Daily Papers

In Recurrent Neural Networks (RNNs), encoding information in a suboptimal or erroneous way can impact the quality of representations based on later elements in the sequence and subsequently lead to wrong predictions and a worse model performance. In humans, challenging cases like garden path sentences (an instance of this being the infamous "The horse raced past the barn fell") can lead their language understanding astray. However, they are still able to correct their representation accordingly and recover when new information is encountered. Inspired by this, I propose an augmentation to standard RNNs in form of a gradient-based correction mechanism: This way I hope to enable such models to dynamically adapt their inner representation of a sentence, adding a way to correct deviations as soon as they occur. This could therefore lead to more robust models using more flexible representations, even during inference time. I conduct different experiments in the context of language modeling, where the impact of using such a mechanism is examined in detail. To this end, I look at modifications based on different kinds of time-dependent error signals and how they influence the model performance. Furthermore, this work contains a study of the model's confidence in its predictions during training and for challenging test samples and the effect of the manipulation thereof. Lastly, I also study the difference in behavior of these novel models compared to a standard LSTM baseline and investigate error cases in detail to identify points of future research. I show that while the proposed approach comes with promising theoretical guarantees and an appealing intuition, it is only able to produce minor improvements over the baseline due to challenges in its practical application and the efficacy of the tested model variants.

Reasoning from sequences of raw sensory data is a ubiquitous problem across fields ranging from medical devices to robotics. These problems often involve using long sequences of raw sensor data (e.g. magnetometers, piezoresistors) to predict sequences of desirable physical quantities (e.g. force, inertial measurements). While classical approaches are powerful for locally-linear prediction problems, they often fall short when using real-world sensors. These sensors are typically non-linear, are affected by extraneous variables (e.g. vibration), and exhibit data-dependent drift. For many problems, the prediction task is exacerbated by small labeled datasets since obtaining ground-truth labels requires expensive equipment. In this work, we present Hierarchical State-Space Models (HiSS), a conceptually simple, new technique for continuous sequential prediction. HiSS stacks structured state-space models on top of each other to create a temporal hierarchy. Across six real-world sensor datasets, from tactile-based state prediction to accelerometer-based inertial measurement, HiSS outperforms state-of-the-art sequence models such as causal Transformers, LSTMs, S4, and Mamba by at least 23% on MSE. Our experiments further indicate that HiSS demonstrates efficient scaling to smaller datasets and is compatible with existing data-filtering techniques. Code, datasets and videos can be found on https://hiss-csp.github.io.

The recovery of time-varying graph signals is a fundamental problem with numerous applications in sensor networks and forecasting in time series. Effectively capturing the spatio-temporal information in these signals is essential for the downstream tasks. Previous studies have used the smoothness of the temporal differences of such graph signals as an initial assumption. Nevertheless, this smoothness assumption could result in a degradation of performance in the corresponding application when the prior does not hold. In this work, we relax the requirement of this hypothesis by including a learning module. We propose a Time Graph Neural Network (TimeGNN) for the recovery of time-varying graph signals. Our algorithm uses an encoder-decoder architecture with a specialized loss composed of a mean squared error function and a Sobolev smoothness operator.TimeGNN shows competitive performance against previous methods in real datasets.

Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required for accurate integration. In this paper, we introduce an inference process that maps complex systems into a simplified representational space and models large jumps in time. To achieve this, we propose Time-lagged Information Bottleneck (T-IB), a principled objective rooted in information theory, which aims to capture relevant temporal features while discarding high-frequency information to simplify the simulation task and minimize the inference error. Our experiments demonstrate that T-IB learns information-optimal representations for accurately modeling the statistical properties and dynamics of the original process at a selected time lag, outperforming existing time-lagged dimensionality reduction methods.

