Recent advances have shown that sequential fine-tuning (SeqFT) of pre-trained vision transformers (ViTs), followed by classifier refinement using approximate distributions of class features, can be an effective strategy for class-incremental learning (CIL). However, this approach is susceptible to distribution drift, caused by the sequential optimization of shared backbone parameters. This results in a mismatch between the distributions of the previously learned classes and that of the updated model, ultimately degrading the effectiveness of classifier performance over time. To address this issue, we introduce a latent space transition operator and propose Sequential Learning with Drift Compensation (SLDC). SLDC aims to align feature distributions across tasks to mitigate the impact of drift. First, we present a linear variant of SLDC, which learns a linear operator by solving a regularized least-squares problem that maps features before and after fine-tuning. Next, we extend this with a weakly nonlinear SLDC variant, which assumes that the ideal transition operator lies between purely linear and fully nonlinear transformations. This is implemented using learnable, weakly nonlinear mappings that balance flexibility and generalization. To further reduce representation drift, we apply knowledge distillation (KD) in both algorithmic variants. Extensive experiments on standard CIL benchmarks demonstrate that SLDC significantly improves the performance of SeqFT. Notably, by combining KD to address representation drift with SLDC to compensate distribution drift, SeqFT achieves performance comparable to joint training across all evaluated datasets.

Modern deep learning models for forecasting groups of time series rely on increasingly longer observation windows. However, the benefit of increasing the window size is often simply attributed to capturing long-range dependencies, and broader discussion on how global forecasting models leverage input observations has been limited. In this paper, we show that forecasting groups of time series involves two objectives: (i) generative process identification (GPI), i.e., inferring the specific process generating the input sequence, and (ii) conditional forecasting (CF), i.e., predicting future values given input observations. From this perspective, optimal predictions can be interpreted as an average over plausible data-generating processes, weighted by their likelihood given the input window. This suggests another explanation for the benefits of long context windows: they reduce the uncertainty about which specific process is generating the input time series during operation. We prove that even for processes with memory length P, an input window size strictly larger than P is necessary to achieve the minimum attainable error. Finally, we show how decoupling GPI and CF can improve computational scalability without compromising accuracy. Experiments on synthetic and real-world data validate our insights and their relevance for designing forecasting architectures.

Deep learning models have grown popular in time series applications. However, the large quantity of newly proposed architectures and the often contradictory empirical results make it difficult to assess which design choice and model component drives performance. In this position paper, we argue that current benchmarking practices fail to identify the factors responsible for performance differences, thus slowing down progress in the field. In particular, differences in crucial design dimensions are overlooked when comparing architectures, ultimately leading to inconsistent outcomes. To support our position, we show that such differences—often treated as mere implementation details—can have a greater impact than adopting specific sequence modeling layers. We discuss how overlooked aspects (such as globality and locality) can (1) fundamentally change the class of the forecasting method and (2) drastically affect empirical results. Our findings suggest rethinking our benchmarking practices and focusing on the foundational aspects of the forecasting problem when designing and comparing architectures. As a concrete step, we propose an , i.e., a template with a set of fields to characterize existing and new forecasting architectures based on key design choices.

Latent categorical variables are frequently found in deep learning architectures. They can model actions in discrete reinforcement-learning environments, represent categories in latent-variable models, or express relations in graph neural networks. Despite their widespread use, their discrete nature poses significant challenges to gradient-descent learning algorithms. While a substantial body of work has offered improved gradient estimation techniques, we take a complementary approach. Specifically, we: 1) revisit the ubiquitous function and demonstrate its limitations from an information-geometric perspective; 2) replace the with the function, a function composed by a sequence of hierarchical binary splits; we prove that this choice offers significant advantages to gradient descent due to the resulting diagonal Fisher Information Matrix. A rich set of experiments - including graph structure learning, variational autoencoders, and reinforcement learning - empirically show that the proposed function improves the learning efficiency and yields models characterized by consistently higher test performance. is simple to implement and seamlessly integrates into existing codebases. Moreover, it remains compatible with standard training stabilization techniques and, as such, offers a better alternative to the function.

