The interplay of robustness and generalization in quantum machine learning

While adversarial robustness and generalization have individually received substantial attention in the recent literature on quantum machine learning, their interplay is much less explored. In this chapter, we address this interplay for variational quantum models, which were recently proposed as function approximators in supervised learning. We discuss recent results quantifying both robustness and generalization via Lipschitz bounds, which explicitly depend on model parameters. Thus, they give rise to a regularization-based training approach for robust and generalizable quantum models, highlighting the importance of trainable data encoding strategies. The practical implications of the theoretical results are demonstrated with an application to time series analysis.

Why Do Class-Dependent Evaluation Effects Occur with Time Series Feature Attributions? A Synthetic Data Investigation

Evaluating feature attribution methods represents a critical challenge in explainable AI (XAI), as researchers typically rely on perturbation-based metrics when ground truth is unavailable. However, recent work demonstrates that these evaluation metrics can show different performance across predicted classes within the same dataset. These "class-dependent evaluation effects" raise questions about whether perturbation analysis reliably measures attribution quality, with direct implications for XAI method development and the trustworthiness of evaluation techniques. We investigate under which conditions these class-dependent effects arise by conducting controlled experiments with synthetic time series data where ground truth feature locations are known. We systematically vary feature types and class contrasts across binary classification tasks, then compare perturbation-based degradation scores with ground truth-based precision-recall metrics using multiple attribution methods. Our experiments demonstrate that class-dependent effects emerge with both evaluation approaches even in simple scenarios with temporally localized features, triggered by basic variations in feature amplitude or temporal extent between classes. Most critically, we find that perturbation-based and ground truth metrics frequently yield contradictory assessments of attribution quality across classes, with weak correlations between evaluation approaches. These findings suggest that researchers should interpret perturbation-based metrics with care, as they may not always align with whether attributions correctly identify discriminating features. These findings reveal opportunities to reconsider what attribution evaluation actually measures and to develop more comprehensive evaluation frameworks that capture multiple dimensions of attribution quality.

Temporal cross-validation impacts multivariate time series subsequence anomaly detection evaluation

Evaluating anomaly detection in multivariate time series (MTS) requires careful consideration of temporal dependencies, particularly when detecting subsequence anomalies common in fault detection scenarios. While time series cross-validation (TSCV) techniques aim to preserve temporal ordering during model evaluation, their impact on classifier performance remains underexplored. This study systematically investigates the effect of TSCV strategy on the precision-recall characteristics of classifiers trained to detect fault-like anomalies in MTS datasets. We compare walk-forward (WF) and sliding window (SW) methods across a range of validation partition configurations and classifier types, including shallow learners and deep learning (DL) classifiers. Results show that SW consistently yields higher median AUC-PR scores and reduced fold-to-fold performance variance, particularly for deep architectures sensitive to localized temporal continuity. Furthermore, we find that classifier generalization is sensitive to the number and structure of temporal partitions, with overlapping windows preserving fault signatures more effectively at lower fold counts. A classifier-level stratified analysis reveals that certain algorithms, such as random forests (RF), maintain stable performance across validation schemes, whereas others exhibit marked sensitivity. This study demonstrates that TSCV design in benchmarking anomaly detection models on streaming time series and provide guidance for selecting evaluation strategies in temporally structured learning environments.

A Survey of Retentive Network

Retentive Network (RetNet) represents a significant advancement in neural network architecture, offering an efficient alternative to the Transformer. While Transformers rely on self-attention to model dependencies, they suffer from high memory costs and limited scalability when handling long sequences due to their quadratic complexity. To mitigate these limitations, RetNet introduces a retention mechanism that unifies the inductive bias of recurrence with the global dependency modeling of attention. This mechanism enables linear-time inference, facilitates efficient modeling of extended contexts, and remains compatible with fully parallelizable training pipelines. RetNet has garnered significant research interest due to its consistently demonstrated cross-domain effectiveness, achieving robust performance across machine learning paradigms including natural language processing, speech recognition, and time-series analysis. However, a comprehensive review of RetNet is still missing from the current literature. This paper aims to fill that gap by offering the first detailed survey of the RetNet architecture, its key innovations, and its diverse applications. We also explore the main challenges associated with RetNet and propose future research directions to support its continued advancement in both academic research and practical deployment.

