In Online Convex Optimization (OCO), when the stochastic gradient has a finite variance, many algorithms provably work and guarantee a sublinear regret. However, limited results are known if the gradient estimate has a heavy tail, i.e., the stochastic gradient only admits a finite $\mathsf{p}$-th central moment for some $\mathsf{p}\in\left(1,2\right]$. Motivated by it, this work examines different old algorithms for OCO (e.g., Online Gradient Descent) in the more challenging heavy-tailed setting. Under the standard bounded domain assumption, we establish new regrets for these classical methods without any algorithmic modification. Remarkably, these regret bounds are fully optimal in all parameters (can be achieved even without knowing $\mathsf{p}$), suggesting that OCO with heavy tails can be solved effectively without any extra operation (e.g., gradient clipping). Our new results have several applications. A particularly interesting one is the first provable convergence result for nonsmooth nonconvex optimization under heavy-tailed noise without gradient clipping. Furthermore, we explore broader settings (e.g., smooth OCO) and extend our ideas to optimistic algorithms to handle different cases simultaneously.

Deep neural networks can memorize corrupted labels, making data quality critical for model performance, yet real-world datasets are frequently compromised by both label noise and input noise. This paper proposes a mutual information-based framework for data selection under hybrid noise scenarios that quantifies statistical dependencies between inputs and labels. We compute each sample's pointwise contribution to the overall mutual information and find that lower contributions indicate noisy or mislabeled instances. Empirical validation on MNIST with different synthetic noise settings demonstrates that the method effectively filters low-quality samples. Under label corruption, training on high-MI samples improves classification accuracy by up to 15\% compared to random sampling. Furthermore, the method exhibits robustness to benign input modifications, preserving semantically valid data while filtering truly corrupted samples.

Recent studies have shown that deep learning models are vulnerable to membership inference attacks (MIAs), which aim to infer whether a data record was used to train a target model or not. T o analyze and study these vulnerabilities, various MIA methods have been proposed. Despite the significance and popularity of MIAs, existing works on MIAs are limited in providing guarantees on the false discovery rate (FDR), which refers to the expected proportion of false discoveries among the identified positive discoveries. However, it is very challenging to ensure the false discovery rate guarantees, because the underlying distribution is usually unknown, and the estimated non-member probabilities often exhibit interdependence. T o tackle the above challenges, in this paper, we design a novel membership inference attack method, which can provide the guarantees on the false discovery rate. Additionally, we show that our method can also provide the marginal probability guarantee on labeling true non-member data as member data. Notably, our method can work as a wrapper that can be seamlessly integrated with existing MIA methods in a post-hoc manner, while also providing the FDR control. W e perform the theoretical analysis for our method. Extensive experiments in various settings (e.g., the black-box setting and the lifelong learning setting) are also conducted to verify the desirable performance of our method.

Large language models (LLMs) generate text embeddings from text data, producing vector representations that capture the semantic meaning and contextual relationships of words. However, the high dimensionality of these embeddings often impedes efficiency and drives up computational cost in downstream tasks. To address this, we propose AutoEncoder-Augmented Learning with Text (AEALT), a supervised, factor-augmented framework that incorporates dimension reduction directly into pre-trained LLM workflows. First, we extract embeddings from text documents; next, we pass them through a supervised augmented autoencoder to learn low-dimensional, task-relevant latent factors. By modeling the nonlinear structure of complex embeddings, AEALT outperforms conventional deep-learning approaches that rely on raw embeddings. We validate its broad applicability with extensive experiments on classification, anomaly detection, and prediction tasks using multiple real-world public datasets. Numerical results demonstrate that AEALT yields substantial gains over both vanilla embeddings and several standard dimension reduction methods.