Binary Neural Networks (BNNs), which constrain both weights and activations to binary values, offer substantial reductions in computational complexity, memory footprint, and energy consumption. These advantages make them particularly well suited for deployment on resource-constrained devices. However, training BNNs via gradient-based optimization remains challenging due to the discrete nature of their variables. The dominant approach, quantization-aware training, circumvents this issue by employing surrogate gradients. Yet, this method requires maintaining latent full-precision parameters and performing the backward pass with floating-point arithmetic, thereby forfeiting the efficiency of binary operations during training. While alternative approaches based on local learning rules exist, they are unsuitable for global credit assignment and for back-propagating errors in multi-layer architectures. This paper introduces Binary Error Propagation (BEP), the first learning algorithm to establish a principled, discrete analog of the backpropagation chain rule. This mechanism enables error signals, represented as binary vectors, to be propagated backward through multiple layers of a neural network. BEP operates entirely on binary variables, with all forward and backward computations performed using only bitwise operations. Crucially, this makes BEP the first solution to enable end-to-end binary training for recurrent neural network architectures. We validate the effectiveness of BEP on both multi-layer perceptrons and recurrent neural networks, demonstrating gains of up to $+6.89$% and $+10.57$% in test accuracy, respectively. The proposed algorithm is released as an open-source repository.

This article investigates the prescribed-performance control (P2C) of variable-order fractional-order nonlinear systems (VOFONSs) through a control barrier function (CBF)-embedded adaptive dynamic programming (ADP) method. Owing to the time dependence and the global memory characteristics of the variable-order fractional calculus, the existing analysis methods for traditional integer-order systems cannot be directly applied. By using the variable-order fractional calculus and the integration-by-parts formula, the VOFONS is approximately transformed into a time-varying integer-order nonlinear system. To address the P2C problem, a prescribed-performance function is designed to reformulate the P2C problem as a constrained control problem of the time-varying integer-order nonlinear system. Unlike conventional function transformation-based methods, the proposed CBF-embedded ADP control method incorporates the safety constraints into the ADP-based optimal control framework without requiring explicit state transformation. Since the constructed discounted cost function is time-varying due to the involvement of time-varying CBF, it is approximated by a neural network with a time-varying activation function. Then, a time-varying policy iteration algorithm is developed to solve the Hamilton-Jacobi-Bellman (HJB) equation. Hereafter, the CBF-based control policy is derived to guarantee that the tracking error satisfies the predefined constraint. Simulation results verify the effectiveness of the present CBF-embedded ADP control scheme.

We propose SWING: Space Walks for Implicit Network Graphs, a new class of algorithms for computations involving Graph Random Features on graphs given by implicit representations (i-graphs), where edge-weights are defined as bi-variate functions of feature vectors in the corresponding nodes. Those classes of graphs include several prominent examples, such as: ε-neighborhood graphs, used on regular basis in machine learning. Rather than conducting walks on graphs' nodes, those methods rely on walks in continuous spaces, in which those graphs are embedded. To accurately and efficiently approximate original combinatorial calculations, SWING applies customized Gumbel-softmax sampling mechanism with linearized kernels, obtained via random features coupled with importance sampling techniques. This algorithm is of its own interest. SWING relies on the deep connection between implicitly defined graphs and Fourier analysis, presented in this paper. SWING is accelerator-friendly and does not require input graph materialization. We provide detailed analysis of SWING and complement it with thorough experiments on different classes of i-graphs.