Anomaly Detection and Generation with Diffusion Models: A Survey

Anomaly detection (AD) plays a pivotal role across diverse domains, including cybersecurity, finance, healthcare, and industrial manufacturing, by identifying unexpected patterns that deviate from established norms in real-world data. Recent advancements in deep learning, specifically diffusion models (DMs), have sparked significant interest due to their ability to learn complex data distributions and generate high-fidelity samples, offering a robust framework for unsupervised AD. In this survey, we comprehensively review anomaly detection and generation with diffusion models (ADGDM), presenting a tutorial-style analysis of the theoretical foundations and practical implementations and spanning images, videos, time series, tabular, and multimodal data. Crucially, unlike existing surveys that often treat anomaly detection and generation as separate problems, we highlight their inherent synergistic relationship. We reveal how DMs enable a reinforcing cycle where generation techniques directly address the fundamental challenge of anomaly data scarcity, while detection methods provide critical feedback to improve generation fidelity and relevance, advancing both capabilities beyond their individual potential. A detailed taxonomy categorizes ADGDM methods based on anomaly scoring mechanisms, conditioning strategies, and architectural designs, analyzing their strengths and limitations. We final discuss key challenges including scalability and computational efficiency, and outline promising future directions such as efficient architectures, conditioning strategies, and integration with foundation models (e.g., visual-language models and large language models). By synthesizing recent advances and outlining open research questions, this survey aims to guide researchers and practitioners in leveraging DMs for innovative AD solutions across diverse applications.

Tailored Architectures for Time Series Forecasting: Evaluating Deep Learning Models on Gaussian Process-Generated Data

Developments in Deep Learning have significantly improved time series forecasting by enabling more accurate modeling of complex temporal dependencies inherent in sequential data. The effectiveness of such models is often demonstrated on limited sets of specific real-world data. Although this allows for comparative analysis, it still does not demonstrate how specific data characteristics align with the architectural strengths of individual models. Our research aims at uncovering clear connections between time series characteristics and particular models. We introduce a novel dataset generated using Gaussian Processes, specifically designed to display distinct, known characteristics for targeted evaluations of model adaptability to them. Furthermore, we present TimeFlex, a new model that incorporates a modular architecture tailored to handle diverse temporal dynamics, including trends and periodic patterns. This model is compared to current state-of-the-art models, offering a deeper understanding of how models perform under varied time series conditions.

Almost-Optimal Local-Search Methods for Sparse Tensor PCA

Local-search methods are widely employed in statistical applications, yet interestingly, their theoretical foundations remain rather underexplored, compared to other classes of estimators such as low-degree polynomials and spectral methods. Of note, among the few existing results recent studies have revealed a significant "local-computational" gap in the context of a well-studied sparse tensor principal component analysis (PCA), where a broad class of local Markov chain methods exhibits a notable underperformance relative to other polynomial-time algorithms. In this work, we propose a series of local-search methods that provably "close" this gap to the best known polynomial-time procedures in multiple regimes of the model, including and going beyond the previously studied regimes in which the broad family of local Markov chain methods underperforms. Our framework includes: (1) standard greedy and randomized greedy algorithms applied to the (regularized) posterior of the model; and (2) novel random-threshold variants, in which the randomized greedy algorithm accepts a proposed transition if and only if the corresponding change in the Hamiltonian exceeds a random Gaussian threshold-rather that if and only if it is positive, as is customary. The introduction of the random thresholds enables a tight mathematical analysis of the randomized greedy algorithm's trajectory by crucially breaking the dependencies between the iterations, and could be of independent interest to the community.

