a desirable way. The code is available at https://github.com/tml-epfl/why-weight-decay

We introduce Cautious Weight Decay (CWD), a one-line, optimizer-agnostic modification that applies weight decay only to parameter coordinates whose signs align with the optimizer update. Unlike standard decoupled decay, which implicitly optimizes a regularized or constrained objective, CWD preserves the original loss and admits a bilevel interpretation: it induces sliding-mode behavior upon reaching the stationary manifold, allowing it to search for locally Pareto-optimal stationary points of the unmodified objective. In practice, CWD is a drop-in change for optimizers such as AdamW, Lion, and Muon, requiring no new hyperparameters or additional tuning. For language model pre-training and ImageNet classification, CWD consistently improves final loss and accuracy at million- to billion-parameter scales.

One straightforward metric to evaluate a survival prediction model is based on the Mean Absolute Error (MAE) -- the average of the absolute difference between the time predicted by the model and the true event time, over all subjects. Unfortunately, this is challenging because, in practice, the test set includes (right) censored individuals, meaning we do not know when a censored individual actually experienced the event. In this paper, we explore various metrics to estimate MAE for survival datasets that include (many) censored individuals. Moreover, we introduce a novel and effective approach for generating realistic semi-synthetic survival datasets to facilitate the evaluation of metrics. Our findings, based on the analysis of the semi-synthetic datasets, reveal that our proposed metric (MAE using pseudo-observations) is able to rank models accurately based on their performance, and often closely matches the true MAE -- in particular, is better than several alternative methods.

A growing literature argues that progress in human longevity is slowing, and that this slowdown may signal an approaching biological limit to lifespan. The argument rests on visible flattening of cumulative life expectancy records, evaluated through linear regressions or through comparisons of average gains across decades. These summaries, however, provide only weak evidence for slowing improvements, because they cannot distinguish a true from an apparent slowdown. An apparent slowdown may arise due to periods of low variance around unchanged mean annual gains. Applying a Bayesian change-point framework to annual gains, both at the best-practice frontier and separately for each record-holding country, we find no evidence that the expected annual gain has changed across nearly two centuries, but strong evidence that its variance has moved through distinct historical regimes, with progress most regular in recent decades. The recent flattening is consistent with a low-variance regime and provides little evidence for a decline in the underlying mean pace of improvement. Claims that the best-practice frontier signals a biological ceiling should therefore not rest on the recent bend in the cumulative record alone. The frontier is better read as an empirical benchmark, the highest country-specific survival achieved under observed historical conditions.

Very recently, the two-photon decay width of the η_b meson was computed with lattice QCD methods. This decay has not yet been measured. The knowledge of this width allows for the calculation of the η_b production cross section through photon-photon interactions in ultra-peripheral PbPb collisions. In this work we present this calculation, which is the first application of the lattice result. Since UPCs are gaining an increasing attention of the heavy ion community, we take the opportunity to perform a comprehensive study of the different ways of defining ultra-peripheral collisions and of the different ways to treat the equivalent photon flux.

Age-specific mortality improvements are non-uniform, neither across ages nor across time. We propose a two-step procedure to estimate the rates of mortality improvement (RMI) in age-specific death rates (ASDR) at ages 85 and above for ten European countries from 1950 to 2019. In the first step, we smooth the raw death counts and estimate ASDR using four different methods: one parametric (gamma-Gompertz-Makeham), two non-parametric (P-splines and PCLM), and a novel Bayesian procedure to handle fluctuations resulting from ages with zero death counts. We compare the goodness of fit of the four smoothing methods and calculate the year-to-year ASDR differences according to the best-fitting one. We fit a piecewise linear function to these differences in the second step. The slope in each linear segment captures the average RMI in the respective year range. For each age, we calculate the goodness of fit in the last linear segment to assess how informative the estimated RMI of current mortality change is. The estimated rates of mortality improvement or deterioration (RMI) can be used to make short-term social, health, and social planning, as well as more precise mortality forecasts.

New light particles have received considerable attention in recent years. Baryon-number-violating (BNV) nucleon decays involving such light particles are able to provide stringent constraints. They exhibit distinctive experimental signatures that merit thorough investigation. We systematically investigate BNV nucleon decay with a light scalar in an effective field theory framework. Within this framework, we set stringent bounds on BNV operators using available experimental data and predict the occurrence of several BNV three-body nucleon decays. We further study contributions to dinucleon to dilepton transitions in a nucleus mediated by the scalar, which complements single nucleon decay. Finally, we provide three ultraviolet-complete models that can generate different subsets of BNV operators in leading order. Our theoretical framework will facilitate experimental searches for those exotic nucleon decays.

Massive activations, residual-stream coordinates with magnitudes far larger than typical activations, are associated with attention sinks in transformers, but how their scale is regulated during training remains incompletely understood. Combining training-trajectory analyses and controlled interventions, we trace their emergence, growth, and consolidation. Sink-carrying channels vary across random seeds but stabilize early within each run. Over longer training, surrounding channels erode and the sink concentrates onto a few redundant carriers. Across ablations, gradient attenuation follows the sink token's collective root-mean-square magnitude rather than any single channel, making collective scale central to understanding their effects. Our central result is that weight decay causally controls the turnover of global activation scale. In controlled continuations, removing decay near the peak allows this scale to keep rising, whereas retaining it produces decline even at constant learning rate. We develop a balance model for the rise and peak of massive-activation magnitude, in which AdamW-preconditioned growth opposes weight decay. Sweeping the decay coefficient λ shifts peak timing approximately log-linearly and yields peak magnitudes scaling approximately as λ^{-1/2}, consistent with this balance. Optimizer measurements further show that preconditioning sustains the large-channel cohort against decay even when raw maintaining forces are too small to do so. Together, these findings connect the observed life cycle to scale-regulating training dynamics and establish weight decay as a training-time lever on activation magnitude.

We study a spectral regularization of the Dean--Kawasaki equation and quantify how the failure of positivity preservation affects its weak approximation of the empirical measure of independent Brownian particles. For initial densities bounded away from zero, we prove a uniform-in-time weak error measured through the Laplace transform and prove a superpolynomial convergence rate for smooth test functions. When the initial density is allowed to vanish, the negative part of the regularized solution leads to weaker upper bounds, and a one-dimensional example gives a lower error bound ruling out superpolynomial convergence. We also present numerical experiments that confirm the theoretical results and illustrate main observations.

Accurate remaining useful life (RUL) prediction hinges on the quality of health indicators (HIs), yet existing methods often fail to disentangle complex degradation mechanisms in multi-sensor systems or quantify uncertainty in HI reliability. This paper introduces a novel framework for HI construction, advancing three key contributions. First, we adapt Reconstruction along Projected Pathways (RaPP) as a health indicator (HI) for RUL prediction for the first time, showing that it outperforms traditional reconstruction error metrics. Second, we show that augmenting RaPP-derived HIs with aleatoric and epistemic uncertainty quantification (UQ) via Monte Carlo dropout and probabilistic latent spaces- significantly improves RUL-prediction robustness. Third, and most critically, we propose indicator groups, a paradigm that isolates sensor subsets to model system-specific degradations, giving rise to our novel method, I-GLIDE which enables interpretable, mechanism-specific diagnostics. Evaluated on data sourced from aerospace and manufacturing systems, our approach achieves marked improvements in accuracy and generalizability compared to state-of-the-art HI methods while providing actionable insights into system failure pathways. This work bridges the gap between anomaly detection and prognostics, offering a principled framework for uncertainty-aware degradation modeling in complex systems.

We here propose a machine learning approach for monitoring particle detectors in real-time. The goal is to assess the compatibility of incoming experimental data with a reference dataset, characterising the data behaviour under normal circumstances, via a likelihood-ratio hypothesis test. The model is based on a modern implementation of kernel methods, nonparametric algorithms that can learn any continuous function given enough data. The resulting approach is efficient and agnostic to the type of anomaly that may be present in the data. Our study demonstrates the effectiveness of this strategy on multivariate data from drift tube chamber muon detectors.

Survival analysis is the problem of estimating probability distributions for future event times, which can be seen as a problem in uncertainty quantification. Although there are fundamental theories on strictly proper scoring rules for uncertainty quantification, little is known about those for survival analysis. In this paper, we investigate extensions of four major strictly proper scoring rules for survival analysis and we prove that these extensions are proper under certain conditions, which arise from the discretization of the estimation of probability distributions. We also compare the estimation performances of these extended scoring rules by using real datasets, and the extensions of the logarithmic score and the Brier score performed the best.

Belle II has reported a 2.7σ excess in B^+to K^+νbarν over its Standard Model prediction, recently interpreted as arising from an axion-like particle mediating a thermal dark matter candidate. We reassess this interpretation using a new mass-differential measurement of the same data set and adding two visible-decay searches that earlier analyses omitted. The resulting bounds leave the predictions from a standard cosmological history only marginally compatible with the excess, viable in a narrow window of parameter space. Thus, we consider a situation where dark matter freezes out during a low-temperature reheating era, featuring entropy injection diluting the relic abundance. This requires smaller couplings compared to those in standard cosmology in order to match the observed dark matter density, opening a region of parameter space where the compatibility of the model with the Belle II excess is significantly improved.

Exemplar methods separate a mixture by picking one learned spectrum per source and deforming it until it explains the observation, making one deformation class both reconstructor and selector. We show that the second role is empty as soon as the class can interpolate: the rule then ranks candidates on its regulariser, a choice made before the data, and the estimates sum back to the mixture whichever candidate wins. The condition is a parameter count, so the diagnosis runs before any experiment. On free per-bin deformation of complex spectra it explains the observed pathologies at once: a criterion that ranks candidates by their loudness, and half an output that is a mask on the mixture rather than an exemplar. The same theorem prescribes the repair, a selection class poorer than the reconstruction class: one complex gain and one pure delay rank the candidates, and a local combination of the best-aligned atoms, fitted jointly in closed form, rebuilds them. On MUSDB18 against the exact ceiling of the masking class, the distance between the criterion and an oracle inside its own candidate pool falls under the rigid selector from 6.2-7.7 to 0.5-2.8 dB, though only 0.9-1.2 dB of that reaches the output, and the per-frame latency of the deployed rule by a factor of 47 to 806. One lock remains, quantified: atoms are scored against the mixture, so the score carries a term for the other source that absorbs the capacity the reconstruction class gains, leaving the output 10.0 dB under the ceiling. Ranking hypotheses by the residual of a fit free enough to interpolate ranks them on the regulariser alone.

A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple hypothesis testing. However, there is a fundamental disconnect between the theoretical results and the practice of data analysis: the theory of statistical inference assumes a fixed collection of hypotheses to be tested, or learning algorithms to be applied, selected non-adaptively before the data are gathered, whereas in practice data is shared and reused with hypotheses and new analyses being generated on the basis of data exploration and the outcomes of previous analyses. In this work we initiate a principled study of how to guarantee the validity of statistical inference in adaptive data analysis. As an instance of this problem, we propose and investigate the question of estimating the expectations of m adaptively chosen functions on an unknown distribution given n random samples. We show that, surprisingly, there is a way to estimate an exponential in n number of expectations accurately even if the functions are chosen adaptively. This gives an exponential improvement over standard empirical estimators that are limited to a linear number of estimates. Our result follows from a general technique that counter-intuitively involves actively perturbing and coordinating the estimates, using techniques developed for privacy preservation. We give additional applications of this technique to our question.

Analyzing outcomes in long-term cancer survivor studies can be complex. The effects of predictors on the failure process may be difficult to assess over longer periods of time, as the commonly used assumption of proportionality of hazards holding over an extended period is often questionable. In this manuscript, we compare seven different survival models that estimate the hazard rate and the effects of proportional and non-proportional covariates. In particular, we focus on an extension of the the multi-resolution hazard (MRH) estimator, combining a non-proportional hierarchical MRH approach with a data-driven pruning algorithm that allows for computational efficiency and produces robust estimates even in times of few observed failures. Using data from a large-scale randomized prostate cancer clinical trial, we examine patterns of biochemical failure and estimate the time-varying effects of androgen deprivation therapy treatment and other covariates. We compare the impact of different modeling strategies and smoothness assumptions on the estimated treatment effect. Our results show that the benefits of treatment diminish over time, possibly with implications for future treatment protocols.