In this paper we present a new framework for time-series modeling that combines the best of traditional statistical models and neural networks. We focus on time-series with long-range dependencies, needed for monitoring fine granularity data (e.g. minutes, seconds, milliseconds), prevalent in operational use-cases. Traditional models, such as auto-regression fitted with least squares (Classic-AR) can model time-series with a concise and interpretable model. When dealing with long-range dependencies, Classic-AR models can become intractably slow to fit for large data. Recently, sequence-to-sequence models, such as Recurrent Neural Networks, which were originally intended for natural language processing, have become popular for time-series. However, they can be overly complex for typical time-series data and lack interpretability. A scalable and interpretable model is needed to bridge the statistical and deep learning-based approaches. As a first step towards this goal, we propose modelling AR-process dynamics using a feed-forward neural network approach, termed AR-Net. We show that AR-Net is as interpretable as Classic-AR but also scales to long-range dependencies. Our results lead to three major conclusions: First, AR-Net learns identical AR-coefficients as Classic-AR, thus being equally interpretable. Second, the computational complexity with respect to the order of the AR process, is linear for AR-Net as compared to a quadratic for Classic-AR. This makes it possible to model long-range dependencies within fine granularity data. Third, by introducing regularization, AR-Net automatically selects and learns sparse AR-coefficients. This eliminates the need to know the exact order of the AR-process and allows to learn sparse weights for a model with long-range dependencies.

Temporal Point Processes (TPP) are probabilistic generative frameworks. They model discrete event sequences localized in continuous time. Generally, real-life events reveal descriptive information, known as marks. Marked TPPs model time and marks of the event together for practical relevance. Conditioned on past events, marked TPPs aim to learn the joint distribution of the time and the mark of the next event. For simplicity, conditionally independent TPP models assume time and marks are independent given event history. They factorize the conditional joint distribution of time and mark into the product of individual conditional distributions. This structural limitation in the design of TPP models hurt the predictive performance on entangled time and mark interactions. In this work, we model the conditional inter-dependence of time and mark to overcome the limitations of conditionally independent models. We construct a multivariate TPP conditioning the time distribution on the current event mark in addition to past events. Besides the conventional intensity-based models for conditional joint distribution, we also draw on flexible intensity-free TPP models from the literature. The proposed TPP models outperform conditionally independent and dependent models in standard prediction tasks. Our experimentation on various datasets with multiple evaluation metrics highlights the merit of the proposed approach.

Neural operators have proven to be a promising approach for modeling spatiotemporal systems in the physical sciences. However, training these models for large systems can be quite challenging as they incur significant computational and memory expense -- these systems are often forced to rely on autoregressive time-stepping of the neural network to predict future temporal states. While this is effective in managing costs, it can lead to uncontrolled error growth over time and eventual instability. We analyze the sources of this autoregressive error growth using prototypical neural operator models for physical systems and explore ways to mitigate it. We introduce architectural and application-specific improvements that allow for careful control of instability-inducing operations within these models without inflating the compute/memory expense. We present results on several scientific systems that include Navier-Stokes fluid flow, rotating shallow water, and a high-resolution global weather forecasting system. We demonstrate that applying our design principles to neural operators leads to significantly lower errors for long-term forecasts as well as longer time horizons without qualitative signs of divergence compared to the original models for these systems. We open-source our https://github.com/mikemccabe210/stabilizing_neural_operators{code} for reproducibility.

Moments when a time series changes its behaviour are called change points. Detection of such points is a well-known problem, which can be found in many applications: quality monitoring of industrial processes, failure detection in complex systems, health monitoring, speech recognition and video analysis. Occurrence of change point implies that the state of the system is altered and its timely detection might help to prevent unwanted consequences. In this paper, we present two online change-point detection approaches based on neural networks. These algorithms demonstrate linear computational complexity and are suitable for change-point detection in large time series. We compare them with the best known algorithms on various synthetic and real world data sets. Experiments show that the proposed methods outperform known approaches.

The Diffusion models, widely used for image generation, face significant challenges related to their broad applicability due to prolonged inference times and high memory demands. Efficient Post-Training Quantization (PTQ) is crucial to address these issues. However, unlike traditional models, diffusion models critically rely on the time-step for the multi-round denoising. Typically, each time-step is encoded into a hypersensitive temporal feature by several modules. Despite this, existing PTQ methods do not optimize these modules individually. Instead, they employ unsuitable reconstruction objectives and complex calibration methods, leading to significant disturbances in the temporal feature and denoising trajectory, as well as reduced compression efficiency. To address these challenges, we introduce a novel quantization framework that includes three strategies: 1) TIB-based Maintenance: Based on our innovative Temporal Information Block (TIB) definition, Temporal Information-aware Reconstruction (TIAR) and Finite Set Calibration (FSC) are developed to efficiently align original temporal features. 2) Cache-based Maintenance: Instead of indirect and complex optimization for the related modules, pre-computing and caching quantized counterparts of temporal features are developed to minimize errors. 3) Disturbance-aware Selection: Employ temporal feature errors to guide a fine-grained selection between the two maintenance strategies for further disturbance reduction. This framework preserves most of the temporal information and ensures high-quality end-to-end generation. Extensive testing on various datasets, diffusion models and hardware confirms our superior performance and acceleration..

