The spherical noise added to gradients in differentially private (DP) training undermines the performance of adaptive optimizers like AdaGrad and Adam, and hence many recent works have proposed algorithms to address this challenge. However, the empirical results in these works focus on simple tasks and models and the conclusions may not generalize to model training in practice. In this paper we survey several of these variants, and develop better theoretical intuition for them as well as perform empirical studies comparing them. We find that a common intuition of aiming for unbiased estimates of second moments of gradients in adaptive optimizers is misguided, and instead that a simple technique called scale-then-privatize (which does not achieve unbiased second moments) has more desirable theoretical behaviors and outperforms all other variants we study on a small-scale language model training task. We additionally argue that scale-then-privatize causes the noise addition to better match the application of correlated noise mechanisms which are more desirable to use in practice.

Accurate identification of meteoroid streams is central to understanding their origins and evolution. However, overlapping clusters and background noise hinder classification, an issue amplified for missions such as ESA's LUMIO that rely on meteor shower observations to infer lunar meteoroid impact parameters. This study evaluates the performance of the Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) algorithm for unsupervised meteoroid stream identification, comparing its outcomes with the established Cameras for All-Sky Meteor Surveillance (CAMS) look-up table method. We analyze the CAMS Meteoroid Orbit Database v3.0 using three feature vectors: LUTAB (CAMS geocentric parameters), ORBIT (heliocentric orbital elements), and GEO (adapted geocentric parameters). HDBSCAN is applied with varying minimum cluster sizes and two cluster selection methods (eom and leaf). To align HDBSCAN clusters with CAMS classifications, the Hungarian algorithm determines the optimal mapping. Clustering performance is assessed via the Silhouette score, Normalized Mutual Information, and F1 score, with Principal Component Analysis further supporting the analysis. With the GEO vector, HDBSCAN confirms 39 meteoroid streams, 21 strongly aligning with CAMS. The ORBIT vector identifies 30 streams, 13 with high matching scores. Less active showers pose identification challenges. The eom method consistently yields superior performance and agreement with CAMS. Although HDBSCAN requires careful selection of the minimum cluster size, it delivers robust, internally consistent clusters and outperforms the look-up table method in statistical coherence. These results underscore HDBSCAN's potential as a mathematically consistent alternative for meteoroid stream identification, although further validation is needed to assess physical validity.

Stochastic control problems in high dimensions are notoriously difficult to solve due to the curse of dimensionality. An alternative to traditional dynamic programming is Pontryagin's Maximum Principle (PMP), which recasts the problem as a system of Forward-Backward Stochastic Differential Equations (FBSDEs). In this paper, we introduce a formal framework for solving such problems with deep learning by defining a \textbf{Neural Hamiltonian Operator (NHO)}. This operator parameterizes the coupled FBSDE dynamics via neural networks that represent the feedback control and an ansatz for the value function's spatial gradient. We show how the optimal NHO can be found by training the underlying networks to enforce the consistency conditions dictated by the PMP. By adopting this operator-theoretic view, we situate the deep FBSDE method within the rigorous language of statistical inference, framing it as a problem of learning an unknown operator from simulated data. This perspective allows us to prove the universal approximation capabilities of NHOs under general martingale drivers and provides a clear lens for analyzing the significant optimization challenges inherent to this class of models.

We present an analysis of landscape features for predicting the performance of multi-objective combinatorial optimization algorithms. We consider features from the recently proposed compressed Pareto Local Optimal Solutions Networks (C-PLOS-net) model of combinatorial landscapes. The benchmark instances are a set of rmnk-landscapes with 2 and 3 objectives and various levels of ruggedness and objective correlation. We consider the performance of three algorithms -- Pareto Local Search (PLS), Global Simple EMO Optimizer (GSEMO), and Non-dominated Sorting Genetic Algorithm (NSGA-II) - using the resolution and hypervolume metrics. Our tailored analysis reveals feature combinations that influence algorithm performance specific to certain landscapes. This study provides deeper insights into feature importance, tailored to specific rmnk-landscapes and algorithms.

Automation in Security Operations Centers (SOCs) plays a prominent role in alert classification and incident escalation. However, automated methods must be robust in the presence of imbalanced input data, which can negatively affect performance. Additionally, automated methods should make explainable decisions. In this work, we evaluate the effect of label imbalance on the classification of network intrusion alerts. As our use-case we employ DeepCASE, the state-of-the-art method for automated alert classification. We show that label imbalance impacts both classification performance and correctness of the classification explanations offered by DeepCASE. We conclude tuning the detection rules used in SOCs can significantly reduce imbalance and may benefit the performance and explainability offered by alert post-processing methods such as DeepCASE. Therefore, our findings suggest that traditional methods to improve the quality of input data can benefit automation.