We study how the next-token prediction of an autoregressive Transformer language model changes under small perturbations of earlier input token embeddings. Motivated by operator learning and iterative solvers for differential equations, we investigate how the influence of one token on another decays with distance in a trained model. In multilevel methods for differential equations, such as domain decomposition, multigrid, and multilevel preconditioning, one often exploits a separation between strong local interactions and weaker but essential global interactions. The latter correspond to the long tail of the Green's function and are typically handled by a coarse-level operator. Inspired by this perspective, we compute an empirical, distance-resolved gradient profile of token dependencies using autograd. Experiments on trained Pythia models and Qwen2.5-0.5B show that, over the measured distance range, the median Jacobian sensitivity is much better described by a power-law-type decay than by an exponential alternative: the diagonal-normalized profile is well described by $overline G(r) approx γ+β(r+1)^{-p} with exponents p \approx 0.7--0.9 (typically 0.8--0.9$). This behavior appears on coherent text from Gutenberg and WikiText-103. Token-shuffling experiments show that the power-law profile persists even when syntax and prediction quality collapse, whereas randomly initialized models do not exhibit it. The slowly decaying long-range sensitivity thus appears to be a learned property of trained autoregressive Transformer operators. These findings suggest that hierarchical or coarse-level mechanisms in language models may be able to exploit the long-tailed sensitivity profiles.

Test data from public benchmarks inevitably leaks into pretraining corpora, inflating evaluation scores once memorized. Contamination mitigation evaluation intervenes in the decoding process to suppress memorization and restore a contaminated model's genuine capability, but its prevailing metric, the G-AP (Gap of Aggregate Performance), is flawed. Discrete correct/incorrect readouts cannot characterize per-question performance, averaging before differencing lets over- and under-suppression cancel out, and uniform per-question weighting invites strategies to push solve probabilities onto the clean model's high-frequency values. We propose SA-PPG (Stratified Aggregate of Per-question Probability Gaps): estimate each question's solve probability by sampling, difference it against the clean model per question, and aggregate within groups defined by the clean model's solve probability. Existing mitigation strategies first estimate where contamination lies and then operate on the estimate, so they are only as correct as the estimate. RailCap instead judges contamination during generation: whenever a sample falls back onto the greedy trajectory, the next trajectory token is capped to the runner-up, accumulating suppression until the response distribution becomes sufficiently dispersed. Across multiple contaminated models and benchmarks, SA-PPG reveals that prior strategies' restoration is substantially overestimated, while RailCap attains the lowest SA-PPG.

We derive bounds on the lifetime of an evaporating black hole. The bound follows from energy conservation and purification, within the framework of `asymptotically semiclassical spacetimes'. We use the recently derived expression for the Bondi flux of Hawking radiation, together with the expression for the entanglement entropy of Hawking radiation at null infinity, to investigate the purification phase after the last semiclassical ray. We discuss the energy-cost of entanglement purification and we find a lower bound on the purification time of the black hole, which scales as M_0^4/hbar^{3/2}, where M_0 is the initial black hole mass. Additionally, motivated by quantum gravity considerations, we include the additional assumption that a Planck mass black hole is metastable. With this assumption, we find that the the purification time is extended to be exponential in the square of the initial black hole mass, i.e. in its initial area. We find that the redshift exponent is negative in this purification phase, which indicates the existence of a white-hole remnant which releases information slowly. We comment on phenomenological implications for primordial black hole remnants.

Statistical data fusion combines two panels that share a block of covariates but observe disjoint outcome blocks, and in its traditional form no row observes both outcomes at once. That rules out the discriminative criterion one would rather train a Deep Boltzmann Machine with, since multi-prediction training needs ground truth for whatever it holds out. We propose observed-block multi-prediction, which restricts the multi-prediction objective to targets drawn from what each row actually observes. It is well defined for any missingness pattern and reduces to the original criterion when rows are complete. Having a discriminative criterion that survives the setting lets us ask whether the joint model is needed at all, by separating what it contributes into a representation part and an inference part. On two consumer panels, on grids over sample size and covariate width spanning 35 cells and 875 runs, the fine-tuned DBM is the best of fifteen methods in every cell; but almost none of that advantage comes from generative pre-training, which is confined to the smallest sample size on one dataset and absent on the other. It comes from conditioning on one outcome block when predicting the other. This term amounts to +0.19 and +0.07 percentage points, is positive in all 35 cells, and, unlike every other contribution we measure, neither decays as the panels grow, nor requires a second hidden layer, nor requires more inference. Permuting one outcome block to destroy its association with the other removes the gain entirely, which is what the account predicts. The margins are small. But a small effect that does not decay is a different object from one that does, because it rests on evidence that no model mapping covariates to outcomes can accept.

In the era of mega-constellations, the need for accurate and publicly available information has become fundamental for satellite operators to guarantee the safety of spacecrafts and the Low Earth Orbit (LEO) space environment. This study critically evaluates the accuracy and reliability of publicly available ephemeris data for a LEO mega-constellation - Starlink. The goal of this work is twofold: (i) compare and analyze the quality of the data against high-precision numerical propagation. (ii) Leverage Physics-Informed Machine Learning to extract relevant satellite quantities, such as non-conservative forces, during the decay process. By analyzing two months of real orbital data for approximately 1500 Starlink satellites, we identify discrepancies between high precision numerical algorithms and the published ephemerides, recognizing the use of simplified dynamics at fixed thresholds, planned maneuvers, and limitations in uncertainty propagations. Furthermore, we compare data obtained from multiple sources to track and analyze deorbiting satellites over the same period. Empirically, we extract the acceleration profile of satellites during deorbiting and provide insights relating to the effects of non-conservative forces during reentry. For non-deorbiting satellites, the position Root Mean Square Error (RMSE) was approximately 300 m, while for deorbiting satellites it increased to about 600 m. Through this in-depth analysis, we highlight potential limitations in publicly available data for accurate and robust Space Situational Awareness (SSA), and importantly, we propose a data-driven model of satellite decay in mega-constellations.

We study nonparametric density estimation in non-stationary drift settings. Given a sequence of independent samples taken from a distribution that gradually changes in time, the goal is to compute the best estimate for the current distribution. We prove tight minimax risk bounds for both discrete and continuous smooth densities, where the minimum is over all possible estimates and the maximum is over all possible distributions that satisfy the drift constraints. Our technique handles a broad class of drift models, and generalizes previous results on agnostic learning under drift.

This paper presents the first numerical realization of Suzuki's Weil-Quadratic-Form operator, a candidate for the Hilbert--Pólya program linking spectral positivity to the Riemann Hypothesis (RH). Suzuki's 2026 construction was purely theoretical; here, the operator is instantiated via P1 finite-element discretization and Richardson extrapolation. Key results include: (R1) In the prime-free regime, the spectrum follows a closed Archimedean law A_k(a) = log(1/a) + log(k-2) + B_0 + O(a), with B_0 = log q - 2log 2, confirmed to 30-digit precision. (R2) A Mellin double-pole argument proves the head coefficient B(ν) and shows B_0 depends only on the conductor q, independent of the Archimedean parameter. (R2b) The degree d of an L-function appears directly as the logarithmic slope of the spectrum. (R3) Total spectral intensity follows the prime number theorem, S(a) sim (2a)^3/6. (R4) Nontrivial zeros are not eigenvalues but occur in the explicit-formula error term of the prime symbol. (R5) The best-match line σ^*(a) descends toward the critical line. (R6) Weil's positivity criterion is realized in operator form: bounded residual growth corresponds to all zeros on the line, while an injected off-line zero causes exponential blow-up. (R7) The lowest eigenvalue λ_1(a) is strictly positive, decays superexponentially, and passes smoothly through the first prime threshold. (R8) The characteristic function W(a,0;z) is computed for the first time, with all zeros confirmed real. (R9) Indirect traces of GUE statistics appear in the moment structure, even where direct detection is blocked. The authors emphasize that this work does not prove RH. All results are Archimedean and universal, with significance lying in the faithful numerical realization of classical identities rather than new arithmetic.

We investigate the stability of superconducting strings as bound states of strings and fermion zero modes at both the classical and quantum levels. The dynamics of these superconducting strings can result in a stable configuration, known as a vorton. We mainly focus on global strings, but the majority of the discussion can be applied to local strings. Using lattice simulations, we study the classical dynamics of superconducting strings and confirm that they relax to the vorton configuration through Nambu-Goldstone boson radiation, with no evidence of over-shooting that would destabilize the vorton. We explore the tunneling of fermion zero modes out of the strings. Both our classical analysis and quantum calculations yield consistent results: the maximum energy of the zero mode significantly exceeds the fermion mass, in contrast to previous literature. Additionally, we introduce a world-sheet formalism to evaluate the decay rate of zero modes into other particles, which constitute the dominant decay channel. We also identify additional processes that trigger zero-mode decay due to non-adiabatic changes of the string configuration. In these decay processes, the rates are suppressed by the curvature of string loops, with exponential suppression for large masses of the final states. We further study the scattering with light charged particles surrounding the string core produced by the zero-mode current and find that a wide zero-mode wavefunction can enhance vorton stability.

In this paper, we study multidimensional perturbations of radially symmetric rarefactive flows for the compressible Euler equations. No assumptions on the smallness of the background are imposed. We derive lower bounds on both the classical lifespan and stability timespan of the perturbed solution. These lower bounds are demonstrated to tend to infinity as the size of the perturbation approaches zero. Furthermore, owing to the rarefactive nature of the background, the resulting estimate is shown to be substantially longer than the corresponding estimate for a general classical background with bounded first derivatives.

In location estimation, we are given n samples from a known distribution f shifted by an unknown translation lambda, and want to estimate lambda as precisely as possible. Asymptotically, the maximum likelihood estimate achieves the Cram\'er-Rao bound of error mathcal N(0, 1{nmathcal I}), where mathcal I is the Fisher information of f. However, the n required for convergence depends on f, and may be arbitrarily large. We build on the theory using smoothed estimators to bound the error for finite n in terms of mathcal I_r, the Fisher information of the r-smoothed distribution. As n to infty, r to 0 at an explicit rate and this converges to the Cram\'er-Rao bound. We (1) improve the prior work for 1-dimensional f to converge for constant failure probability in addition to high probability, and (2) extend the theory to high-dimensional distributions. In the process, we prove a new bound on the norm of a high-dimensional random variable whose 1-dimensional projections are subgamma, which may be of independent interest.

Capability evaluation of large language models (LLMs) is increasingly shadowed by rising concerns of data contamination that cast doubts on whether static benchmarks measure genuine reasoning or mere memorization. We present an empirical study using an infinitely scalable framework to synthesize research-level QA directly from arXiv papers, harnessing the natural temporal structure of research publications where performance decay after knowledge cutoffs may indicate potential contamination. We evaluated 4 frontier model represented by 2 models of different knowledge cutoff dates per family on 1,643 multi-step reasoning questions synthesized from 20,277 arXiv papers stratified over 26 months, covering at least 6 months before and after all cutoff dates. Our results consistently showed a lack of significant performance decay near knowledge cutoff dates for models of various sizes, developers, and release dates. We further performed a comparative analysis with previous longitudinal studies that reported significant post-cutoff performance decay using directly retrieved questions based on public data. we hypothesize that the multi-step reasoning required by our synthesis pipeline offered additional complexity that goes deeper than shallow memorization, which effectively serves a mitigation strategy against benchmark contamination. We fully open source our code and dataset to aid reproducibility and advocate for a paradigm shift that prioritize reasoning-driven synthesis to construct benchmarks over simply collecting newly released questions periodically.

A Mamba state-space model trained only for next-step prediction appears to recover Granger-causal structure through a simple readout S = |W_{out} W_{in}|, with early experiments suggesting the phenomenon generalized across architectures and benefited from interventional data at p < 10^{-5}. We package the protocol used to test that claim -- standardized synthetic generators (VAR/Lorenz/CauseMe-style), three intervention semantics (do(X=c), soft-noise, random-forcing), edge-provenance cards on three real datasets, and size-matched control arms -- as a reusable falsification benchmark, and walk the claim through it in five stages. The method-level claim does not survive: (i) a plain linear bottleneck does as well or better; (ii) tuned Lasso beats the bottleneck on synthetic CauseMe-style benchmarks, and on Lorenz-96 (the only real benchmark with unambiguous ground truth) classical PCMCI and Granger lead a tight cluster in which the bottleneck trails; (iii) the headline intervention advantage is roughly 60% a sample-size confound, and the residual disappears under standard do(X=c) interventions, surviving only under a non-standard random-forcing scheme; (iv) even that residual reproduces, with a larger effect, in classical bivariate Granger -- the effect is method-agnostic. What survives is a narrow characterization result; the benchmark is the lasting artifact, and each stage above is one of its control arms.

