Characterizing the differential privacy (DP) of learning algorithms has become a major challenge in recent years. In parallel, many studies suggested investigating the behavior of stochastic gradient descent (SGD) with heavy-tailed noise, both as a model for modern deep learning models and to improve their performance. However, most DP bounds focus on light-tailed noise, where satisfactory guarantees have been obtained but the proposed techniques do not directly extend to the heavy-tailed setting. Recently, the first DP guarantees for heavy-tailed SGD were obtained. These results provide $(0,δ)$-DP guarantees without requiring gradient clipping. Despite casting new light on the link between DP and heavy-tailed algorithms, these results have a strong dependence on the number of parameters and cannot be extended to other DP notions like the well-established Rényi differential privacy (RDP). In this work, we propose to address these limitations by deriving the first RDP guarantees for heavy-tailed SDEs, as well as their discretized counterparts. Our framework is based on new Rényi flow computations and the use of well-established fractional Poincaré inequalities. Under the assumption that such inequalities are satisfied, we obtain DP guarantees that have a much weaker dependence on the dimension compared to prior art.

Ordinary differential equations (ODEs) are a conventional way to describe the observed dynamics of physical systems. Scientists typically hypothesize about dynamical behavior, propose a mathematical model, and compare its predictions to data. However, modern computing and algorithmic advances now enable purely data-driven learning of governing dynamics directly from observations. In data-driven settings, one learns the ODE's right-hand side (RHS). Dense measurements are often assumed, yet high temporal resolution is typically both cumbersome and expensive. Consequently, one usually has only sparsely sampled data. In this work we introduce ChaosODE (CODE), a Polynomial Chaos ODE Expansion in which we use an arbitrary Polynomial Chaos Expansion (aPCE) for the ODE's right-hand side, resulting in a global orthonormal polynomial representation of dynamics. We evaluate the performance of CODE in several experiments on the Lotka-Volterra system, across varying noise levels, initial conditions, and predictions far into the future, even on previously unseen initial conditions. CODE exhibits remarkable extrapolation capabilities even when evaluated under novel initial conditions and shows advantages compared to well-examined methods using neural networks (NeuralODE) or kernel approximators (KernelODE) as the RHS representer. We observe that the high flexibility of NeuralODE and KernelODE degrades extrapolation capabilities under scarce data and measurement noise. Finally, we provide practical guidelines for robust optimization of dynamics-learning problems and illustrate them in the accompanying code.

The Gini score is a popular statistical tool in model validation. The Gini score has originally been introduced and used for binary responses Y {0, 1}, and there are many equivalent formulations of the (binary) Gini score such as the receiver operating curve (ROC) and the area under the curve (AUC); see, e.g., [Bamber (1975)], [Hanley-McNeil (1982)] and [Fawcett (2006)]. These different formulations are also equivalent to the Wilcoxon-Mann-Whitney's U statistic, see [Hanley-McNeil (1982)], [DeLong et al. (1988)], [Byrne (2016)], and to [Somers (1962)]'s D, see [Newson (2002)]. Thus, there are at least five equivalent formulations of the Gini score in a binary context, and there is a broad literature on its behavior which is well understood. When it comes to general real-valued responses, things become more difficult, and definitions and results on the Gini score are mainly found in the credit risk and actuarial literature. In this stream of literature, the Gini score has been introduced by [Gourieroux-Jasiak (2007)], [Frees et al. (2011), Frees et al. (2013)]. Furthermore, in the real-valued setting the Gini score is studied in much detail in [Denuit et al. (2019)] and [Denuit-Trufin (2021)]. The Gini score is a statistic that assesses whether a given risk ranking is correct.