Ensuring the safety of autonomous vehicles (AVs) is paramount in their development and deployment. Safety-critical scenarios pose more severe challenges, necessitating efficient testing methods to validate AVs safety. This study focuses on designing an accelerated testing algorithm for AVs in safety-critical scenarios, enabling swift recognition of their driving capabilities. First, typical logical scenarios were extracted from real-world crashes in the China In-depth Mobility Safety Study-Traffic Accident (CIMSS-TA) database, obtaining pre-crash features through reconstruction. Second, Baidu Apollo, an advanced black-box automated driving system (ADS) is integrated to control the behavior of the ego vehicle. Third, we proposed an adaptive large-variable neighborhood-simulated annealing algorithm (ALVNS-SA) to expedite the testing process. Experimental results demonstrate a significant enhancement in testing efficiency when utilizing ALVNS-SA. It achieves an 84.00% coverage of safety-critical scenarios, with crash scenario coverage of 96.83% and near-crash scenario coverage of 92.07%. Compared to genetic algorithm (GA), adaptive large neighborhood-simulated annealing algorithm (ALNS-SA), and random testing, ALVNS-SA exhibits substantially higher coverage in safety-critical scenarios.

--Personalised music-based interventions offer a powerful means of supporting motor rehabilitation by dynamically tailoring auditory stimuli to provide external timekeeping cues, modulate affective states, and stabilise gait patterns. Gener-alisable Brain-Computer Interfaces (BCIs) thus hold promise for adapting these interventions across individuals. However, inter-subject variability in EEG signals, further compounded by movement-induced artefacts and motor planning differences, hinders the generalisability of BCIs and results in lengthy calibration processes. We propose Individual T angent Space Alignment (ITSA), a novel pre-alignment strategy incorporating subject-specific recentering, distribution matching, and supervised rotational alignment to enhance cross-subject generalisation. Using leave-one-subject-out cross-validation, 'ITSA' demonstrates significant performance improvements across subjects and conditions. The parallel fusion approach shows the greatest enhancement over its sequential counterpart, with robust performance maintained across varying data conditions and electrode configurations. The code will be made publicly available at the time of publication. Brain-computer interfaces (BCI) are effective tools for motor rehabilitation and understanding musical stimulus effects on motor function [1]-[4]. In stroke rehabilitation, BCIs decode the user's intention from brain electrical activity to provide sensorimotor feedback and enable control of external devices or motor functions [5], [6]. The use of these BCI strategies for motor rehabilitation has been grouped into either assistive or rehabilitative. The former focuses on bypassing the damaged neuronal pathways to provide alternative control of the external devices, whereas the latter aims to exploit neuro-plasticity by promoting the recovery of damaged pathways and therefore restoring impaired motor functions [5]. Electroen-cephalography signals are often used for the input of BCIs as they provide portable, non-invasive, low-cost solutions and have high temporal resolution [7].

We propose a joint learning framework for Byzantine-resilient spectrum sensing and secure intelligent reflecting surface (IRS)--assisted opportunistic access under channel state information (CSI) uncertainty. The sensing stage performs logit-domain Bayesian updates with trimmed aggregation and attention-weighted consensus, and the base station (BS) fuses network beliefs with a conservative minimum rule, preserving detection accuracy under a bounded number of Byzantine users. Conditioned on the sensing outcome, we pose downlink design as sum mean-squared error (MSE) minimization under transmit-power and signal-leakage constraints and jointly optimize the BS precoder, IRS phase shifts, and user equalizers. With partial (or known) CSI, we develop an augmented-Lagrangian alternating algorithm with projected updates and provide provable sublinear convergence, with accelerated rates under mild local curvature. With unknown CSI, we perform constrained Bayesian optimization (BO) in a geometry-aware low-dimensional latent space using Gaussian process (GP) surrogates; we prove regret bounds for a constrained upper confidence bound (UCB) variant of the BO module, and demonstrate strong empirical performance of the implemented procedure. Simulations across diverse network conditions show higher detection probability at fixed false-alarm rate under adversarial attacks, large reductions in sum MSE for honest users, strong suppression of eavesdropper signal power, and fast convergence. The framework offers a practical path to secure opportunistic communication that adapts to CSI availability while coherently coordinating sensing and transmission through joint learning.