The decays of pseudoscalar mesons to real and virtual photons as well as neutrino-antineutrino pairs are considered in the framework of the dispersive method based on Anomaly Sum Rules. The contribution of singlet channel involving the new non-perturbative gluon form factor of virtual photon B(q^2) is systematically taken into account. The detailed analysis of its dependence on photon virtuality q^2 relying on the available data for meson transition fomfactors is performed. It is shown that B has quite a nontrivial structure at q^2 sim 1 GeV^2 which may be a signal of the existence of pseudoscalar glueball with a mass about 1.5-2 GeV. The calculation of the decay to νbar ν pairs leads to the compatibility with the result of Arnellos, Marciano and Parsa of 1982, when pion decay is considered neglecting the mixing effects. The account for these effects results, however, in the enhancement of pion branching ratio by a factor of 3, while that for eta decay is larger by several orders of magnitude. It is stressed, that dependence on the pair invariant mass is entirely defined by QCD and coincides with that of the meson transition form factor. The role of obtained results for the physics at HHaS detector at HIAF is discussed.

Adaptive optimizers with decoupled weight decay, such as AdamW, are the de facto standard for pre-training large transformer-based generative models. Yet the quadratic nature of the ell_2 penalty embedded in weight decay drives all parameters toward the origin at the same rate, making the update vulnerable to rare but extreme gradient directions and often over-penalizing well-conditioned coordinates. We propose AdamHuberDecay, a drop-in replacement for AdamW that substitutes the ell_2 penalty with a decoupled smooth Huber regularizer. The resulting update decays parameters quadratically while their magnitude remains below a threshold δ, and linearly (ell_1-like) once they exceed δ, yielding (i) bounded regularization gradients, (ii) invariance to per-coordinate second-moment rescaling, and (iii) stronger sparsity pressure on overgrown weights. We derive the closed-form decoupled Huber decay step and show how to integrate it with any Adam-family optimizer at O(1) extra cost. Extensive experiments on GPT-2 and GPT-3 pre-training demonstrate that AdamHuberDecay (a) converges 10-15% faster in wall-clock time, (b) reduces validation perplexity by up to 4 points, (c) delivers performance improvements of 2.5-4.7% across downstream tasks, and (d) yields visibly sparser weight histograms that translate into 20-30% memory savings after magnitude pruning, without tuning the decay coefficient beyond the default grid used for AdamW. Ablations confirm robustness to outlier gradients and large-batch regimes, together with theoretical analyses that bound the expected parameter norm under noisy updates. AdamHuberDecay therefore provides a simple, principled path toward more efficient and resilient training of next-generation foundational generative transformers.

The Muon optimizer has rapidly emerged as a powerful, geometry-aware alternative to AdamW, demonstrating strong performance in large-scale training of neural networks. However, a critical theory-practice disconnect exists: Muon's efficiency relies on fast, approximate orthogonalization, yet all prior theoretical work analyzes an idealized, computationally intractable version assuming exact SVD-based updates. This work moves beyond the ideal by providing the first analysis of the inexact orthogonalized update at Muon's core. We develop our analysis within the general framework of Linear Minimization Oracle (LMO)-based optimization, introducing a realistic additive error model to capture the inexactness of practical approximation schemes. Our analysis yields explicit bounds that quantify performance degradation as a function of the LMO inexactness/error. We reveal a fundamental coupling between this inexactness and the optimal step size and momentum: lower oracle precision requires a smaller step size but larger momentum parameter. These findings elevate the approximation procedure (e.g., the number of Newton-Schulz steps) from an implementation detail to a critical parameter that must be co-tuned with the learning schedule. NanoGPT experiments directly confirm the predicted coupling, with optimal learning rates clearly shifting as approximation precision changes.

Applying weight decay (WD) to matrix layers is standard practice in large-language-model pretraining. Prior work suggests that stochastic gradient noise induces a Brownian-like expansion of the weight matrices W, whose growth is counteracted by WD, leading to a WD-noise equilibrium with a certain weight norm ||W||. In this work, we view the equilibrium norm as a harmful artifact of the training procedure, and address it by introducing learnable multipliers to learn the optimal scale. First, we attach a learnable scalar multiplier to W and confirm that the WD-noise equilibrium norm is suboptimal: the learned scale adapts to data and improves performance. We then argue that individual row and column norms are similarly constrained, and free their scale by introducing learnable per-row and per-column multipliers. Our method can be viewed as a learnable, more expressive generalization of muP multipliers. It outperforms a well-tuned muP baseline, reduces the computational overhead of multiplier tuning, and surfaces practical questions such as forward-pass symmetries and the width-scaling of the learned multipliers. Finally, we validate learnable multipliers with both Adam and Muon optimizers, where it shows improvement in downstream evaluations matching the improvement of the switching from Adam to Muon.

One-proton emission is a direct probe of nuclear structure near the proton drip line and plays a critical role in understanding exotic decay modes and nucleosynthesis processes. In this study, we investigate the half-lives of one-proton emitters for 71 leq Z leq 83 odd-Z nuclei by employing the WKB approximation with nuclear potentials obtained from the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) and, for comparison, the relativistic continuum Hartree-Bogoliubov theory (RCHB). We first compare the calculated half-lives with available experimental data. The inclusion of quadrupole deformation via the DRHBc hardly contributes to improving the predictions of half-lives for the deformed nuclei. We find that all the studied nuclei exhibit ground states with |β_{2,{rm DRHBc}}| < 0.15, and within this limited deformation range the spectroscopic factor provides the dominant contribution to the half-life, compared to the decay width. In particular, for nuclei exhibiting shape coexistence in DRHBc, such as ^{170}Au, where the half-life varies significantly with the quadrupole deformation through its effect on the spectroscopic factor, we expect shape coexistence to exert a substantial influence on the variation of half-lives. Finally, we discuss the half-lives in consideration of shape coexistence. Our results indicate that the calculated half-life is governed not by the total-energy difference between coexisting minima but rather by the spectroscopic factor influenced by the deformation.

The decay of metastable 'false vacuum' states via bubble nucleation plays a crucial role in many cosmological scenarios. Cold-atom analog experiments will soon provide the first empirical probes of this process, with potentially far-reaching implications for early-Universe cosmology and high-energy physics. However, an inevitable difference between these analog systems and the early Universe is that the former have a boundary. We show, using a combination of Euclidean calculations and real-time lattice simulations, that these boundaries generically cause rapid bubble nucleation on the edge of the experiment, obscuring the bulk nucleation that is relevant for cosmology. We demonstrate that implementing a high-density 'trench' region at the boundary completely eliminates this problem, and recovers the desired cosmological behavior. Our findings are relevant for ongoing efforts to probe vacuum decay in the laboratory, providing a practical solution to a key experimental obstacle.

Decentralized reputation schemes present a promising area of experimentation in blockchain applications. These solutions aim to overcome the shortcomings of simple monetary incentive mechanisms of naive tokenomics. However, there is a significant research gap regarding the limitations and benefits of such solutions. We formulate these trade-offs as a conjecture on the irreconcilability of three desirable properties of the reputation system in this context. Such a system can not be simultaneously generalizable, trustless, and Sybil resistant. To handle the limitations of this trilemma, we propose MeritRank: Sybil tolerant feedback aggregation mechanism for reputation. Instead of preventing Sybil attacks, our approach successfully bounds the benefits of these attacks. Using a dataset of participants' interactions in MakerDAO, we run experiments to demonstrate Sybil tolerance of MeritRank. Decay parameters of reputation in MeritRank: transitivity decay and connectivity decay, allow for a fine-tuning of desirable levels of reputation utility and Sybil tolerance in different use contexts.

In many application domains (e.g., recommender systems, intelligent tutoring systems), the rewards associated to the actions tend to decrease over time. This decay is either caused by the actions executed in the past (e.g., a user may get bored when songs of the same genre are recommended over and over) or by an external factor (e.g., content becomes outdated). These two situations can be modeled as specific instances of the rested and restless bandit settings, where arms are rotting (i.e., their value decrease over time). These problems were thought to be significantly different, since Levine et al. (2017) showed that state-of-the-art algorithms for restless bandit perform poorly in the rested rotting setting. In this paper, we introduce a novel algorithm, Rotting Adaptive Window UCB (RAW-UCB), that achieves near-optimal regret in both rotting rested and restless bandit, without any prior knowledge of the setting (rested or restless) and the type of non-stationarity (e.g., piece-wise constant, bounded variation). This is in striking contrast with previous negative results showing that no algorithm can achieve similar results as soon as rewards are allowed to increase. We confirm our theoretical findings on a number of synthetic and dataset-based experiments.

In the BCS theory of superconductivity the amplitude (Higgs) mode is degenerate with the pair-breaking threshold: its frequency coincides with 2Δ, so it is an edge singularity rather than a true collective mode. This is why after a sudden weak perturbation at t=0 its oscillations decay algebraically as 1/t. We show that the retardation effects due to the phonon dynamics in the strong-coupling theory lift this degeneracy. The Higgs mode detaches from the pair-breaking edge 2Δ_g, set by the spectral gap, and becomes a sharp subgap excitation. We determine its frequency from the longitudinal pair susceptibility evaluated directly on the real frequency axis, using the Eilenberger equations for Migdal--Eliashberg theory with the Einstein phonon spectrum. The response of the mass renormalization supplies at least two fifths of the displacement, and possibly all of it: with it switched off, the binding falls below the resolution of the calculation. Its consequences, however, are significant because a percent-level shift transfers about a quarter of the spectral weight of the amplitude channel out of the two-quasiparticle continuum into a discrete energy level. What experiment sees is therefore not the displacement itself but its consequence: amplitude oscillations that persist instead of decaying as 1/t.

Whether a language model has improved itself is increasingly judged not by mean accuracy but by which individual problems it gains and loses. Tracking these transitions means differencing two noisy estimates, leaving them vulnerable to measurement artifacts. Auditing three rounds of rank-32 LoRA self-training on Qwen3-8B against a frozen control pushed through the identical pipeline, we identify seven measurement failures, each of which inverts a reported finding when its control is absent. Several are standard practice. A ledger built on a single greedy decode manufactures capability changes on an untrained model, largely an artifact of inference batching; the expansion statistic separating acquisition from sharpening assigns that same model a rate of 0.280. The natural threshold repair does not survive replication: estimated across the frozen comparisons such a design already contains, its null stays non-zero. We replace it with a per-problem exact test against a pooled baseline under false-discovery-rate control, which detects nothing on any held-out replicate and is unchanged under the multiple-testing rule, error rate and pool size. Applied to a ladder of arms matched in stream, volume and evaluation, the audit finds that external distillation improves problems the base model rarely reaches while three forms of self-training do not; a regression rejects this asymmetry as a by-product of distillation's larger overall gain (p < 10^{-8}). On the far smaller set of problems the base model never reaches, the evidence is inconclusive, while self-training corrupts problems solved at baseline at rates well above the measured floor. Transition-level auditing therefore requires a separately measured null for every statistic it reports: nulls that cost no new experiments, built from baseline replicates a multi-arm study already owns, though not from as few as most possess.

We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. Several recent works have analyzed stochastic samplers using tools like Girsanov's theorem and a chain rule variant of the interpolation argument. Unfortunately, these techniques give vacuous bounds when applied to deterministic samplers. We give a new operational interpretation for deterministic sampling by showing that one step along the probability flow ODE can be expressed as two steps: 1) a restoration step that runs gradient ascent on the conditional log-likelihood at some infinitesimally previous time, and 2) a degradation step that runs the forward process using noise pointing back towards the current iterate. This perspective allows us to extend denoising diffusion implicit models to general, non-linear forward processes. We then develop the first polynomial convergence bounds for these samplers under mild conditions on the data distribution.