Class-incremental learning (CIL) with Vision Transformers (ViTs) faces a major computational bottleneck during the classifier reconstruction phase, where most existing methods rely on costly iterative stochastic gradient descent (SGD). We observe that analytic Regularized Gaussian Discriminant Analysis (RGDA) provides a Bayes-optimal alternative with accuracy comparable to SGD-based classifiers; however, its quadratic inference complexity limits its use in large-scale CIL scenarios. To overcome this, we propose Low-Rank Factorized RGDA (LR-RGDA), a scalable classifier that combines RGDA's expressivity with the efficiency of linear classifiers. By exploiting the low-rank structure of the covariance via the Woodbury matrix identity, LR-RGDA decomposes the discriminant function into a global affine term refined by a low-rank quadratic perturbation, reducing the inference complexity from 𝒪(Cd^2) to 𝒪(d^2 + Crd^2), where C is the class number, d the feature dimension, and r ≪ d the subspace rank. To mitigate representation drift caused by backbone updates, we further introduce Hopfield-based Distribution Compensator (HopDC), a training-free mechanism that uses modern continuous Hopfield Networks to recalibrate historical class statistics through associative memory dynamics on unlabeled anchors, accompanied by a theoretical bound on the estimation error. Extensive experiments on diverse CIL benchmarks demonstrate that our framework achieves state-of-the-art performance, providing a scalable solution for large-scale class-incremental learning with ViTs. Code: https://github.com/raoxuan98-hash/lr_rgda_hopdc.

Deep learning methods achieve remarkable predictive performance in modeling complex, large-scale data. However, assessing the quality of derived models has become increasingly challenging, as more classical sta tistical assumptions may no longer apply. These difficulties are particularly pronounced for spatio-temporal data, which exhibit dependencies across both space and time and are often characterized by nonlinear dynamics, time variance, and missing observations, hence calling for new accuracy assessment methodologies. This paper intro duces a residual correlation analysis framework for assessing the optimality of spatio-temporal relational-enabled neural predictive models, notably in settings with incomplete and heterogeneous data. By leveraging the prin ciple that residual correlation indicates information not captured by the model, enabling the identification and localization of regions in space and time where predictive performance can be improved. A strength of the pro posed approach is that it operates under minimal assumptions, allowing for robust evaluation of deep learning models applied to multivariate time series, even in the presence of missing and heterogeneous data. In detail, the methodology constructs tailored spatio-temporal graphs to encode sparse spatial and temporal dependencies and employs asymptotically distribution-free summary statistics to detect time intervals and spatial regions where the model underperforms. The effectiveness of what proposed is demonstrated through experiments on both synthetic and real-world datasets using state-of-the-art predictive models.

We address the problem of detecting anomalies as samples that do not conform to structured patterns represented by low-dimensional manifolds. To this end, we conceive a general anomaly detection framework called Preference Isolation Forest (PIF), that combines the benefits of adaptive isolation-based methods with the flexibility of preference embedding. The key intuition is to embed the data into a high-dimensional preference space by fitting low-dimensional manifolds, and to identify anomalies as isolated points. We propose three isolation approaches to identify anomalies: i) Voronoi-iForest, the most general solution, ii) RuzHash-iForest, that avoids explicit computation of distances via Local Sensitive Hashing, and iii) Sliding-PIF, that leverages a locality prior to improve efficiency and effectiveness.

Recent time series modeling faces a sharp divide between numerical generation and semantic understanding, with research showing that generation models often rely on superficial pattern matching, while understanding-oriented models struggle with high-fidelity numerical output. Although unified multimodal models (UMMs) have bridged this gap in vision, their potential for time series remains untapped. We propose TimeOmni-VL, the first vision-centric framework that unifies time series understanding and generation through two key innovations: (1) Fidelity-preserving bidirectional mapping between time series and images (Bi-TSI), which advances Time Series-to-Image (TS2I) and Image-to-Time Series (I2TS) conversions to ensure near-lossless transformations. (2) Understanding-guided generation. We introduce TSUMM-Suite, a novel dataset consists of six understanding tasks rooted in time series analytics that are coupled with two generation tasks. With a calibrated Chain-of-Thought (CoT), TimeOmni-VL is the first to leverage time series understanding as an explicit control signal for high-fidelity generation. Experiments confirm that this unified approach significantly improves both semantic understanding and numerical precision, establishing a new frontier for multimodal time series modeling.