Hyperspectral imaging (HSI) is an advanced sensing modality that simultaneously captures spatial and spectral information, enabling non-invasive, label-free analysis of material, chemical, and biological properties. This Primer presents a comprehensive overview of HSI, from the underlying physical principles and sensor architectures to key steps in data acquisition, calibration, and correction. We summarize common data structures and highlight classical and modern analysis methods, including dimensionality reduction, classification, spectral unmixing, and AI-driven techniques such as deep learning. Representative applications across Earth observation, precision agriculture, biomedicine, industrial inspection, cultural heritage, and security are also discussed, emphasizing HSI's ability to uncover sub-visual features for advanced monitoring, diagnostics, and decision-making. Persistent challenges, such as hardware trade-offs, acquisition variability, and the complexity of high-dimensional data, are examined alongside emerging solutions, including computational imaging, physics-informed modeling, cross-modal fusion, and self-supervised learning. Best practices for dataset sharing, reproducibility, and metadata documentation are further highlighted to support transparency and reuse. Looking ahead, we explore future directions toward scalable, real-time, and embedded HSI systems, driven by sensor miniaturization, self-supervised learning, and foundation models. As HSI evolves into a general-purpose, cross-disciplinary platform, it holds promise for transformative applications in science, technology, and society.

Reliable digital twins of lithium-ion batteries must achieve high physical fidelity with sub-millisecond speed. In this work, we benchmark three operator-learning surrogates for the Single Particle Model (SPM): Deep Operator Networks (DeepONets), Fourier Neural Operators (FNOs) and a newly proposed parameter-embedded Fourier Neural Operator (PE-FNO), which conditions each spectral layer on particle radius and solid-phase diffusivity. Models are trained on simulated trajectories spanning four current families (constant, triangular, pulse-train, and Gaussian-random-field) and a full range of State-of-Charge (SOC) (0 % to 100 %). DeepONet accurately replicates constant-current behaviour but struggles with more dynamic loads. The basic FNO maintains mesh invariance and keeps concentration errors below 1 %, with voltage mean-absolute errors under 1.7 mV across all load types. Introducing parameter embedding marginally increases error, but enables generalisation to varying radii and diffusivities. PE-FNO executes approximately 200 times faster than a 16-thread SPM solver. Consequently, PE-FNO's capabilities in inverse tasks are explored in a parameter estimation task with Bayesian optimisation, recovering anode and cathode diffusivities with 1.14 % and 8.4 % mean absolute percentage error, respectively, and 0.5918 percentage points higher error in comparison with classical methods. These results pave the way for neural operators to meet the accuracy, speed and parametric flexibility demands of real-time battery management, design-of-experiments and large-scale inference. PE-FNO outperforms conventional neural surrogates, offering a practical path towards high-speed and high-fidelity electrochemical digital twins.

Symbolic Regression (SR) is a well-established framework for generating interpretable or white-box predictive models. Although SR has been successfully applied to create interpretable estimates of the average of the outcome, it is currently not well understood how it can be used to estimate the relationship between variables at other points in the distribution of the target variable. Such estimates of e.g. the median or an extreme value provide a fuller picture of how predictive variables affect the outcome and are necessary in high-stakes, safety-critical application domains. This study introduces Symbolic Quantile Regression (SQR), an approach to predict conditional quantiles with SR. In an extensive evaluation, we find that SQR outperforms transparent models and performs comparably to a strong black-box baseline without compromising transparency. We also show how SQR can be used to explain differences in the target distribution by comparing models that predict extreme and central outcomes in an airline fuel usage case study. We conclude that SQR is suitable for predicting conditional quantiles and understanding interesting feature influences at varying quantiles.