Continual learning treats degradation on previously seen data as evidence of failure, a convention inherited from settings with a stationary prediction target, where a correct label remains correct indefinitely. World models do not satisfy this condition. Their prediction target is the environment, which changes, so knowledge that was accurate when acquired may later become false, and discarding it is required behavior rather than a defect. Non-stationary ground truth is well studied in the concept drift literature and in the temporal factuality of language models, but has not been formulated for world models, which are distinctive in that they also encode knowledge that must never be revised. We argue that continual world models require retention stratified by invariance timescale, separating invariants such as physics and object permanence, which must never be revised, from instance-level facts that should be revised as soon as the environment changes. Standard forgetting metrics cannot distinguish a world model that has correctly revised outdated knowledge from one that has suffered catastrophic forgetting, and consequently rank a frozen model highest, while existing physical-reasoning benchmarks evaluate only frozen checkpoints. We propose differential retention, which reports invariant regression testing across the adaptation stream jointly with revision latency, without aggregation.

Positronium is the simplest bound state, built of an electron and a positron. Studies of positronium in vacuum and its decays in medium tell us about Quantum Electrodynamics, QED, and about the structure of matter and biological processes of living organisms at the nanoscale, respectively. Spectroscopic measurements constrain our understanding of QED bound state theory. Searches for rare decays and measurements of the effect of gravitation on positronium are used to look for new physics phenomena. In biological materials positronium decays are sensitive to the inter- and intra-molecular structure and to the metabolism of living organisms ranging from single cells to human beings. This leads to new ideas of positronium imaging in medicine using the fact that during positron emission tomography (PET) as much as 40% of positron annihilation occurs through the production of positronium atoms inside the patient's body. A new generation of the high sensitivity and multi-photon total-body PET systems opens perspectives for clinical applications of positronium as a biomarker of tissue pathology and the degree of tissue oxidation.

LLMs are commonly trained with a learning rate (LR) warmup, followed by cosine decay to 10% of the maximum (10x decay). In a large-scale empirical study, we show that under an optimal peak LR, a simple linear decay-to-zero (D2Z) schedule consistently outperforms other schedules when training at compute-optimal dataset sizes. D2Z is superior across a range of model sizes, batch sizes, datasets, and vocabularies. Benefits increase as dataset size increases. Leveraging a novel interpretation of AdamW as an exponential moving average of weight updates, we show how linear D2Z optimally balances the demands of early training (moving away from initial conditions) and late training (averaging over more updates in order to mitigate gradient noise). In experiments, a 610M-parameter model trained for 80 tokens-per-parameter (TPP) using D2Z achieves lower loss than when trained for 200 TPP using 10x decay, corresponding to an astonishing 60% compute savings. Models such as Llama2-7B, trained for 286 TPP with 10x decay, could likely have saved a majority of compute by training with D2Z.

In this paper we introduce the concept of what we call "NUDAR" (NeUtrino Direction and Ranging), making the point that measurements of the observed energy and direction vectors can be employed to passively deduce the exact three-dimensional location and thermal power of geophysical and anthropogenic neutrino sources from even a single detector. We present the most precise background estimates to date, all handled in full three dimensions, as functions of depth and geographical location. For the present calculations, we consider a hypothetical 138 kiloton detector which can be transported to an ocean site and deployed to an operational depth. We present a Bayesian estimation framework to incorporate any a priori knowledge of the reactor that we are trying to detect, as well as the estimated uncertainty in the background and the oscillation parameters. Most importantly, we fully employ the knowledge of the reactor spectrum and the distance-dependent effects of neutrino oscillations on such spectra. The latter, in particular, makes possible determination of range from one location, given adequate signal statistics. Further, we explore the rich potential of improving detection with even modest improvements in individual neutrino direction determination. We conclude that a 300 MWth reactor can indeed be geolocated, and its operating power estimated with one or two detectors in the hundred kiloton class at ranges out to a few hundred kilometers. We note that such detectors would have natural and non-interfering utility for scientific studies of geo-neutrinos, neutrino oscillations, and astrophysical neutrinos. This motivates the development of cost effective methods of constructing and deploying such next generation detectors.

In the era of proliferation of large language and image generation models, the phenomenon of "model collapse" refers to the situation whereby as a model is trained recursively on data generated from previous generations of itself over time, its performance degrades until the model eventually becomes completely useless, i.e the model collapses. In this work, we study this phenomenon in the setting of high-dimensional regression and obtain analytic formulae which quantitatively outline this phenomenon in a broad range of regimes. In the special case of polynomial decaying spectral and source conditions, we obtain modified scaling laws which exhibit new crossover phenomena from fast to slow rates. We also propose a simple strategy based on adaptive regularization to mitigate model collapse. Our theoretical results are validated with experiments.

L_2 regularization and weight decay regularization are equivalent for standard stochastic gradient descent (when rescaled by the learning rate), but as we demonstrate this is not the case for adaptive gradient algorithms, such as Adam. While common implementations of these algorithms employ L_2 regularization (often calling it "weight decay" in what may be misleading due to the inequivalence we expose), we propose a simple modification to recover the original formulation of weight decay regularization by decoupling the weight decay from the optimization steps taken w.r.t. the loss function. We provide empirical evidence that our proposed modification (i) decouples the optimal choice of weight decay factor from the setting of the learning rate for both standard SGD and Adam and (ii) substantially improves Adam's generalization performance, allowing it to compete with SGD with momentum on image classification datasets (on which it was previously typically outperformed by the latter). Our proposed decoupled weight decay has already been adopted by many researchers, and the community has implemented it in TensorFlow and PyTorch; the complete source code for our experiments is available at https://github.com/loshchil/AdamW-and-SGDW

I examine some analytical properties of a nonlinear reaction-diffusion system that has been used to model the propagation of a wildfire. I establish global-in-time existence and uniqueness of bounded mild solutions to the Cauchy problem for this system given bounded initial data. In particular, this shows that the model does not allow for thermal blow-up. If the initial temperature and fuel density also satisfy certain integrability conditions, the L^2-norms of these global solutions are uniformly bounded in time. Additionally, I use a bootstrap argument to show that small initial temperatures give rise to solutions that decay to zero as time goes to infinity, proving the existence of initial states that do not develop into travelling combustion waves.

Longitudinal observational data are often subject to informative missingness. For example, in healthcare research using electronic health records, covariates and outcomes are measured only when patients interact with the healthcare system. Whether these data are observed usually depends on the unobserved variable values themselves, introducing a common form of data missing not at random. We develop identification and estimation methods for the effects of longitudinal modified treatment policies under a self-censoring model which explicitly models this dependence. We consider effects of treatments that can be modified only at measurement times (e.g., interactions with the heathcare system). We study two settings: one in which the observed history suffices for treatment confounding control, and another in which confounder control requires covariate values that were not measured at missed visits. In both settings, we combine longitudinal causal identification with shadow-variable conditional moment restrictions to obtain recursive identification formulas for the counterfactual outcome mean. We derive gradients of the pathwise derivatives and second-order remainder expansions, and use these results to construct estimators that accommodate machine learning for nuisance-function estimation. Under suitable product-rate conditions and cross-fitting, the estimators are asymptotically linear and permit root-n inference, including simultaneous inference across outcome times. We also describe conditional-moment learning and ensemble approaches for estimating the nuisance functions required by our approach, together with a pool-and-smooth strategy that borrows information across sparsely measured outcomes.

We reanalyze the spectral lag data for GRB 160625B using frequentist inference in order to constrain the energy scale (E_{QG}) of Lorentz Invariance Violation (LIV). For this purpose, we use profile likelihood to deal with the astrophysical nuisance parameters. This is in contrast to Bayesian inference implemented in previous works, where marginalization was carried out over the nuisance parameters. We show that with profile likelihood, we do not find a global minimum for chi^2 as a function of E_{QG} below the Planck scale for both linear and quadratic models of LIV, whereas bounded credible intervals were previously obtained using Bayesian inference. Therefore, we can set one-sided lower limits in a straightforward manner. We find that E_{QG} geq 2.55 times 10^{16} GeV and E_{QG} geq 1.85 times 10^7 GeV at 95\% c.l., for linear and quadratic LIV, respectively. Therefore, this is the first proof-of-principles application of profile likelihood method to the analysis of GRB spectral lag data to constrain LIV.

The Laser Interferometer Space Antenna (LISA) will enable precision studies of Extreme and Intermediate Mass Ratio Inspirals (EMRIs/IMRIs), providing unique probes of astrophysical environments of galactic nuclei and strong-field gravity. Using a fully relativistic pipeline across primary masses m_1 in [5times10^4, 10^7],M_odot and secondary masses m_2 in [1, 10^4],M_odot, we map instrumental performance directly to detection horizons and parameter measurement precision. EMRIs with m_1 = 10^7,M_odot and m_2 sim 1,M_odot are the most sensitive to instrument degradation, with redshift horizons at z sim 0.01, while IMRIs are the least sensitive to degradation and reach redshifts z sim 1-3. All prograde systems considered achieve sub-percent spin precision within three months of observation. The full 4.5-year mission increases the horizon of systems with m_1 = 10^7,M_odot and m_2 sim 1,M_odot by a factor of sim 4 and improves sky localization by one to two orders of magnitude reaching < 10,deg^2. IMRI detection is robust against degradation, but their parameter estimation is more vulnerable due to fewer cycles in band. With the full baseline, EMRI observations constrain scalar dipole emission and Kerr quadrupole deviations below ground-based bounds by one to two orders of magnitude. We release the accompanying software and an interactive website to enable the community to rapidly quantify the scientific potential of EMRIs and IMRIs.

We propose a novel method to probe the persistent hints of Lepton Flavour Universality violation observed in semileptonic B decays. Relying on the specific properties of the Belle II experiment, it consists in comparing the inclusive rates of Υ(4S) to e^pm μ^mp X, Υ(4S) to μ^pm τ_{rm had}^mp X and Υ(4S) to e^pm τ_{rm had}^mp X. We show that such a measurement can be directly related to the ratio R(X)_{τell} equiv Γ(bto X τν) / Γ(b to X ell ν) (ell=e or μ), once appropriate experimental cuts are applied to suppress the effects of neutral B mixing and leptons emitted through charm or tau decays. Such a measurement would thus constitute an additional and potentially competitive probe of Lepton Flavour Universality in bto cellν transitions, complementary to existing exclusive measurements, accessible in the Belle II environment.

Practitioners make three prompt-design decisions with almost no controlled evidence behind them: how to format instructions and context (markdown, plain text, prose, or tabular), how many simultaneous instructions a system prompt can carry before compliance degrades, and how much context a model can hold before recall and honesty degrade. We report two controlled experiments crossing all three factors on one held, contamination-free synthetic corpus (the "Book of Veyra," 8,780 uniquely-named entities, deterministically regenerable from a fixed seed), evaluated across five models. Experiment 1 (960 calls/model) measures instruction-following decay as rule count N grows from 10 to 160, crossed with four formats and system-prompt vs. user-turn placement. Perfect-response rate collapses to zero by N=80 for every model, format, and placement. Placement produces effects at least as large as format at N=160 in most models, but the direction is model-specific. No model shows a reliable markdown advantage; one 35B model favors plain text instead. Experiment 2 (5,520 calls/model) measures recall accuracy, false-premise sycophancy, and absent-fact fabrication across a 2k-to-512k-token context ladder in the same four formats. Recall stays near ceiling through 64-128k tokens, then degrades sharply and format-dependently: one model's accuracy spread reaches 48 points at 128k tokens. Fabrication never occurs (0/5,760 probes), and sycophancy stays negligible (<=8.3%). What rises sharply near each model's context ceiling is outright refusal to answer (0% to 79-90%), distinct from sycophancy or fabrication. Neither pre-registered format ordering holds, and token overhead (+22% to +37% over plain text) further changes which format is preferable where accuracy spread is genuine. We release the full harness, corpus generator, and raw results (VeyraBench): https://github.com/iNetanel/veyrabench

Large Language Models (LLMs) are widely deployed in real-world applications, yet little is known about their training dynamics at the token level. Evaluation typically relies on aggregated training loss, measured at the batch level, which overlooks subtle per-token biases arising from (i) varying token-level dynamics and (ii) structural biases introduced by hyperparameters. While weight decay is commonly used to stabilize training, we reveal that it silently introduces performance biases detectable only at the token level. In fact, we empirically show across different dataset sizes, model architectures and sizes ranging from 270M to 3B parameters that as weight decay increases, low-frequency tokens are disproportionately depreciated. This is particularly concerning, as these neglected low-frequency tokens represent the vast majority of the token distribution in most languages, calling for novel regularization techniques that ensure fairness across all available tokens.