This paper provides a proof of the consistency of sparse grid quadrature for numerical integration of high dimensional distributions. In a first step, a transport map is learned that normalizes the distribution to a noise distribution on the unit cube. This step is built on the statistical learning theory of neural ordinary differential equations, which has been established recently. Secondly, the composition of the generative map with the quantity of interest is integrated numerically using the Clenshaw-Curtis sparse grid quadrature. A decomposition of the total numerical error in quadrature error and statistical error is provided. As main result it is proven in the framework of empirical risk minimization that all error terms can be controlled in the sense of PAC (probably approximately correct) learning and with high probability the numerical integral approximates the theoretical value up to an arbitrary small error in the limit where the data set size is growing and the network capacity is increased adaptively.

Accurately predicting magnetic behavior across diverse materials systems remains a longstanding challenge due to the complex interplay of structural and electronic factors and is pivotal for the accelerated discovery and design of next-generation magnetic materials. In this work, a refined descriptor is proposed that significantly improves the prediction of two critical magnetic properties -- magnetic ordering (Ferromagnetic vs. Ferrimagnetic) and magnetic moment per atom -- using only the structural information of materials. Unlike previous models limited to Mn-based or lanthanide-transition metal compounds, the present approach generalizes across a diverse dataset of 5741 stable, binary and ternary, ferromagnetic and ferrimagnetic compounds sourced from the Materials Project. Leveraging an enriched elemental vector representation and advanced feature engineering, including nonlinear terms and reduced matrix sparsity, the LightGBM-based model achieves an accuracy of 82.4% for magnetic ordering classification and balanced recall across FM and FiM classes, addressing a key limitation in prior studies. The model predicts magnetic moment per atom with a correlation coefficient of 0.93, surpassing the Hund's matrix and orbital field matrix descriptors. Additionally, it accurately estimates formation energy per atom, enabling assessment of both magnetic behavior and material stability. This generalized and computationally efficient framework offers a robust tool for high-throughput screening of magnetic materials with tailored properties.

Time series forecasting models have diverse real world applications (e.g., from electricity metrics to software workload). Latest foundational models trained for time series forecasting show strengths (e.g., for long sequences and in zero-shot settings). However, foundational model was not yet used for forecasting rare, spiky events, i.e., a challenging target because those are a corner case of extreme events. In this paper, we optimize a state-of-the-art foundational model to forecast sporadic or spiky production outages of high-performance machine learning services powering billions of client devices. We evaluate the forecasting errors of the foundational model compared with classical stochastic forecasting models (e.g., moving average and autoregressive). The analysis helps us understand how each of the evaluated models performs for the sporadic or spiky events. For example, it identifies the key patterns in the target data that are well tracked by the foundational model vs. each of the stochastic models. We use the models with optimal parameters to estimate a year-long outage statistics of a particular root cause with less than 6% value errors.

Scientific applications of machine learning often rely on small, specialized models tuned to particular domains. Such models often achieve excellent performance, but lack flexibility. Foundation models offer versatility, but typically underperform specialized approaches, especially on non-traditional modalities and long-tail domains. We propose MARVIS (Modality Adaptive Reasoning over VISualizations), a training-free method that enables even small vision-language models to predict any data modality with high accuracy. MARVIS transforms latent embedding spaces into visual representations and then leverages the spatial and fine-grained reasoning skills of VLMs to successfully interpret and utilize them. MARVIS achieves competitive performance on vision, audio, biological, and tabular domains using a single 3B parameter model, achieving results that beat Gemini by 16\% on average and approach specialized methods, without exposing personally identifiable information (P.I.I.) or requiring any domain-specific training. We open source our code and datasets at https://github.com/penfever/marvis

Data factorization methods have met with considerable success in discovering latent features of the signals encountered in wide-ranging applications. In this way, the representation bases, which make up the columns of the basis matrix or dictionary, are learned from the available samples of the target environment. An example is the sparse representation (SR) in which the dictionary is intended to best represent the data with a small number of atoms, much smaller than the dimension of the signal space. It has been shown that, in addition to a more informative representation of signals, imposing sparsity constraints on the representation coefficients can improve the generalization performance and the computational efficiency [1, 2, 3]. Furthermore, the sparse representation is more robust to noise, redundancy, and missing data. These features are mainly attributed to the fact that the intrinsic dimension of natural signals is usually much smaller than their apparent dimension and hence SR in an appropriate dictionary can extract these intrinsic features more efficiently. SR has been a successful strategy and has received considerable attention and achieved state-of-the-art results in many applications, e.g.