Recent advances in Large Language Models (LLMs) have opened new possibilities for time series forecasting by enabling alignment between temporal patterns and pretrained word embeddings. However, most LLM-based methods overlook the heterogeneous nature of time series, where dynamic fluctuations and invariant semantics are entangled. This entanglement introduces spurious correlations during the alignment, as dynamic components act as confounders by simultaneously influencing invariant components and the resulting aligned embeddings. To address this issue, a variable-level alignment framework CVAformer is proposed. CVAformer explicitly disentangles each variable into invariant and dynamic components just before alignment, and applies causal intervention to mitigate the confounding effect of the dynamics. To better support variable-level alignment, CVAformer replaces the standard causal attention in LLMs with a non-causal attention mechanism that captures interactions among variables at each time step. Extensive experiments across long-term, short-term, few-shot, and zero-shot forecasting settings indicate that CVAformer matches or exceeds state-of-the-art performance on most datasets, and in some cases achieves notably better accuracy. Experimental results validate the effectiveness of variable-level alignment and dynamic disentanglement in CVAformer, offering a new perspective for LLM-based time series tasks.

Catastrophic forgetting is one of the main obstacles for Online Continual Graph Learning (OCGL), where nodes arrive one by one, distribution drifts may occur at any time and offline training on task-specific subgraphs is not feasible. In this work, we explore a surprisingly simple yet highly effective approach for OCGL: we use a fixed, randomly initialized encoder to generate robust and expressive node embeddings by aggregating neighborhood information, training online only a lightweight classifier. By freezing the encoder, we eliminate drifts of the representation parameters, a key source of forgetting, obtaining embeddings that are both expressive and stable. When evaluated across several OCGL benchmarks, despite its simplicity and lack of memory buffer, this approach yields consistent gains over state-of-the-art methods, with surprising improvements of up to 30% and performance often approaching that of the joint offline-training upper bound. These results suggest that in OCGL, catastrophic forgetting can be minimized without complex replay or regularization by embracing architectural simplicity and stability.

Accurate weather forecasts are essential for supporting a wide range of activities and decision-making processes, as well as mitigating the impacts of adverse weather events. While traditional numerical weather prediction (NWP) remains the cornerstone of operational forecasting, machine learning is emerging as a powerful alternative for fast, flexible, and scalable predictions. We introduce PeakWeather, a high-quality dataset of surface weather observations collected every 10 minutes over more than 8 years from the ground stations of the Federal Office of Meteorology and Climatology MeteoSwiss's measurement network. The dataset includes a diverse set of meteorological variables from 302 station locations distributed across Switzerland's complex topography and is complemented with topographical indices derived from digital height models for context. Ensemble forecasts from the currently operational high-resolution NWP model are provided as a baseline forecast against which to evaluate new approaches. The dataset's richness supports a broad spectrum of spatiotemporal tasks, including time series forecasting at various scales, graph structure learning, imputation, and virtual sensing. As such, PeakWeather serves as a real-world benchmark to advance both foundational machine learning research, meteorology, and sensor-based applications.

Catheter ablation of Atrial Fibrillation (AF) consists of a one-size-fits-all treatment with limited success in persistent AF. This may be due to our inability to map the dynamics of AF with the limited resolution and coverage provided by sequential contact mapping catheters, preventing effective patient phenotyping for personalised, targeted ablation. Here we introduce FibMap, a graph recurrent neural network model that reconstructs global AF dynamics from sparse measurements. Trained and validated on 51 non-contact whole atria recordings, FibMap reconstructs whole atria dynamics from 10 achieving a 210 performance in tracking phase singularities compared to baseline methods. Clinical utility of FibMap is demonstrated on real-world contact mapping recordings, achieving reconstruction fidelity comparable to non-contact mapping. FibMap's state-spaces and patient-specific parameters offer insights for electrophenotyping AF. Integrating FibMap into clinical practice could enable personalised AF care and improve outcomes.