Marcinkiewicz strong law of large numbers, {n^{-frac1p}}sum_{k=1}^{n} (d_{k}- d)rightarrow 0 almost surely with pin(1,2), are developed for products d_k=prod_{r=1}^s x_k^{(r)}, where the x_k^{(r)} = sum_{l=-infty}^{infty}c_{k-l}^{(r)}xi_l^{(r)} are two-sided linear processes with coefficients {c_l^{(r)}}_{lin Z} and i.i.d. zero-mean innovations {xi_l^{(r)}}_{lin Z}. The decay of the coefficients c_l^{(r)} as |l|toinfty, can be slow enough for {x_k^{(r)}} to have long memory while {d_k} can have heavy tails. The long-range dependence and heavy tails for {d_k} are handled simultaneously and a decoupling property shows the convergence rate is dictated by the worst of long-range dependence and heavy tails, but not their combination. The Marcinkiewicz strong law of large numbers is also extended to the multivariate linear process case.

Decoupled weight decay, solely responsible for the performance advantage of AdamW over Adam, has long been set to proportional to learning rate γ without questioning. Some researchers have recently challenged such assumption and argued that decoupled weight decay should be set propto γ^2 instead based on orthogonality arguments at steady state. To the contrary, we find that eliminating the contribution of the perpendicular component of the update to the weight norm leads to little change to the training dynamics. Instead, we derive that decoupled weight decay propto γ^2 results in stable weight norm based on the simple assumption that updates become independent of the weights at steady state, regardless of the nature of the optimizer. Based on the same assumption, we derive and empirically verify that the Total Update Contribution (TUC) of a minibatch under the Scion optimizer is better characterized by the momentum-dependent effective learning rate whose optimal value transfers and we show that decoupled weight decay propto γ^2 leads to stable weight and gradient norms and allows us to better control the training dynamics and improve the model performance.

This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of the solution, \(Δu |_{\partial Ω}\) and \( \partial_{n}(Δu)|_{\partial Ω}.\) We first prove that the associated system operator generates a contraction semigroup, which ensures the well-posedness of the forward problem. A key observability inequality is then derived via multiplier techniques. Building on this foundation, explicit stability estimates for the inverse problem are obtained. These estimates demonstrate that the biharmonic structure inherently enhances the stability of parameter identification, with the stability constants exhibiting an explicit dependence on the damping coefficient via the factor \( (1 + γ)^{1/2} \). This work provides a rigorous theoretical basis for applications in non-destructive testing and dynamic inversion.

In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter second-moment estimators requires memory equal to the number of parameters. For the case of neural network weight matrices, we propose maintaining only the per-row and per-column sums of these moving averages, and estimating the per-parameter second moments based on these sums. We demonstrate empirically that this method produces similar results to the baseline. Secondly, we show that adaptive methods can produce larger-than-desired updates when the decay rate of the second moment accumulator is too slow. We propose update clipping and a gradually increasing decay rate scheme as remedies. Combining these methods and dropping momentum, we achieve comparable results to the published Adam regime in training the Transformer model on the WMT 2014 English-German machine translation task, while using very little auxiliary storage in the optimizer. Finally, we propose scaling the parameter updates based on the scale of the parameters themselves.

Using a fully Bayesian approach, Gaussian Process regression is extended to include marginalisation over the kernel choice and kernel hyperparameters. In addition, Bayesian model comparison via the evidence enables direct kernel comparison. The calculation of the joint posterior was implemented with a transdimensional sampler which simultaneously samples over the discrete kernel choice and their hyperparameters by embedding these in a higher-dimensional space, from which samples are taken using nested sampling. Kernel recovery and mean function inference were explored on synthetic data from exoplanet transit light curve simulations. Subsequently, the method was extended to marginalisation over mean functions and noise models and applied to the inference of the present-day Hubble parameter, H_0, from real measurements of the Hubble parameter as a function of redshift, derived from the cosmologically model-independent cosmic chronometer and ΛCDM-dependent baryon acoustic oscillation observations. The inferred H_0 values from the cosmic chronometers, baryon acoustic oscillations and combined datasets are H_0= 66 pm 6, km,s^{-1},Mpc^{-1}, H_0= 67 pm 10, km,s^{-1},Mpc^{-1} and H_0= 69 pm 6, km,s^{-1},Mpc^{-1}, respectively. The kernel posterior of the cosmic chronometers dataset prefers a non-stationary linear kernel. Finally, the datasets are shown to be not in tension with ln R=12.17pm 0.02.

The antenna-elements that make up a radio interferometer form a spatial filter that samples components of the Fourier transform of a target radio astronomical source brightness. Along the signal path, there are multiplicative and additive perturbation effects that alter the signal and that should be corrected. The process of mitigating these perturbation effects is called calibration. In this work, we develop a new and fast Maximum Likelihood based estimator of these perturbation effects using the Exponential Map and Lie groups. To evaluate its performance, we compare it to the Cramér-Rao Lower Bound and, to test the estimation time, we compare it with the Expectation Maximization algorithm, another fast Maximum Likelihood estimator. Finally, we apply our estimator to a real observation of the protoplanetary disk AS 209 made with the Submillimeter Array. We found that our proposed estimator meets the Cramér-Rao Lower Bound and it was approximately 40 times faster than the Expectation Maximization algorithm.

We present a catalog of 689 galaxy cluster candidates detected at significance ξ>4 via their thermal Sunyaev-Zel'dovich (SZ) effect signature in 95 and 150 GHz data from the 500-square-degree SPTpol survey. We use optical and infrared data from the Dark Energy Camera and the Wide-field Infrared Survey Explorer (WISE) and \spitzer \ satellites, to confirm 544 of these candidates as clusters with sim94% purity. The sample has an approximately redshift-independent mass threshold at redshift z>0.25 and spans 1.5 times 10^{14} < M_{500c} < 9.1 times 10^{14} M_odot/h_{70} \ and 0.03<zlesssim1.6 in mass and redshift, respectively; 21\% of the confirmed clusters are at z>1. We use external radio data from the Sydney University Molonglo Sky Survey (SUMSS) to estimate contamination to the SZ signal from synchrotron sources. The contamination reduces the recovered ξ by a median value of 0.032, or sim0.8% of the ξ=4 threshold value, and sim7% of candidates have a predicted contamination greater than Δξ= 1. With the exception of a small number of systems (<1%), an analysis of clusters detected in single-frequency 95 and 150 GHz data shows no significant contamination of the SZ signal by emission from dusty or synchrotron sources. This cluster sample will be a key component in upcoming astrophysical and cosmological analyses of clusters. The SPTpol millimeter-wave maps and associated data products used to produce this sample are available at https://pole.uchicago.edu/public/data/sptpol_500d_clusters/index.html, and the NASA LAMBDA website. An interactive sky server with the SPTpol maps and Dark Energy Survey data release 2 images is also available at NCSA https://skyviewer.ncsa.illinois.edu.

Identifying and reconstructing hadronic τ decays (τ_{h}) is an important task at current and future high-energy physics experiments, as τ_{h} represent an important tool to analyze the production of Higgs and electroweak bosons as well as to search for physics beyond the Standard Model. The identification of τ_{h} can be viewed as a generalization and extension of jet-flavour tagging, which has in the recent years undergone significant progress due to the use of deep learning. Based on a granular simulation with realistic detector effects and a particle flow-based event reconstruction, we show in this paper that deep learning-based jet-flavour-tagging algorithms are powerful τ_{h} identifiers. Specifically, we show that jet-flavour-tagging algorithms such as LorentzNet and ParticleTransformer can be adapted in an end-to-end fashion for discriminating τ_{h} from quark and gluon jets. We find that the end-to-end transformer-based approach significantly outperforms contemporary state-of-the-art τ_{h} reconstruction and identification algorithms currently in use at the Large Hadron Collider.

Monitoring machine learning models once they are deployed is challenging. It is even more challenging to decide when to retrain models in real-case scenarios when labeled data is beyond reach, and monitoring performance metrics becomes unfeasible. In this work, we use non-parametric bootstrapped uncertainty estimates and SHAP values to provide explainable uncertainty estimation as a technique that aims to monitor the deterioration of machine learning models in deployment environments, as well as determine the source of model deterioration when target labels are not available. Classical methods are purely aimed at detecting distribution shift, which can lead to false positives in the sense that the model has not deteriorated despite a shift in the data distribution. To estimate model uncertainty we construct prediction intervals using a novel bootstrap method, which improves upon the work of Kumar & Srivastava (2012). We show that both our model deterioration detection system as well as our uncertainty estimation method achieve better performance than the current state-of-the-art. Finally, we use explainable AI techniques to gain an understanding of the drivers of model deterioration. We release an open source Python package, doubt, which implements our proposed methods, as well as the code used to reproduce our experiments.

We prove a single-logarithm bound for the eigenvalues in the plunge region of Fourier concentration operators, removing the extra logarithmic factor in the Kulikov--Dam Larsen bound for two general admissible sets throughout each fixed exponential window. For bounded spatial and frequency sets A,BsubsetR^d of positive measure with finite upper codimension-one Minkowski boundary content, the number Λ_varepsilon(cA,B) of eigenvalues in (varepsilon,1-varepsilon) satisfies Λ_varepsilon(cA,B)le C(d,A,B,β)c^{d-1}D(1+log_+(c/D)), where D=log(1/(varepsilon(1-varepsilon))), for every fixed β>0, cge2, 0<varepsilon<1/2, and Dleβc, with log_+t=max(0,log t). The argument uses positive band-limited smoothing and requires no symmetry, convexity, or connectedness. In dimension two, the corresponding exponential-window estimate has a constant uniform in the window parameter. We also determine the optimal coordinate-Lipschitz constant d-1 for recursive decompositions of balls and standard simplices in every dimension, and obtain box-frequency estimates with explicit geometric constants. For C^1 convex bodies in three dimensions, the optimal infimum of recursive coordinate slopes is 2. Uniform real-order Bessel estimates give independent disk and ball bounds at every spectral threshold, including an explicit deep-tail term. For smooth strictly convex planar frequency bodies with positive curvature, we prove correlation estimates for aligned Gaussian packets at arbitrary relative scales and quantitative lower bounds on the cost of estimating spatial blocks separately. Together these results connect the global spectral bound with sharp geometric constructions and the cancellation retained by grouping boundary interactions.

An amplitude analysis of B^-rightarrow D^- D^0 K_S^0 decays is performed using proton-proton collision data, corresponding to an integrated luminosity of 9,fb^{-1}, collected with the LHCb detector at center-of-mass energies of 7, 8, and 13,Tekern -0.1em V. A resonant structure of spin-parity 0^+ is observed in the D^0 K_S^0 invariant-mass spectrum with a significance of 5.3,sigma. The mass and width of the state, modeled with a Breit-Wigner lineshape, are determined to be 2883pm11pm6,Mekern -0.1em V!/c^2 and 87_{-47}^{+22}pm6,Mekern -0.1em V respectively, where the first uncertainties are statistical and the second systematic. These properties and the quark content are consistent with those of the open-charm tetraquark state T_{cs 0}^{*}(2870)^0 observed previously in the D^+ K^- final state of the B^-rightarrow D^- D^+ K^- decay. This result confirms the existence of the T_{cs 0}^{*}(2870)^0 state in a new decay mode. The T_{cs1}^{*}(2900)^0 state, reported in the B^-rightarrow D^- D^+ K^- decay, is also searched for in the D^0 K_S^0 invariant-mass spectrum of the B^- rightarrow D^- D^0 K_S^0 decay, without finding evidence for it.

We propose a new localized inference algorithm for answering marginalization queries in large graphical models with the correlation decay property. Given a query variable and a large graphical model, we define a much smaller model in a local region around the query variable in the target model so that the marginal distribution of the query variable can be accurately approximated. We introduce two approximation error bounds based on the Dobrushin's comparison theorem and apply our bounds to derive a greedy expansion algorithm that efficiently guides the selection of neighbor nodes for localized inference. We verify our theoretical bounds on various datasets and demonstrate that our localized inference algorithm can provide fast and accurate approximation for large graphical models.