Multivariate time series is prevalent in many scientific and industrial domains. Modeling multivariate signals is challenging due to their long-range temporal dependencies and intricate interactions--both direct and indirect. To confront these complexities, we introduce a method of representing multivariate signals as nodes in a graph with edges indicating interdependency between them. Specifically, we leverage graph neural networks (GNN) and attention mechanisms to efficiently learn the underlying relationships within the time series data. Moreover, we suggest employing hierarchical signal decompositions running over the graphs to capture multiple spatial dependencies. The effectiveness of our proposed model is evaluated across various real-world benchmark datasets designed for long-term forecasting tasks. The results consistently showcase the superiority of our model, achieving an average 23\% reduction in mean squared error (MSE) compared to existing models.

With significant advancements in diffusion models, addressing the potential risks of dataset bias becomes increasingly important. Since generated outputs directly suffer from dataset bias, mitigating latent bias becomes a key factor in improving sample quality and proportion. This paper proposes time-dependent importance reweighting to mitigate the bias for the diffusion models. We demonstrate that the time-dependent density ratio becomes more precise than previous approaches, thereby minimizing error propagation in generative learning. While directly applying it to score-matching is intractable, we discover that using the time-dependent density ratio both for reweighting and score correction can lead to a tractable form of the objective function to regenerate the unbiased data density. Furthermore, we theoretically establish a connection with traditional score-matching, and we demonstrate its convergence to an unbiased distribution. The experimental evidence supports the usefulness of the proposed method, which outperforms baselines including time-independent importance reweighting on CIFAR-10, CIFAR-100, FFHQ, and CelebA with various bias settings. Our code is available at https://github.com/alsdudrla10/TIW-DSM.

Early time classification algorithms aim to label a stream of features without processing the full input stream, while maintaining accuracy comparable to that achieved by applying the classifier to the entire input. In this paper, we introduce a statistical framework that can be applied to any sequential classifier, formulating a calibrated stopping rule. This data-driven rule attains finite-sample, distribution-free control of the accuracy gap between full and early-time classification. We start by presenting a novel method that builds on the Learn-then-Test calibration framework to control this gap marginally, on average over i.i.d. instances. As this algorithm tends to yield an excessively high accuracy gap for early halt times, our main contribution is the proposal of a framework that controls a stronger notion of error, where the accuracy gap is controlled conditionally on the accumulated halt times. Numerical experiments demonstrate the effectiveness, applicability, and usefulness of our method. We show that our proposed early stopping mechanism reduces up to 94% of timesteps used for classification while achieving rigorous accuracy gap control.

Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained increased interest. The practical utility of such neural PDE solvers relies on their ability to provide accurate, stable predictions over long time horizons, which is a notoriously hard problem. In this work, we present a large-scale analysis of common temporal rollout strategies, identifying the neglect of non-dominant spatial frequency information, often associated with high frequencies in PDE solutions, as the primary pitfall limiting stable, accurate rollout performance. Based on these insights, we draw inspiration from recent advances in diffusion models to introduce PDE-Refiner; a novel model class that enables more accurate modeling of all frequency components via a multistep refinement process. We validate PDE-Refiner on challenging benchmarks of complex fluid dynamics, demonstrating stable and accurate rollouts that consistently outperform state-of-the-art models, including neural, numerical, and hybrid neural-numerical architectures. We further demonstrate that PDE-Refiner greatly enhances data efficiency, since the denoising objective implicitly induces a novel form of spectral data augmentation. Finally, PDE-Refiner's connection to diffusion models enables an accurate and efficient assessment of the model's predictive uncertainty, allowing us to estimate when the surrogate becomes inaccurate.