Multivariate Long-term Time Series Forecasting with Fourier Neural Filter

Multivariate long-term time series forecasting has been suffering from the challenge of capturing both temporal dependencies within variables and spatial correlations across variables simultaneously. Current approaches predominantly repurpose backbones from natural language processing or computer vision (e.g., Transformers), which fail to adequately address the unique properties of time series (e.g., periodicity). The research community lacks a dedicated backbone with temporal-specific inductive biases, instead relying on domain-agnostic backbones supplemented with auxiliary techniques (e.g., signal decomposition). We introduce FNF as the backbone and DBD as the architecture to provide excellent learning capabilities and optimal learning pathways for spatio-temporal modeling, respectively. Our theoretical analysis proves that FNF unifies local time-domain and global frequency-domain information processing within a single backbone that extends naturally to spatial modeling, while information bottleneck theory demonstrates that DBD provides superior gradient flow and representation capacity compared to existing unified or sequential architectures. Our empirical evaluation across 11 public benchmark datasets spanning five domains (energy, meteorology, transportation, environment, and nature) confirms state-of-the-art performance with consistent hyperparameter settings. Notably, our approach achieves these results without any auxiliary techniques, suggesting that properly designed neural architectures can capture the inherent properties of time series, potentially transforming time series modeling in scientific and industrial applications.

crossMoDA Challenge: Evolution of Cross-Modality Domain Adaptation Techniques for Vestibular Schwannoma and Cochlea Segmentation from 2021 to 2023

The cross-Modality Domain Adaptation (crossMoDA) challenge series, initiated in 2021 in conjunction with the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), focuses on unsupervised cross-modality segmentation, learning from contrast-enhanced T1 (ceT1) and transferring to T2 MRI. The task is an extreme example of domain shift chosen to serve as a meaningful and illustrative benchmark. From a clinical application perspective, it aims to automate Vestibular Schwannoma (VS) and cochlea segmentation on T2 scans for more cost-effective VS management. Over time, the challenge objectives have evolved to enhance its clinical relevance. The challenge evolved from using single-institutional data and basic segmentation in 2021 to incorporating multi-institutional data and Koos grading in 2022, and by 2023, it included heterogeneous routine data and sub-segmentation of intra- and extra-meatal tumour components. In this work, we report the findings of the 2022 and 2023 editions and perform a retrospective analysis of the challenge progression over the years. The observations from the successive challenge contributions indicate that the number of outliers decreases with an expanding dataset. This is notable since the diversity of scanning protocols of the datasets concurrently increased. The winning approach of the 2023 edition reduced the number of outliers on the 2021 and 2022 testing data, demonstrating how increased data heterogeneity can enhance segmentation performance even on homogeneous data. However, the cochlea Dice score declined in 2023, likely due to the added complexity from tumour sub-annotations affecting overall segmentation performance. While progress is still needed for clinically acceptable VS segmentation, the plateauing performance suggests that a more challenging cross-modal task may better serve future benchmarking.

From Images to Signals: Are Large Vision Models Useful for Time Series Analysis?

Transformer-based models have gained increasing attention in time series research, driving interest in Large Language Models (LLMs) and foundation models for time series analysis. As the field moves toward multi-modality, Large Vision Models (LVMs) are emerging as a promising direction. In the past, the effectiveness of Transformer and LLMs in time series has been debated. When it comes to LVMs, a similar question arises: are LVMs truely useful for time series analysis? To address it, we design and conduct the first principled study involving 4 LVMs, 8 imaging methods, 18 datasets and 26 baselines across both high-level (classification) and low-level (forecasting) tasks, with extensive ablation analysis. Our findings indicate LVMs are indeed useful for time series classification but face challenges in forecasting. Although effective, the contemporary best LVM forecasters are limited to specific types of LVMs and imaging methods, exhibit a bias toward forecasting periods, and have limited ability to utilize long look-back windows. We hope our findings could serve as a cornerstone for future research on LVM- and multimodal-based solutions to different time series tasks.