Co-citation structure is widely assumed to provide stable retrieval signal in legal information systems. We test this assumption longitudinally by constructing UA-StatuteRetrieval, a benchmark that measures co-citation predictability across 20 annual snapshots (2007-2026) of 396 million codex citations from 101 million Ukrainian court decisions. Using a leave-one-out protocol over the full bipartite citation graph, we find that Adamic-Adar MRR declines 33% on a fixed set of articles (from 0.43 to 0.29) and 47% under a train/test temporal split (from 0.51 to 0.27) confirming genuine temporal decay rather than compositional shift or evaluation artifact. The decay is non-uniform: criminal procedure maintains stable co-citation patterns (MRR ~0.40), while civil law degrades from 0.35 to 0.15, coinciding with the 2017 judicial reform. Hub articles (>100K citations) resist decay, but mid-frequency articles (1K-10K) -- the practical retrieval frontier lose half their predictability. A BM25 text baseline decays even faster (31%), and embedding drift analysis with E5-large reveals a 4.3% semantic shift in how articles are cited, providing a mechanistic explanation for the observed decay. The benchmark is released at https://huggingface.co/datasets/overthelex/ua-statute-retrieval.

This article presents a review about the main CERN n\_TOF contributions to the field of neutron-capture experiments of interest for s-process nucleosynthesis studies over the last 25 years, with special focus on the measurement of radioactive isotopes. A few recent capture experiments on stable isotopes of astrophysical interest are also discussed. Results on s-process branching nuclei are appropriate to illustrate how advances in detection systems and upgrades in the facility have enabled increasingly challenging experiments and, as a consequence, have led to a better understanding and modeling of the s-process mechanism of nucleosynthesis. New endeavors combining radioactive-ion beams from ISOLDE for the production of radioisotopically pure samples for activation experiments at the new NEAR facility at n\_TOF are briefly discussed. On the basis of these new exciting results, also current limitations of state-of-the-art TOF and activation techniques will be depicted, thereby showing the pressing need for further upgrades and enhancements on both facilities and detection systems. A brief account of the potential technique based on inverse kinematics for direct neutron-capture measurements is also presented.

Survival analysis can sometimes involve individuals who will not experience the event of interest, forming what is known as the cured group. Identifying such individuals is not always possible beforehand, as they provide only right-censored data. Ignoring the presence of the cured group can introduce bias in the final model. This paper presents a method for estimating a semiparametric additive hazards model that accounts for the cured fraction. Unlike regression coefficients in a hazard ratio model, those in an additive hazard model measure hazard differences. The proposed method uses a primal-dual interior point algorithm to obtain constrained maximum penalized likelihood estimates of the model parameters, including the regression coefficients and the baseline hazard, subject to certain non-negativity constraints.

Constant-stepsize stochastic approximation (SA) is widely used in learning for computational efficiency. For a fixed stepsize, the iterates typically admit a stationary distribution that is rarely tractable. Prior work shows that as the stepsize αdownarrow 0, the centered-and-scaled steady state converges weakly to a Gaussian random vector. However, for fixed α, this weak convergence offers no usable error bound for approximating the steady-state by its Gaussian limit. This paper provides explicit, non-asymptotic error bounds for fixed α. We first prove general-purpose theorems that bound the Wasserstein distance between the centered-scaled steady state and an appropriate Gaussian distribution, under regularity conditions for drift and moment conditions for noise. To ensure broad applicability, we cover both i.i.d. and Markovian noise models. We then instantiate these theorems for three representative SA settings: (1) stochastic gradient descent (SGD) for smooth strongly convex objectives, (2) linear SA, and (3) contractive nonlinear SA. We obtain dimension- and stepsize-dependent, explicit bounds in Wasserstein distance of order α^{1/2}log(1/α) for small α. Building on the Wasserstein approximation error, we further derive non-uniform Berry--Esseen-type tail bounds that compare the steady-state tail probability to Gaussian tails. We achieve an explicit error term that decays in both the deviation level and stepsize α. We adapt the same analysis for SGD beyond strongly convexity and study general convex objectives. We identify a non-Gaussian (Gibbs) limiting law under the correct scaling, which is validated numerically, and provide a corresponding pre-limit Wasserstein error bound.

This paper derives confidence intervals (CI) and time-uniform confidence sequences (CS) for the classical problem of estimating an unknown mean from bounded observations. We present a general approach for deriving concentration bounds, that can be seen as a generalization and improvement of the celebrated Chernoff method. At its heart, it is based on a class of composite nonnegative martingales, with strong connections to testing by betting and the method of mixtures. We show how to extend these ideas to sampling without replacement, another heavily studied problem. In all cases, our bounds are adaptive to the unknown variance, and empirically vastly outperform existing approaches based on Hoeffding or empirical Bernstein inequalities and their recent supermartingale generalizations. In short, we establish a new state-of-the-art for four fundamental problems: CSs and CIs for bounded means, when sampling with and without replacement.

This paper presents a differentially private approach to Kaplan-Meier estimation that achieves accurate survival probability estimates while safeguarding individual privacy. The Kaplan-Meier estimator is widely used in survival analysis to estimate survival functions over time, yet applying it to sensitive datasets, such as clinical records, risks revealing private information. To address this, we introduce a novel algorithm that applies time-indexed Laplace noise, dynamic clipping, and smoothing to produce a privacy-preserving survival curve while maintaining the cumulative structure of the Kaplan-Meier estimator. By scaling noise over time, the algorithm accounts for decreasing sensitivity as fewer individuals remain at risk, while dynamic clipping and smoothing prevent extreme values and reduce fluctuations, preserving the natural shape of the survival curve. Our results, evaluated on the NCCTG lung cancer dataset, show that the proposed method effectively lowers root mean squared error (RMSE) and enhances accuracy across privacy budgets (epsilon). At epsilon = 10, the algorithm achieves an RMSE as low as 0.04, closely approximating non-private estimates. Additionally, membership inference attacks reveal that higher epsilon values (e.g., epsilon geq 6) significantly reduce influential points, particularly at higher thresholds, lowering susceptibility to inference attacks. These findings confirm that our approach balances privacy and utility, advancing privacy-preserving survival analysis.

Training compute is increasingly outpacing the availability of high-quality data. This shifts the central challenge from optimal compute allocation to extracting maximum value from limited data. The widely adopted Chinchilla scaling law assumes every training token is unique. This limits its ability to guide pretraining decisions in data-constrained regimes. We model the excess loss under repetition with a simple additive overfitting penalty and find that it accurately describes model behavior. Our scaling law yields qualitatively new compute-optimal allocation advice. Beyond a point, further repetition is counterproductive and compute is better spent on model capacity. We show that following our law's recommended configuration improves performance in data-constrained regimes. Finally, because our one-parameter form isolates overfitting in a single coefficient, it enables direct comparison across training configurations. As a case study, we show that strong weight decay (λ=1.0) reduces this coefficient by approximately 70%, providing a scaling-law explanation for recent findings that optimal weight decay in data-constrained regimes is an order of magnitude larger than standard practice.

We study two-step recurrences with positive step sizes and nonnegative momentum coefficients whose terminal residual is the Chebyshev minimax polynomial on a prescribed spectral interval [μ,L]. These recurrences have the same terminal error on a fixed quadratic, but their first-order responses to stepwise Hessian perturbations can differ. We prove that the sine-Jacobi recurrence of Part I is asymptotically optimal for this response norm within a factor of 1.000004, uniformly over 0<μ<L. Every terminal-exact recurrence satisfies A_Nge(2c_{cert}-o(1))N^{3/2}ε_N^star/(L-μ) with c_{cert}>1.14268353624, whereas the sine-Jacobi recurrence attains the constant 2c_{sin} with c_{sin}<1.14269218. The proof reduces the gain to the diagonal energy of a Jacobi Green matrix. A centering lift represents this matrix by an exponential kernel; packing its diagonal into a density on the line preserves the energy and controls the change in the Birman-Schwinger spectrum. A calibrated identity gives a lower bound using the ground parameter and one Fredholm determinant. Two further determinants and a trace observation improve the bound through a pointwise inequality on an explicit compact state region. One rational certificate verifies this inequality by interval arithmetic. A second certificate constructs a density satisfying the selected observations and both normalizations with energy below the sine value. Finally, no C^1 function of finitely many observations of the specified kinds gives a locally sharp lower bound at the sine density.

Training language models currently requires pre-determining a fixed compute budget because the typical cosine learning rate schedule depends on the total number of steps. In contrast, the Warmup-Stable-Decay (WSD) schedule uses a constant learning rate to produce a main branch of iterates that can in principle continue indefinitely without a pre-specified compute budget. Then, given any compute budget, one can branch out from the main branch at a proper time with a rapidly decaying learning rate to produce a strong model. Empirically, WSD generates a non-traditional loss curve: the loss remains elevated during the stable phase but sharply declines during the decay phase. Towards explaining this phenomenon, we conjecture that pretraining loss exhibits a river valley landscape, which resembles a deep valley with a river at its bottom. Under this assumption, we show that during the stable phase, the iterate undergoes large oscillations due to the high learning rate, yet it progresses swiftly along the river. During the decay phase, the rapidly dropping learning rate minimizes the iterate's oscillations, moving it closer to the river and revealing true optimization progress. Therefore, the sustained high learning rate phase and fast decaying phase are responsible for progress in the river and the mountain directions respectively, and are both critical. Our analysis predicts phenomenons consistent with empirical observations and shows that this landscape can emerge from pretraining on a simple bi-gram dataset. Inspired by the theory, we introduce WSD-S, a variant of WSD that reuses previous checkpoints' decay phases and keeps only one main branch, where we resume from a decayed checkpoint. WSD-S empirically outperforms WSD and Cyclic-Cosine in obtaining multiple language model checkpoints across various compute budgets in a single run for parameters scaling from 0.1B to 1.2B.

Hampering the interpretation of benchmark scores, evaluation data contamination has become a growing concern in the evaluation of LLMs, and an active area of research studies its effects. While evaluation data contamination is easily understood intuitively, it is surprisingly difficult to define precisely which samples should be considered contaminated and, consequently, how it impacts benchmark scores. We propose that these questions should be addressed together and that contamination metrics can be assessed based on whether models benefit from the examples they mark contaminated. We propose a novel analysis method called ConTAM, and show with a large scale survey of existing and novel n-gram based contamination metrics across 13 benchmarks and 7 models from 2 different families that ConTAM can be used to better understand evaluation data contamination and its effects. We find that contamination may have a much larger effect than reported in recent LLM releases and benefits models differently at different scales. We also find that considering only the longest contaminated substring provides a better signal than considering a union of all contaminated substrings, and that doing model and benchmark specific threshold analysis greatly increases the specificity of the results. Lastly, we investigate the impact of hyperparameter choices, finding that, among other things, both using larger values of n and disregarding matches that are infrequent in the pre-training data lead to many false negatives. With ConTAM, we provide a method to empirically ground evaluation data contamination metrics in downstream effects. With our exploration, we shed light on how evaluation data contamination can impact LLMs and provide insight into the considerations important when doing contamination analysis. We end our paper by discussing these in more detail and providing concrete suggestions for future work.

We consider the classic supervised learning problem, where a continuous non-negative random label Y (i.e. a random duration) is to be predicted based upon observing a random vector X valued in R^d with dgeq 1 by means of a regression rule with minimum least square error. In various applications, ranging from industrial quality control to public health through credit risk analysis for instance, training observations can be right censored, meaning that, rather than on independent copies of (X,Y), statistical learning relies on a collection of ngeq 1 independent realizations of the triplet (X, ; min{Y,; C},; δ), where C is a nonnegative r.v. with unknown distribution, modeling censorship and δ=I{Yleq C} indicates whether the duration is right censored or not. As ignoring censorship in the risk computation may clearly lead to a severe underestimation of the target duration and jeopardize prediction, we propose to consider a plug-in estimate of the true risk based on a Kaplan-Meier estimator of the conditional survival function of the censorship C given X, referred to as Kaplan-Meier risk, in order to perform empirical risk minimization. It is established, under mild conditions, that the learning rate of minimizers of this biased/weighted empirical risk functional is of order O_{P}(log(n)/n) when ignoring model bias issues inherent to plug-in estimation, as can be attained in absence of censorship. Beyond theoretical results, numerical experiments are presented in order to illustrate the relevance of the approach developed.