Models that can predict the occurrence of events ahead of time with low false-alarm rates are critical to the acceptance of decision support systems in the medical community. This challenging task is typically treated as a simple binary classification, ignoring temporal dependencies between samples, whereas we propose to exploit this structure. We first introduce a common theoretical framework unifying dynamic survival analysis and early event prediction. Following an analysis of objectives from both fields, we propose Temporal Label Smoothing (TLS), a simpler, yet best-performing method that preserves prediction monotonicity over time. By focusing the objective on areas with a stronger predictive signal, TLS improves performance over all baselines on two large-scale benchmark tasks. Gains are particularly notable along clinically relevant measures, such as event recall at low false-alarm rates. TLS reduces the number of missed events by up to a factor of two over previously used approaches in early event prediction.

Time series data from observations of black hole ringdown gravitational waves are often analyzed in the time domain by using damped sinusoid models with acyclic boundary conditions. Data conditioning operations, including downsampling, filtering, and the choice of data segment duration, reduce the computational cost of such analyses and can improve numerical stability. Here we analyze simulated damped sinsuoid signals to illustrate how data conditioning operations, if not carefully applied, can undesirably alter the analysis' posterior distributions. We discuss how currently implemented downsampling and filtering methods, if applied too aggressively, can introduce systematic errors and skew tests of general relativity. These issues arise because current downsampling and filtering methods do not operate identically on the data and model. Alternative downsampling and filtering methods which identically operate on the data and model may be achievable, but we argue that the current operations can still be implemented safely. We also show that our preferred anti-alias filtering technique, which has an instantaneous frequency-domain response at its roll-off frequency, preserves the structure of posterior distributions better than other commonly used filters with transient frequency-domain responses. Lastly, we highlight that exceptionally long data segments may need to be analyzed in cases where thin lines in the noise power spectral density overlap with central signal frequencies. Our findings may be broadly applicable to any analysis of truncated time domain data with acyclic boundary conditions.

Catastrophic regime shifts in complex natural systems may be averted through advanced detection. Recent work has provided a proof-of-principle that many systems approaching a catastrophic transition may be identified through the lens of early warning indicators such as rising variance or increased return times. Despite widespread appreciation of the difficulties and uncertainty involved in such forecasts, proposed methods hardly ever characterize their expected error rates. Without the benefits of replicates, controls, or hindsight, applications of these approaches must quantify how reliable different indicators are in avoiding false alarms, and how sensitive they are to missing subtle warning signs. We propose a model based approach in order to quantify this trade-off between reliability and sensitivity and allow comparisons between different indicators. We show these error rates can be quite severe for common indicators even under favorable assumptions, and also illustrate how a model-based indicator can improve this performance. We demonstrate how the performance of an early warning indicator varies in different data sets, and suggest that uncertainty quantification become a more central part of early warning predictions.

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

We study the problem of estimating the time delay between two signals representing delayed, irregularly sampled and noisy versions of the same underlying pattern. We propose and demonstrate an evolutionary algorithm for the (hyper)parameter estimation of a kernel-based technique in the context of an astronomical problem, namely estimating the time delay between two gravitationally lensed signals from a distant quasar. Mixed types (integer and real) are used to represent variables within the evolutionary algorithm. We test the algorithm on several artificial data sets, and also on real astronomical observations of quasar Q0957+561. By carrying out a statistical analysis of the results we present a detailed comparison of our method with the most popular methods for time delay estimation in astrophysics. Our method yields more accurate and more stable time delay estimates: for Q0957+561, we obtain 419.6 days for the time delay between images A and B. Our methodology can be readily applied to current state-of-the-art optical monitoring data in astronomy, but can also be applied in other disciplines involving similar time series data.

Causal discovery, i.e., inferring underlying cause-effect relationships from observations of a scene or system, is an inherent mechanism in human cognition, but has been shown to be highly challenging to automate. The majority of approaches in the literature aiming for this task consider constrained scenarios with fully observed variables or data from stationary time-series. In this work we aim for causal discovery in a more general class of scenarios, scenes with non-stationary behavior over time. For our purposes we here regard a scene as a composition objects interacting with each other over time. Non-stationarity is modeled as stationarity conditioned on an underlying variable, a state, which can be of varying dimension, more or less hidden given observations of the scene, and also depend more or less directly on these observations. We propose a probabilistic deep learning approach called State-Dependent Causal Inference (SDCI) for causal discovery in such conditionally stationary time-series data. Results in two different synthetic scenarios show that this method is able to recover the underlying causal dependencies with high accuracy even in cases with hidden states.

