While exact reliability computation for binarystate networks is NP-hard/#P-hard, existing approximation methods face critical tradeoffs between accuracy, scalability, and data efficiency. This study evaluates 20 machine learning methods across three reliability regimes--full range (0.0-1.0), high reliability (0.9-1.0), and ultra-high reliability (0.99-1.0)--to address these gaps. We demonstrate that large-scale networks with arc reliability 0.9 exhibit near-unity system reliability, enabling computational simplifications. Further, we establish a datasetscale-driven paradigm for algorithm selection: Artificial Neural Networks (ANN) excel with limited data (size < m), while Polynomial Regression (PR) achieves superior accuracy in data-rich environments (size m). Our findings reveal ANN's Test-MSE of 7.24E 05 at 30,000 samples and PR's optimal performance (5.61E 05) at 40,000 samples, outperforming traditional Monte Carlo simulations. These insights provide actionable guidelines for balancing accuracy, interpretability, and computational efficiency in reliability engineering, with implications for infrastructure resilience and system optimization. Keywords: Binary-State Networks; Network Reliability Approximated Function; Reliability Thresholds; Dataset Scalability; Artificial Neural Networks (ANN); Polynomial Regression; Monte Carlo Simulation (MCS); Binary-Addition-Tree Algorithm (BAT); BAT-MCS 1. INTRODUCTION Modern infrastructure systems--from power grids and communication networks to IoT ecosystems--demand rigorous reliability analysis to ensure operational resilience. These systems are often modeled as binary-state networks, where components (arcs/nodes) operate in either functional (1) or failed (0) states [1, 2, 3]. Within this paradigm, network reliability--the probability of maintaining 2 connectivity between specified nodes under given conditions--serves as a critical performance metric [4, 5-7].

A popular machine-learning model for regression tasks, including stock-market prediction, weather forecasting and real-estate pricing, is the classical support vector regression (SVR). However, a practically realisable quantum SVR remains to be formulated. We devise annealing-based algorithms, namely simulated and quantum-classical hybrid, for training two SVR models and compare their empirical performances against the SVR implementation of Python's scikit-learn package for facial-landmark detection (FLD), a particular use case for SVR. Our method is to derive a quadratic-unconstrained-binary formulation for the optimisation problem used for training a SVR model and solve this problem using annealing. Using D-Wave's hybrid solver, we construct a quantum-assisted SVR model, thereby demonstrating a slight advantage over classical models regarding FLD accuracy. Furthermore, we observe that annealing-based SVR models predict landmarks with lower variances compared to the SVR models trained by gradient-based methods. Our work is a proof-of-concept example for applying quantum-assisted SVR to a supervised-learning task with a small training dataset.

The process generates substantial amounts of data with highly complex structures, leading to the development of numerous nonlinear statistical methods. However, most of these methods rely on computations involving large-scale dense kernel matrices. This dependence poses significant challenges in meeting the high computational demands and real-time responsiveness required by online monitoring systems. To alleviate the computational burden of dense large-scale matrix multiplication, we incorporate the bootstrap sampling concept into random feature mapping and propose a novel random Bernoulli principal component analysis method to efficiently capture nonlinear patterns in the process. We derive a convergence bound for the kernel matrix approximation constructed using random Bernoulli features, ensuring theoretical robustness. Subsequently, we design four fast process monitoring methods based on random Bernoulli principal component analysis to extend its nonlinear capabilities for handling diverse fault scenarios. Finally, numerical experiments and real-world data analyses are conducted to evaluate the performance of the proposed methods. Results demonstrate that the proposed methods offer excellent scalability and reduced computational complexity, achieving substantial cost savings with minimal performance loss compared to traditional kernel-based approaches.

Contextual stochastic optimization provides a framework for decision-making under uncertainty incorporating observable contextual information through covariates. We analyze statistical inference for weighted sample average approximation (wSAA), a widely-used method for solving contextual stochastic optimization problems. We first establish central limit theorems for wSAA estimates of optimal values when problems can be solved exactly, characterizing how estimation uncertainty scales with covariate sample size. We then investigate practical scenarios with computational budget constraints, revealing a fundamental tradeoff between statistical accuracy and computational cost as sample sizes increase. Through central limit theorems for budget-constrained wSAA estimates, we precisely characterize this statistical-computational tradeoff. We also develop "over-optimizing" strategies for solving wSAA problems that ensure valid statistical inference. Extensive numerical experiments on both synthetic and real-world datasets validate our theoretical findings.

We study how multi-head softmax attention models are trained to perform in-context learning on linear data. Through extensive empirical experiments and rigorous theoretical analysis, we demystify the emergence of elegant attention patterns: a diagonal and homogeneous pattern in the key-query (KQ) weights, and a last-entry-only and zero-sum pattern in the output-value (OV) weights. Remarkably, these patterns consistently appear from gradient-based training starting from random initialization. Our analysis reveals that such emergent structures enable multi-head attention to approximately implement a debiased gradient descent predictor -- one that outperforms single-head attention and nearly achieves Bayesian optimality up to proportional factor. Furthermore, compared to linear transformers, the softmax attention readily generalizes to sequences longer than those seen during training. We also extend our study to scenarios with non-isotropic covariates and multi-task linear regression. In the former, multi-head attention learns to implement a form of pre-conditioned gradient descent. In the latter, we uncover an intriguing regime where the interplay between head number and task number triggers a superposition phenomenon that efficiently resolves multi-task in-context learning. Our results reveal that in-context learning ability emerges from the trained transformer as an aggregated effect of its architecture and the underlying data distribution, paving the way for deeper understanding and broader applications of in-context learning.