Post-merger gravitational wave echoes provide a unique opportunity to probe the near-horizon structure of astrophysical black holes, that may be modified due to non-perturbative quantum gravity phenomena. However, since the waveform is subject to large theoretical uncertainties, it is necessary to develop model-agnostic search methods for detecting echoes from observational data. A promising strategy is to identify the characteristic quasinormal modes (QNMs) associated with echoes, {\it in frequency space}, which complements existing searches of quasiperiodic pulses in time. In this study, we build upon our previous work targeting these modes by incorporating relative phase information to optimize the Bayesian search algorithm. Using a new phase-marginalized likelihood, the performance can be significantly improved for well-resolved QNMs. This enables an efficient model-agnostic search for QNMs of different shapes by using a simple search template. To demonstrate the robustness of the search algorithm, we construct four complementary benchmarks for the echo waveform that span a diverse range of different theoretical possibilities for the near-horizon structure. We then validate our Bayesian search algorithms by injecting the benchmark models into different realizations of Gaussian noise. Using two types of phase-marginalized likelihoods, we find that the search algorithm can efficiently detect the corresponding QNMs. Therefore, our search strategy provides a concrete Bayesian and model-agnostic approach to "quantum black hole seismology".

Results are presented from searches for the standard model Higgs boson in proton-proton collisions at sqrt(s) = 7 and 8 TeV in the Compact Muon Solenoid experiment at the LHC, using data samples corresponding to integrated luminosities of up to 5.1 inverse femtobarns at 7 TeV and 5.3 inverse femtobarns at 8 TeV. The search is performed in five decay modes: gamma gamma, ZZ, WW, tau tau, and b b-bar. An excess of events is observed above the expected background, with a local significance of 5.0 standard deviations, at a mass near 125 GeV, signalling the production of a new particle. The expected significance for a standard model Higgs boson of that mass is 5.8 standard deviations. The excess is most significant in the two decay modes with the best mass resolution, gamma gamma and ZZ; a fit to these signals gives a mass of 125.3 +/- 0.4 (stat.) +/- 0.5 (syst.) GeV. The decay to two photons indicates that the new particle is a boson with spin different from one.

The leakage of benchmark data into the training data has emerged as a significant challenge for evaluating the capabilities of large language models (LLMs). In this work, we challenge the common assumption that small-scale contamination renders benchmark evaluations invalid. First, we experimentally quantify the magnitude of benchmark overfitting based on scaling along three dimensions: The number of model parameters (up to 1.6B), the number of times an example is seen (up to 144), and the number of training tokens (up to 40B). If model and data follow the Chinchilla scaling laws, minor contamination indeed leads to overfitting. At the same time, even 144 times of contamination can be forgotten if the training data is scaled beyond five times Chinchilla, a regime characteristic of many modern LLMs. Continual pre-training of OLMo-7B corroborates these results. Next, we study the impact of the weight decay parameter on example forgetting, showing that empirical forgetting occurs faster than the cumulative weight decay. This allows us to gauge the degree of example forgetting in large-scale training runs, indicating that many LLMs, including Lllama 3 405B, have forgotten the data seen at the beginning of training.

The transition of an impulsively excited kink oscillation of a solar coronal loop to an oscillation with a stationary amplitude, i.e., the damping pattern, is determined using the low-dimensional self-oscillation model. In the model, the decayless kink oscillations are sustained by the interaction of the oscillating loop with an external quasi-steady flow. The analytical solution is based on the assumption that the combined effect of the effective dissipation, for example, by resonant absorption, and interaction with an external flow, is weak. The effect is characterised by a dimensionless coupling parameter. The damping pattern is found to depend upon the initial amplitude and the coupling parameter. The approximate expression shows a good agreement with a numerical solution of the self-oscillation equation. The plausibility of the established damping pattern is demonstrated by an observational example. Notably, the damping pattern is not exponential, and the characteristic decay time is different from the time determined by the traditionally used exponential damping fit. Implications of this finding for seismology of the solar coronal plasmas are discussed. In particular, it is suggested that a very rapid, in less than the oscillation period, decay of the oscillation to the stationary level, achieved for larger values of the coupling parameter, can explain the relative rareness of the kink oscillation events.

We study regressions with multiple treatments and a set of controls that is flexible enough to purge omitted variable bias. We show that these regressions generally fail to estimate convex averages of heterogeneous treatment effects -- instead, estimates of each treatment's effect are contaminated by non-convex averages of the effects of other treatments. We discuss three estimation approaches that avoid such contamination bias, including the targeting of easiest-to-estimate weighted average effects. A re-analysis of nine empirical applications finds economically and statistically meaningful contamination bias in observational studies; contamination bias in experimental studies is more limited due to smaller variability in propensity scores.

Recent experimental results in B physics from Belle, BaBar and LHCb suggest new physics (NP) in the weak bto c charged-current and the bto s neutral-current processes. Here we focus on the charged-current case and specifically on the decay modes Bto D^{*+}ell^- barν with ell = e, μ, and τ. The world averages of the ratios R_D and R_D^{*} currently differ from the Standard Model (SM) by 3.4σ while ΔA_{FB} = A_{FB}(Bto D^{*} μν) - A_{FB} (Bto D^{*} e ν) is found to be 4.1σ away from the SM prediction in an analysis of 2019 Belle data. These intriguing results suggest an urgent need for improved simulation and analysis techniques in Bto D^{*+}ell^- barν decays. Here we describe a Monte Carlo Event-generator tool based on EVTGEN developed to allow simulation of the NP signatures in Bto D^*ell^- ν, which arise due to the interference between the SM and NP amplitudes. As a demonstration of the proposed approach, we exhibit some examples of NP couplings that are consistent with current data and could explain the ΔA_{FB} anomaly in Bto D^*ell^- ν while remaining consistent with other constraints. We show that the Δ-type observables such as ΔA_{FB} and ΔS_5 eliminate most QCD uncertainties from form factors and allow for clean measurements of NP. We introduce correlated observables that improve the sensitivity to NP. We discuss prospects for improved observables sensitive to NP couplings with the expected 50 ab^{-1} of Belle II data, which seems to be ideally suited for this class of measurements.

We study and explore the low scale implications of Yukawa unification in the minimal gauge mediated supersymmetry breaking models. We also assume non-zero non-holomorphic terms, with which the YU solutions can be accommodated in the cases with μ> 0. These results can be considered a direct effect from the non-holomorphic terms, but they also lead to testable low scale implications compatible with YU. We observe abundant solutions consistent with the Higgs boson mass. This constraint leads to heavy strongly interacting supersymmetric particles, while the electroweak sector can be realized relatively lighter and they can be probed by several experiments. We find that the chargino can be lighter than 1 TeV and it is degenerate with the lightest neutralino in most of such solutions. Consistent solutions in this region can accommodate charginos as light as about 120 GeV, and they will be tested more likely soon by the analyses over the compressed spectra. These solutions are also be subjected in the lifetime analyses. Our analyses identify such light charginos decaying in about 10^{-2} ns. Probing such points may need a slight improvement in sensitivity of the analyses, and one can expect them to be tested very soon. In the same region, stau is realized to be another light supersymmetric particle, and some of the solutions can be inconsistently lighter. We find that it can weigh as light as about 600 GeV consistently, and it can be tested also soon over its lifetime. We summarize and also exemplify our findings with five benchmark scenarios. Most of the benchmark solutions also reveal that the solutions can be tested in heavy Higgs boson searches, which shape the whole Higgs boson spectrum in models.

Learning rate schedules used in practice bear little resemblance to those recommended by theory. We close much of this theory/practice gap, and as a consequence are able to derive new problem-adaptive learning rate schedules. Our key technical contribution is a refined analysis of learning rate schedules for a wide class of optimization algorithms (including SGD). In contrast to most prior works that study the convergence of the average iterate, we study the last iterate, which is what most people use in practice. When considering only worst-case analysis, our theory predicts that the best choice is the linear decay schedule: a popular choice in practice that sets the stepsize proportionally to 1 - t/T, where t is the current iteration and T is the total number of steps. To go beyond this worst-case analysis, we use the observed gradient norms to derive schedules refined for any particular task. These refined schedules exhibit learning rate warm-up and rapid learning rate annealing near the end of training. Ours is the first systematic approach to automatically yield both of these properties. We perform the most comprehensive evaluation of learning rate schedules to date, evaluating across 10 diverse deep learning problems, a series of LLMs, and a suite of logistic regression problems. We validate that overall, the linear-decay schedule matches or outperforms all commonly used default schedules including cosine annealing, and that our schedule refinement method gives further improvements.

As AI model size grows, neural scaling laws have become a crucial tool to predict the improvements of large models when increasing capacity and the size of original (human or natural) training data. Yet, the widespread use of popular models means that the ecosystem of online data and text will co-evolve to progressively contain increased amounts of synthesized data. In this paper we ask: How will the scaling laws change in the inevitable regime where synthetic data makes its way into the training corpus? Will future models, still improve, or be doomed to degenerate up to total (model) collapse? We develop a theoretical framework of model collapse through the lens of scaling laws. We discover a wide range of decay phenomena, analyzing loss of scaling, shifted scaling with number of generations, the ''un-learning" of skills, and grokking when mixing human and synthesized data. Our theory is validated by large-scale experiments with a transformer on an arithmetic task and text generation using the large language model Llama2.

Human aging is marked by a steady rise in the risk of dying with age-a process demographers call senescence. Over the past century, life expectancy has risen dramatically, but is this because we are aging slower, or simply starting it later? Vaupel hypothesizes that the pace at which individuals age may be constant, with gains in longevity coming from the delayed onset of senescence rather than its slowing down. We test this idea using a new framework that decomposes the pace of senescence into three components: a biological baseline, a long-term trend, and the cumulative impact of period shocks. Applying this to cohort mortality data above age 80 from 12 countries, we find that once period shocks are accounted for, there is no statistical evidence of a long-term trend, consistent with Vaupel's hypothesis. Analyses using lower starting ages yield the same qualitative conclusion. Rather than indicating a change in the process that drives senescence, these variations are consistent with echoes of shared historical events. These results suggest that while longevity has shifted, the rhythm of human aging may be conserved.

We consider the problem of linear estimation, and establish an extension of the Gauss-Markov theorem, in which the bias operator is allowed to be non-zero but bounded with respect to a matrix norm of Schatten type. We derive simple and explicit formulas for the optimal estimator in the cases of Nuclear and Spectral norms (with the Frobenius case recovering ridge regression). Additionally, we analytically derive the generalization error in multiple random matrix ensembles, and compare with Ridge regression. Finally, we conduct an extensive simulation study, in which we show that the cross-validated Nuclear and Spectral regressors can outperform Ridge in several circumstances.

Trajectory Inference (TI) seeks to recover latent dynamical processes from snapshot data, where only independent samples from time-indexed marginals are observed. In applications such as single-cell genomics, destructive measurements make path-space laws non-identifiable from finitely many marginals, leaving held-out marginal prediction as the dominant but limited evaluation protocol. We introduce a general framework for estimating the Kullback-Leibler divergence (KL) divergence between probability measures on function space, yielding a tractable, data-driven estimator that is scalable to realistic snapshot datasets. We validate the accuracy of our estimator on a benchmark suite, where the estimated functional KL closely matches the analytic KL. Applying this framework to synthetic and real scRNA-seq datasets, we show that current evaluation metrics often give inconsistent assessments, whereas path-space KL enables a coherent comparison of trajectory inference methods and exposes discrepancies in inferred dynamics, especially in regions with sparse or missing data. These results support functional KL as a principled criterion for evaluating trajectory inference under partial observability.