We experimentally demonstrate the effectiveness of a new Machine Learning-based monitoring algorithm to detect in real time anomalies occurring in DWDM coherent optical networks, allowing the user to be notified before the occurrence of faults.

Accurate predictions of spatio-temporal systems are crucial for tasks such as system management, control, and crisis prevention. However, the inherent time variance of many spatio-temporal systems poses challenges to achieving accurate predictions whenever stationarity is not granted. In order to address non-stationarity, we propose a Distribution and Relation Adaptive Network (DRAN) capable of dynamically adapting to relation and distribution changes over time. While temporal normalization and de-normalization are frequently used techniques to adapt to distribution shifts, this operation is not suitable for the spatio-temporal context as temporal normalization scales the time series of nodes and possibly disrupts the spatial relations among nodes. In order to address this problem, a Spatial Factor Learner (SFL) module is developed that enables the normalization and de-normalization process. To adapt to dynamic changes in spatial relationships among sensors, we propose a Dynamic-Static Fusion Learner (DSFL) module that effectively integrates features learned from both dynamic and static relations through an adaptive fusion ratio mechanism. Furthermore, we introduce a Stochastic Learner to capture the noisy components of spatio-temporal representations. Our approach outperforms state-of-the-art methods on weather prediction and traffic flow forecasting tasks.Experimental results show that our SFL efficiently preserves spatial relationships across various temporal normalization operations. Visualizations of the learned dynamic and static relations demonstrate that DSFL can capture both local and distant relationships between nodes.

Strong priors are imposed on the search space of differentiable architecture search (DARTS), such that cells of the same type share the same topological structure and each intermediate node retains two operators from distinct nodes. While these priors reduce optimization difficulties and improve the applicability of searched architectures, they hinder the subsequent development of automated machine learning (auto-ML) and prevent the optimization algorithm from exploring more powerful neural networks through improved architectural flexibility. This article aims to reduce these prior constraints by eliminating restrictions on cell topology and modifying the discretization mechanism for super-networks. Specifically, the flexible DARTS (FX-DARTS) method, which leverages an entropy-based super-network shrinking (ESS) framework, is presented to address the challenges arising from the elimination of prior constraints. Notably, FX-DARTS enables the derivation of neural architectures without strict prior rules while maintaining the stability in the enlarged search space. Experimental results on image classification benchmarks demonstrate that FX-DARTS is capable of exploring a set of neural architectures with competitive trade-offs between performance and computational complexity within a single search procedure.

Graph-based deep learning methods have become popular tools to process collections of correlated time series. Differently from traditional multivariate forecasting methods, neural graph-based predictors take advantage of pairwise relationships by conditioning forecasts on a (possibly dynamic) graph spanning the time series collection. The conditioning can take the form of an architectural inductive bias on the neural forecasting architecture, resulting in a family of deep learning models called spatiotemporal graph neural networks. Such relational inductive biases enable the training of global forecasting models on large time-series collections, while at the same time localizing predictions w.r.t. each element in the set (i.e., graph nodes) by accounting for local correlations among them (i.e., graph edges). Indeed, recent theoretical and practical advances in graph neural networks and deep learning for time series forecasting make the adoption of such processing frameworks appealing and timely. However, most of the studies in the literature focus on proposing variations of existing neural architectures by taking advantage of modern deep learning practices, while foundational and methodological aspects have not been subject to systematic investigation. To fill the gap, this paper aims to introduce a comprehensive methodological framework that formalizes the forecasting problem and provides design principles for graph-based predictive models and methods to assess their performance. At the same time, together with an overview of the field, we provide design guidelines, recommendations, and best practices, as well as an in-depth discussion of open challenges and future research directions.