We propose the Signal Dice Similarity Coefficient (SDSC), a structure-aware metric function for time series self-supervised representation learning. Most Self-Supervised Learning (SSL) methods for signals commonly adopt distance-based objectives such as mean squared error (MSE), which are sensitive to amplitude, invariant to waveform polarity, and unbounded in scale. These properties hinder semantic alignment and reduce interpretability. SDSC addresses this by quantifying structural agreement between temporal signals based on the intersection of signed amplitudes, derived from the Dice Similarity Coefficient (DSC).Although SDSC is defined as a structure-aware metric, it can be used as a loss by subtracting from 1 and applying a differentiable approximation of the Heaviside function for gradient-based optimization. A hybrid loss formulation is also proposed to combine SDSC with MSE, improving stability and preserving amplitude where necessary. Experiments on forecasting and classification benchmarks demonstrate that SDSC-based pre-training achieves comparable or improved performance over MSE, particularly in in-domain and low-resource scenarios. The results suggest that structural fidelity in signal representations enhances the semantic representation quality, supporting the consideration of structure-aware metrics as viable alternatives to conventional distance-based methods.

We present a constraint-based algorithm for learning causal structures from observational time-series data, in the presence of latent confounders. We assume a discrete-time, stationary structural vector autoregressive process, with both temporal and contemporaneous causal relations. One may ask if temporal and contemporaneous relations should be treated differently. The presented algorithm gradually refines a causal graph by learning long-term temporal relations before short-term ones, where contemporaneous relations are learned last. This ordering of causal relations to be learnt leads to a reduction in the required number of statistical tests. We validate this reduction empirically and demonstrate that it leads to higher accuracy for synthetic data and more plausible causal graphs for real-world data compared to state-of-the-art algorithms.

Earthquakes are evaluated among the most destructive disasters for human beings, as also experienced for Turkiye region. Data science has the property of discovering hidden patterns in case a sufficient volume of data is supplied. Time dependency of events, specifically being defined by co-occurrence in a specific time window, may be handled as an associate rule mining task such as a market-basket analysis application. In this regard, we assumed each day's seismic activity as a single basket of events, leading to discovering the association patterns between these events. Consequently, this study presents the most prominent association rules for the earthquakes recorded in Turkiye region in the last 5 years, each year presented separately. Results indicate statistical inference with events recorded from regions of various distances, which could be further verified with geologic evidence from the field. As a result, we believe that the current study may form a statistical basis for the future works with the aid of machine learning algorithm performed for associate rule mining.

Deep neural networks, including transformers and convolutional neural networks, have significantly improved multivariate time series classification (MTSC). However, these methods often rely on supervised learning, which does not fully account for the sparsity and locality of patterns in time series data (e.g., diseases-related anomalous points in ECG). To address this challenge, we formally reformulate MTSC as a weakly supervised problem, introducing a novel multiple-instance learning (MIL) framework for better localization of patterns of interest and modeling time dependencies within time series. Our novel approach, TimeMIL, formulates the temporal correlation and ordering within a time-aware MIL pooling, leveraging a tokenized transformer with a specialized learnable wavelet positional token. The proposed method surpassed 26 recent state-of-the-art methods, underscoring the effectiveness of the weakly supervised TimeMIL in MTSC. The code will be available at https://github.com/xiwenc1/TimeMIL.

Time series anomaly detection (TSAD) is a critical task, but developing models that generalize to unseen data in a zero-shot manner remains a major challenge. Prevailing foundation models for TSAD predominantly rely on reconstruction-based objectives, which suffer from a fundamental objective mismatch: they struggle to identify subtle anomalies while often misinterpreting complex normal patterns, leading to high rates of false negatives and positives. To overcome these limitations, we introduce TimeRCD, a novel foundation model for TSAD built upon a new pre-training paradigm: Relative Context Discrepancy (RCD). Instead of learning to reconstruct inputs, TimeRCD is explicitly trained to identify anomalies by detecting significant discrepancies between adjacent time windows. This relational approach, implemented with a standard Transformer architecture, enables the model to capture contextual shifts indicative of anomalies that reconstruction-based methods often miss. To facilitate this paradigm, we develop a large-scale, diverse synthetic corpus with token-level anomaly labels, providing the rich supervisory signal necessary for effective pre-training. Extensive experiments demonstrate that TimeRCD significantly outperforms existing general-purpose and anomaly-specific foundation models in zero-shot TSAD across diverse datasets. Our results validate the superiority of the RCD paradigm and establish a new, effective path toward building robust and generalizable foundation models for time series anomaly detection.