We present constraints on the spacetime variation of the fine-structure constant alpha at redshifts 2.5le z<9.5 using JWST emission-line galaxies. The galaxy sample consists of 621 high-quality spectra with strong and narrow [O III] lambdalambda4959,5007 doublet emission lines from 578 galaxies, including 232 spectra at z>5. The [O III] doublet lines are arguably the best emission lines to probe the variation in alpha. We divide our sample into six subsamples based on redshift and calculate the relative variation Deltaalpha/alpha for the individual subsamples. The calculated Deltaalpha/alpha values are consistent with zero within 1sigma at all redshifts, suggesting no time variation in alpha above a level of (1-2) times10^{-4} (1sigma) in the past 13.2 billion years. When the whole sample is combined, the constraint is improved to be Deltaalpha/alpha = (0.2pm0.7) times10^{-4}. We further test the spatial variation in alpha using four subsamples of galaxies in four different directions on the sky. The measured Deltaalpha/alpha values are consistent with zero at a 1sigma level of sim 2times10^{-4}. While the constraints in this work are not as stringent as those from lower-redshift quasar absorption lines in previous studies, this work uses an independent tracer and provides the first constraints on Deltaalpha/alpha at the highest redshifts. With the growing number of emission-line galaxies from JWST, we expect to achieve stronger constraints in the future.

Full quantum tomography of high-dimensional quantum systems is experimentally infeasible due to the exponential scaling of the number of required measurements on the number of qubits in the system. However, several ideas were proposed recently for predicting the limited number of features for these states, or estimating the expectation values of operators, without the need for full state reconstruction. These ideas go under the general name of shadow tomography. Here we provide an experimental demonstration of property estimation based on classical shadows proposed in [H.-Y. Huang, R. Kueng, J. Preskill. Nat. Phys. https://doi.org/10.1038/s41567-020-0932-7 (2020)] and study its performance in the quantum optical experiment with high-dimensional spatial states of photons. We show on experimental data how this procedure outperforms conventional state reconstruction in fidelity estimation from a limited number of measurements.

How do multi-turn reasoning systems fail? The expected answer is logical contradiction, in which the system's maintained state becomes unsatisfiable. We show that the dominant mode is instead satisfiable drift, where the internal state stays consistent while the returned answer silently violates prior commitments. We build DRIFT-Bench (Decomposing Reasoning Into Failure Types), a solver-instrumented benchmark of 816 test problems across three constraint domains, and evaluate four methods on it across four open-weight models (8B-120B parameters). MUS-Repair, which feeds minimal unsatisfiable subsets back to the generator, is strongest in every setting (+1.8 to +15.0 pp over the best non-MUS baseline). But the central finding is what repair leaves behind. After structured feedback, models rarely contradict themselves. They forget. Residual errors are 98-100% satisfiable drift across all settings, while contradiction drops to near zero. Reliable multi-turn systems must separately validate that the returned answer respects the maintained state. Code is available at https://github.com/kaons-research/drift-bench.

Accurate demand estimation is critical for the retail business in guiding the inventory and pricing policies of perishable products. However, it faces fundamental challenges from censored sales data during stockouts, where unobserved demand creates systemic policy biases. Existing datasets lack the temporal resolution and annotations needed to address this censoring effect. To fill this gap, we present FreshRetailNet-50K, the first large-scale benchmark for censored demand estimation. It comprises 50,000 store-product time series of detailed hourly sales data from 898 stores in 18 major cities, encompassing 863 perishable SKUs meticulously annotated for stockout events. The hourly stock status records unique to this dataset, combined with rich contextual covariates, including promotional discounts, precipitation, and temporal features, enable innovative research beyond existing solutions. We demonstrate one such use case of two-stage demand modeling: first, we reconstruct the latent demand during stockouts using precise hourly annotations. We then leverage the recovered demand to train robust demand forecasting models in the second stage. Experimental results show that this approach achieves a 2.73\% improvement in prediction accuracy while reducing the systematic demand underestimation from 7.37\% to near-zero bias. With unprecedented temporal granularity and comprehensive real-world information, FreshRetailNet-50K opens new research directions in demand imputation, perishable inventory optimization, and causal retail analytics. The unique annotation quality and scale of the dataset address long-standing limitations in retail AI, providing immediate solutions and a platform for future methodological innovation. The data (https://huggingface.co/datasets/Dingdong-Inc/FreshRetailNet-50K) and code (https://github.com/Dingdong-Inc/frn-50k-baseline}) are openly released.

Predicting mortality-related outcomes from images offers the prospect of accessible, noninvasive, and scalable health screening. We present a method that leverages pretrained vision transformer foundation models to estimate remaining lifespan from facial and whole-body images, alongside robust uncertainty quantification. We show that predictive uncertainty varies systematically with the true remaining lifespan, and that this uncertainty can be effectively modeled by learning a Gaussian distribution for each sample. Our approach achieves state-of-the-art mean absolute error (MAE) of 7.48 years on an established Dataset, and further improves to 4.79 and 5.07 years MAE on two new, higher-quality datasets curated and published in this work. Importantly, our models provide well-calibrated uncertainty estimates, as demonstrated by a bucketed expected calibration error of 0.62 years. While not intended for clinical deployment, these results highlight the potential of extracting medically relevant signals from images. We make all code and datasets available to facilitate further research.

In this paper, we develop and implement an efficient asymptotic-preserving (AP) scheme to solve the gas mixture of Boltzmann equations under the disparate mass scaling relevant to the so-called "epochal relaxation" phenomenon. The disparity in molecular masses, ranging across several orders of magnitude, leads to significant challenges in both the evaluation of collision operators and the designing of time-stepping schemes to capture the multi-scale nature of the dynamics. A direct implementation of the spectral method faces prohibitive computational costs as the mass ratio increases due to the need to resolve vastly different thermal velocities. Unlike [I. M. Gamba, S. Jin, and L. Liu, Commun. Math. Sci., 17 (2019), pp. 1257-1289], we propose an alternative approach based on proper truncation of asymptotic expansions of the collision operators, which significantly reduces the computational complexity and works well for small varepsilon. By incorporating the separation of three time scales in the model's relaxation process [P. Degond and B. Lucquin-Desreux, Math. Models Methods Appl. Sci., 6 (1996), pp. 405-436], we design an AP scheme that captures the specific dynamics of the disparate mass model while maintaining computational efficiency. Numerical experiments demonstrate the effectiveness of the proposed scheme in handling large mass ratios of heavy and light species, as well as capturing the epochal relaxation phenomenon.

Naturally occurring background radiation is a source of correlated decoherence events in superconducting qubits that will challenge error-correction schemes. To characterize the radiation environment in an unshielded laboratory, we performed broadband, spectroscopic measurements of background events in silicon substrates located inside a millikelvin refrigerator, an environment representative of superconducting qubit systems. We measured the background spectra in silicon substrates of two thicknesses, 0.5 mm and 1.5 mm, and obtained the average event rate and the integrated power deposition. In a 25 mm^2 area and the thinner substrate, these values are 0.023 events per second and 4.9 keV/s, counting events that deposit at least 40 keV. We find the background spectrum to be nearly featureless. Its intensity decreases by a factor of 40,000 between 100 keV and 3 MeV for silicon substrates 0.5 mm thick. We find the cryogenic measurements to be in good agreement with predictions based on measurements of the terrestrial gamma-ray flux, published models of cosmic-ray fluxes, a crude model of the cryostat, and radiation-transport simulations. No free parameters are required to predict the background spectra in the silicon substrates. The good agreement between measurements and predictions allow assessment of the relative contributions of terrestrial and cosmic background sources and their dependence on substrate thickness. Our spectroscopic measurements are performed with superconducting microresonators that transduce deposited energy to a readily detectable electrical signal. We find that gamma-ray emissions from radioisotopes are responsible for the majority of events depositing E<1.5 MeV, while nucleons among the cosmic-ray secondary particles cause most events that deposit more energy. These results suggest several paths to reducing the impact of background radiation on quantum circuits.

The trade-off between regret and computational cost is a fundamental problem for online kernel regression, and previous algorithms worked on the trade-off can not keep optimal regret bounds at a sublinear computational complexity. In this paper, we propose two new algorithms, AOGD-ALD and NONS-ALD, which can keep nearly optimal regret bounds at a sublinear computational complexity, and give sufficient conditions under which our algorithms work. Both algorithms dynamically maintain a group of nearly orthogonal basis used to approximate the kernel mapping, and keep nearly optimal regret bounds by controlling the approximate error. The number of basis depends on the approximate error and the decay rate of eigenvalues of the kernel matrix. If the eigenvalues decay exponentially, then AOGD-ALD and NONS-ALD separately achieves a regret of O(L(f)) and O(d_{eff}(mu)T) at a computational complexity in O(ln^2{T}). If the eigenvalues decay polynomially with degree pgeq 1, then our algorithms keep the same regret bounds at a computational complexity in o(T) in the case of p>4 and pgeq 10, respectively. L(f) is the cumulative losses of f and d_{eff}(mu) is the effective dimension of the problem. The two regret bounds are nearly optimal and are not comparable.

We establish lower bounds on the number of resonances for three-dimensional semiclassical Dirac operators with mass-type potentials. For a pair Dl_j=Dl_0+mbfβv_j, j=1,2, satisfying the exterior analyticity, decay and non-degeneracy assumptions of the paper, we associate a relative distribution μ to the corresponding mass functions. We prove that if E_0>1 is a boundary point of suppμ, then every complex neighbourhood of E_0, and likewise of -E_0, contains in total at least Chbar^{-3} resonances of the two operators, counted with multiplicity. The proof transfers an analytic wave-front singularity of μ to the relative classical density of states and combines this with Khochman's local trace formula and a relative semiclassical trace formula. As a consequence, if v is a single bounded mass-type potential, analytic with power decay in an exterior sector, with inf(1+v)>0 and sup v>0, then Dl=Dl_0+mbfβv has at least Chbar^{-3} resonances in every complex neighbourhood of E_0=1+sup v and of -E_0, for all sufficiently small hbar. The exponent agrees with Khochman's upper bound, the two resonance families are related by spectral symmetry, and E_0 is necessarily a trapping energy. We also prove the relative semiclassical trace formula needed in the argument for general Hermitian matrix-valued perturbations.

Large language models deliver strong reasoning and tool-use skills, yet their computational demands make them impractical for edge or cost-sensitive deployments. We present Xmodel-2.5, a 1.3-billion-parameter small language model designed as a drop-in agent core. Training with maximal-update parameterization (μP) allows hyper-parameters tuned on a 20M-parameter proxy to transfer directly to the full model, even under the parameter-tied tie-word-embedding architecture. A 1.4T-token Warmup--Stable--Decay curriculum is used, and we further show that switching from AdamW to Muon during the decay phase improves the 13-task reasoning average by 4.58\,\% while keeping every other hyper-parameter fixed, verifying that early AdamW stability can be paired with late Muon sharpening for better downstream performance. FP8-mixed-precision training balances accuracy and throughput. All checkpoints, recipes, and evaluation code are released under the Apache-2.0 license.https://huggingface.co/XiaoduoAILab/Xmodel-2.5 and https://huggingface.co/XiaoduoAILab/Xmodel-2.5-history (training checkpoints). Training code and evaluation harness: https://github.com/XiaoduoAILab/Xmodel-2.5.

This document describes the technical layout and the expected performance of the Straw Tube Tracker (STT), the main tracking detector of the PANDA target spectrometer. The STT encloses a Micro-Vertex-Detector (MVD) for the inner tracking and is followed in beam direction by a set of GEM-stations. The tasks of the STT are the measurement of the particle momentum from the reconstructed trajectory and the measurement of the specific energy-loss for a particle identification. Dedicated simulations with full analysis studies of certain proton-antiproton reactions, identified as being benchmark tests for the whole PANDA scientific program, have been performed to test the STT layout and performance. The results are presented, and the time lines to construct the STT are described.

Sharp bounds on two potential-outcome means need not combine into sharp bounds on their difference. We characterize exactly when composition is guaranteed across environments sharing a joint potential-outcome law. For binary treatment and outcome, fix strict selection-probability bounds and interior treatment propensities. Subtracting the full model's sharp mean intervals gives sharp average-treatment-effect bounds for every compatible observed law if and only if the absolute selection bounds coincide across environments. Under this alignment, the complete mean region is rectangular; its endpoints and attaining causal models require O(K) arithmetic operations for K environments. For every mismatch, failure occurs on a relatively open set of positive observed tables at the prescribed propensities and persists under small joint drift. We give computable perturbation certificates and an exact family whose gap is first order in the mismatch. A separate finite-confounding family shows when the lost joint information changes an identified causal sign. These results distinguish local marginal sharpness from joint attainability after combining environments.