Determining and Determining and verifying product provenance remains a critical verifying product provenance is a challenge in global supply chains, challenge in global supply chains, particularly as geopolitical conflicts as geopolitics and the lure of "don't ask, don't tell" with respect to and shifting borders create new incentives for misrepresentation the ecological and social cost creates incentives for misrepresentation of commodities, such as hiding the origin of illegally harvested of commodities, such as hiding the origin of illegally harvested timber or agriculture grown on illegally cleared land. Stable Isotope timber or agriculture grown on illegally cleared land. Ratio Analysis (SIRA), combined with Gaussian process regressionbased Product identification and provenance verification of traded natural isoscapes, has emerged as a powerful tool for geographic resources have emerged as promising research areas, with origin verification. However, the effectiveness of these models is often various combinations of methods used based on the specific natural constrained by data scarcity and suboptimal dataset selection. In resource sector and the level of granularity of species identification this work, we introduce a novel data valuation framework designed and origin-provenance determination. For example, for wood and to enhance the selection and utilization of training data for machine forest products, determining species identification and geographic learning models applied in SIRA. By prioritizing high-informative harvest provenance requires utilizing multiple testing methods and samples, our approach improves model robustness and predictive tools [5, 8, 20].

Decades of research have produced robust methods for unsupervised data visualization, yet supervised visualization$\unicode{x2013}$where expert labels guide representations$\unicode{x2013}$remains underexplored, as most supervised approaches prioritize classification over visualization. Recently, RF-PHATE, a diffusion-based manifold learning method leveraging random forests and information geometry, marked significant progress in supervised visualization. However, its lack of an explicit mapping function limits scalability and prevents application to unseen data, posing challenges for large datasets and label-scarce scenarios. To overcome these limitations, we introduce Random Forest Autoencoders (RF-AE), a neural network-based framework for out-of-sample kernel extension that combines the flexibility of autoencoders with the supervised learning strengths of random forests and the geometry captured by RF-PHATE. RF-AE enables efficient out-of-sample supervised visualization and outperforms existing methods, including RF-PHATE's standard kernel extension, in both accuracy and interpretability. Additionally, RF-AE is robust to the choice of hyper-parameters and generalizes to any kernel-based dimensionality reduction method.

Stochastic first-order methods for empirical risk minimization employ gradient approximations based on sampled data in lieu of exact gradients. Such constructions introduce noise into the learning dynamics, which can be corrected through variance-reduction techniques. There is increasing evidence in the literature that in many modern learning applications noise can have a beneficial effect on optimization and generalization. To this end, the recently proposed variance-reduction technique, alpha-SVRG [Yin et al., 2023] allows for fine-grained control of the level of residual noise in the learning dynamics, and has been reported to empirically outperform both SGD and SVRG in modern deep learning scenarios. By focusing on strongly convex environments, we first provide a unified convergence rate expression for alpha-SVRG under fixed learning rate, which reduces to that of either SGD or SVRG by setting alpha=0 or alpha=1, respectively. We show that alpha-SVRG has faster convergence rate compared to SGD and SVRG under suitable choice of alpha. Simulation results on linear regression validate our theory.

Federated Learning (FL) is an emerging decentralized learning paradigm that can partly address the privacy concern that cannot be handled by traditional centralized and distributed learning. Further, to make FL practical, it is also necessary to consider constraints such as fairness and robustness. However, existing robust FL methods often produce unfair models, and existing fair FL methods only consider one-level (client) fairness and are not robust to persistent outliers (i.e., injected outliers into each training round) that are common in real-world FL settings. We propose \texttt{FedTilt}, a novel FL that can preserve multi-level fairness and be robust to outliers. In particular, we consider two common levels of fairness, i.e., \emph{client fairness} -- uniformity of performance across clients, and \emph{client data fairness} -- uniformity of performance across different classes of data within a client. \texttt{FedTilt} is inspired by the recently proposed tilted empirical risk minimization, which introduces tilt hyperparameters that can be flexibly tuned. Theoretically, we show how tuning tilt values can achieve the two-level fairness and mitigate the persistent outliers, and derive the convergence condition of \texttt{FedTilt} as well. Empirically, our evaluation results on a suite of realistic federated datasets in diverse settings show the effectiveness and flexibility of the \texttt{FedTilt} framework and the superiority to the state-of-the-arts.

We propose the notion of empirical privacy variance and study it in the context of differentially private fine-tuning of language models. Specifically, we show that models calibrated to the same $(\varepsilon, \delta)$-DP guarantee using DP-SGD with different hyperparameter configurations can exhibit significant variations in empirical privacy, which we quantify through the lens of memorization. We investigate the generality of this phenomenon across multiple dimensions and discuss why it is surprising and relevant. Through regression analysis, we examine how individual and composite hyperparameters influence empirical privacy. The results reveal a no-free-lunch trade-off: existing practices of hyperparameter tuning in DP-SGD, which focus on optimizing utility under a fixed privacy budget, often come at the expense of empirical privacy. To address this, we propose refined heuristics for hyperparameter selection that explicitly account for empirical privacy, showing that they are both precise and practically useful. Finally, we take preliminary steps to understand empirical privacy variance. We propose two hypotheses, identify limitations in existing techniques like privacy auditing, and outline open questions for future research.