Spatio-temporal forecasting is essential for real-world applications such as traffic management and urban computing. Although recent methods have shown improved accuracy, they often fail to account for dynamic deviations between current inputs and historical patterns. These deviations contain critical signals that can significantly affect model performance. To fill this gap, we propose ST-SSDL, a Spatio-Temporal time series forecasting framework that incorporates a Self-Supervised Deviation Learning scheme to capture and utilize such deviations. ST-SSDL anchors each input to its historical average and discretizes the latent space using learnable prototypes that represent typical spatio-temporal patterns. Two auxiliary objectives are proposed to refine this structure: a contrastive loss that enhances inter-prototype discriminability and a deviation loss that regularizes the distance consistency between input representations and corresponding prototypes to quantify deviation. Optimized jointly with the forecasting objective, these components guide the model to organize its hidden space and improve generalization across diverse input conditions. Experiments on six benchmark datasets show that ST-SSDL consistently outperforms state-of-the-art baselines across multiple metrics. Visualizations further demonstrate its ability to adaptively respond to varying levels of deviation in complex spatio-temporal scenarios. Our code and datasets are available at https://github.com/Jimmy-7664/ST-SSDL.

Temporal point processes (TPP) are a natural tool for modeling event-based data. Among all TPP models, Hawkes processes have proven to be the most widely used, mainly due to their adequate modeling for various applications, particularly when considering exponential or non-parametric kernels. Although non-parametric kernels are an option, such models require large datasets. While exponential kernels are more data efficient and relevant for specific applications where events immediately trigger more events, they are ill-suited for applications where latencies need to be estimated, such as in neuroscience. This work aims to offer an efficient solution to TPP inference using general parametric kernels with finite support. The developed solution consists of a fast ell_2 gradient-based solver leveraging a discretized version of the events. After theoretically supporting the use of discretization, the statistical and computational efficiency of the novel approach is demonstrated through various numerical experiments. Finally, the method's effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG). Given the use of general parametric kernels, results show that the proposed approach leads to an improved estimation of pattern latency than the state-of-the-art.

Modeling multivariate time series is a well-established problem with a wide range of applications from healthcare to financial markets. Traditional State Space Models (SSMs) are classical approaches for univariate time series modeling due to their simplicity and expressive power to represent linear dependencies. They, however, have fundamentally limited expressive power to capture non-linear dependencies, are slow in practice, and fail to model the inter-variate information flow. Despite recent attempts to improve the expressive power of SSMs by using deep structured SSMs, the existing methods are either limited to univariate time series, fail to model complex patterns (e.g., seasonal patterns), fail to dynamically model the dependencies of variate and time dimensions, and/or are input-independent. We present Chimera that uses two input-dependent 2-D SSM heads with different discretization processes to learn long-term progression and seasonal patterns. To improve the efficiency of complex 2D recurrence, we present a fast training using a new 2-dimensional parallel selective scan. We further present and discuss 2-dimensional Mamba and Mamba-2 as the spacial cases of our 2D SSM. Our experimental evaluation shows the superior performance of Chimera on extensive and diverse benchmarks, including ECG and speech time series classification, long-term and short-term time series forecasting, and time series anomaly detection.

Diffusion models have demonstrated robust data generation capabilities in various research fields. In this paper, a Time Series Diffusion Method (TSDM) is proposed for vibration signal generation, leveraging the foundational principles of diffusion models. The TSDM uses an improved U-net architecture with attention block to effectively segment and extract features from one-dimensional time series data. It operates based on forward diffusion and reverse denoising processes for time-series generation. Experimental validation is conducted using single-frequency, multi-frequency datasets, and bearing fault datasets. The results show that TSDM can accurately generate the single-frequency and multi-frequency features in the time series and retain the basic frequency features for the diffusion generation results of the bearing fault series. Finally, TSDM is applied to the small sample fault diagnosis of three public bearing fault datasets, and the results show that the accuracy of small sample fault diagnosis of the three datasets is improved by 32.380%, 18.355% and 9.298% at most, respectively

This paper studies the error metric selection for long-term memory learning in sequence modelling. We examine the bias towards short-term memory in commonly used errors, including mean absolute/squared error. Our findings show that all temporally positive-weighted errors are biased towards short-term memory in learning linear functionals. To reduce this bias and improve long-term memory learning, we propose the use of a temporally rescaled error. In addition to reducing the bias towards short-term memory, this approach can also alleviate the vanishing gradient issue. We conduct numerical experiments on different long-memory tasks and sequence models to validate our claims. Numerical results confirm the importance of appropriate temporally rescaled error for effective long-term memory learning. To the best of our knowledge, this is the first work that quantitatively analyzes different errors' memory bias towards short-term memory in sequence modelling.