Biological data sets are often high-dimensional, noisy, and governed by complex interactions among sparse signals. This poses major challenges for interpretability and reliable feature selection. Tasks such as identifying motif interactions in genomics exemplify these difficulties, as only a small subset of biologically relevant features (e.g., motifs) are typically active, and their effects are often non-linear and context-dependent. While statistical approaches often result in more interpretable models, deep learning models have proven effective in modeling complex interactions and prediction accuracy, yet their black-box nature limits interpretability. We introduce BaGGLS, a flexible and interpretable probabilistic binary regression model designed for high-dimensional biological inference involving feature interactions. BaGGLS incorporates a Bayesian group global-local shrinkage prior, aligned with the group structure introduced by interaction terms. This prior encourages sparsity while retaining interpretability, helping to isolate meaningful signals and suppress noise. To enable scalable inference, we employ a partially factorized variational approximation that captures posterior skewness and supports efficient learning even in large feature spaces. In extensive simulations, we can show that BaGGLS outperforms the other methods with regard to interaction detection and is many times faster than MCMC sampling under the horseshoe prior. We also demonstrate the usefulness of BaGGLS in the context of interaction discovery from motif scanner outputs and noisy attribution scores from deep learning models. This shows that BaGGLS is a promising approach for uncovering biologically relevant interaction patterns, with potential applicability across a range of high-dimensional tasks in computational biology.

Bayesian Optimization is critically vulnerable to extreme outliers. Existing provably robust methods typically assume a bounded cumulative corruption budget, which makes them defenseless against even a single corruption of sufficient magnitude. To address this, we introduce a new adversary whose budget is only bounded in the frequency of corruptions, not in their magnitude. We then derive RCGP-UCB, an algorithm coupling the famous upper confidence bound (UCB) approach with a Robust Conjugate Gaussian Process (RCGP). We present stable and adaptive versions of RCGP-UCB, and prove that they achieve sublinear regret in the presence of up to $O(T^{1/2})$ and $O(T^{1/3})$ corruptions with possibly infinite magnitude. This robustness comes at near zero cost: without outliers, RCGP-UCB's regret bounds match those of the standard GP-UCB algorithm.

Understanding feature-outcome associations in high-dimensional data remains challenging when relationships vary across subpopulations, yet standard methods assuming global associations miss context-dependent patterns, reducing statistical power and interpretability. We develop a geometric decomposition framework offering two strategies for partitioning inference problems into regional analyses on data-derived Riemannian graphs. Gradient flow decomposition uses path-monotonicity-validated discrete Morse theory to partition samples into gradient flow cells where outcomes exhibit monotonic behavior. Co-monotonicity decomposition utilizes vertex-level coefficients that provide context-dependent versions of the classical Pearson correlation: these coefficients measure edge-based directional concordance between outcome and features, or between feature pairs, defining embeddings of samples into association space. These embeddings induce Riemannian k-NN graphs on which biclustering identifies co-monotonicity cells (coherent regions) and feature modules. This extends naturally to multi-modal integration across multiple feature sets. Both strategies apply independently or jointly, with Bayesian posterior sampling providing credible intervals.

To unveil the hidden mechanisms under LM's incapability to learn long-tail domain-specific knowledge, we investigate the behaviors of a GPT on the Wikipedia dataset.

Amid a blackout of data due to the government shutdown, the $5tn chipmaker's report took on wider significance Markets expectations around Wednesday's quarterly earnings report by the most valuable publicly traded company in the world had risen to a fever pitch. Anxiety over billions in investment in artificial intelligence pervaded, in part because the US has been starved of reliable economic data by the recent government shutdown. Investors hoped that both questions would be in part answered by Nvidia's earnings and by a jobs report due on Thursday morning. "This is a'So goes Nvidia, so goes the market' kind of report," Scott Martin, chief investment officer at Kingsview Wealth Management, told Bloomberg in a concise summary of market sentiment. The prospect of a market mood swing had built in advance of the earnings call, with options markets anticipating Nvidia's shares could move 6%, or $280bn in value, up or down.

We propose a novel and efficient search algorithm which finds initial centers that can be used subsequently for the local search algorithm.

After weeks of silence, NASA has officially dismissed speculation that 3I/ATLAS has anything to do with aliens. After the temporary shutdown of the US government, NASA has finally started its nonessential work back up. It's starting off with a bang: The agency called a press conference to show its hitherto reserved images of the interstellar object 3I/ATLAS. NASA scientists also confirmed that 3I/ATLAS is in fact a comet, contrary to the speculations about alien technology flooding the internet. During the broadcast, a panel of scientists showed the results of observations obtained by different NASA missions across various points in the journey 3I/ATLAS has taken .