Complex, temporally evolving phenomena, from climate to brain activity, are governed by dynamical systems (DS). DS reconstruction (DSR) seeks to infer generative surrogate models of these from observed data, reproducing their long-term behavior. Existing DSR approaches require purpose-training for any new system observed, lacking the zero-shot and in-context inference capabilities known from LLMs. Here we introduce DynaMix, a novel multivariate ALRNN-based mixture-of-experts architecture pre-trained for DSR, the first DSR model able to generalize zero-shot to out-of-domain DS. Just from a provided context signal, without any re-training, DynaMix faithfully forecasts the long-term evolution of novel DS where existing time series (TS) foundation models, like Chronos, fail -- at a fraction of the number of parameters and orders of magnitude faster inference times. DynaMix outperforms TS foundation models in terms of long-term statistics, and often also short-term forecasts, even on real-world time series, like traffic or weather data, typically used for training and evaluating TS models, but not at all part of DynaMix' training corpus. We illustrate some of the failure modes of TS models for DSR problems, and conclude that models built on DS principles may bear a huge potential also for advancing the TS prediction field.

Adapting to concept drift is a challenging task in machine learning, which is usually tackled using incremental learning techniques that periodically re-fit a learning model leveraging newly available data. A primary limitation of these techniques is their reliance on substantial amounts of data for retraining. The necessity of acquiring fresh data introduces temporal delays prior to retraining, potentially rendering the models inaccurate if a sudden concept drift occurs in-between two consecutive retrainings. In communication networks, such issue emerges when performing traffic forecasting following a~failure event: post-failure re-routing may induce a drastic shift in distribution and pattern of traffic data, thus requiring a timely model adaptation. In this work, we address this challenge for the problem of traffic forecasting and propose an approach that exploits adaptive learning algorithms, namely, liquid neural networks, which are capable of self-adaptation to abrupt changes in data patterns without requiring any retraining. Through extensive simulations of failure scenarios, we compare the predictive performance of our proposed approach to that of a reference method based on incremental learning. Experimental results show that our proposed approach outperforms incremental learning-based methods in situations where the shifts in traffic patterns are drastic.

Time series classification (TSC) is a cornerstone of modern web applications, powering tasks such as financial data analysis, network traffic monitoring, and user behavior analysis. In recent years, deep neural networks (DNNs) have greatly enhanced the performance of TSC models in these critical domains. However, DNNs are vulnerable to backdoor attacks, where attackers can covertly implant triggers into models to induce malicious outcomes. Existing backdoor attacks targeting DNN-based TSC models remain elementary. In particular, early methods borrow trigger designs from computer vision, which are ineffective for time series data. More recent approaches utilize generative models for trigger generation, but at the cost of significant computational complexity. In this work, we analyze the limitations of existing attacks and introduce an enhanced method, FreqBack. Drawing inspiration from the fact that DNN models inherently capture frequency domain features in time series data, we identify that improper perturbations in the frequency domain are the root cause of ineffective attacks. To address this, we propose to generate triggers both effectively and efficiently, guided by frequency analysis. FreqBack exhibits substantial performance across five models and eight datasets, achieving an impressive attack success rate of over 90%, while maintaining less than a 3% drop in model accuracy on clean data.

Multivariate long-term and efficient time series forecasting is a key requirement for a variety of practical applications, and there are complex interleaving time dynamics in time series data that require decomposition modeling. Traditional time series decomposition methods are single and rely on fixed rules, which are insufficient for mining the potential information of the series and adapting to the dynamic characteristics of complex series. On the other hand, the Transformer-based models for time series forecasting struggle to effectively model long sequences and intricate dynamic relationships due to their high computational complexity. To overcome these limitations, we introduce KARMA, with an Adaptive Time Channel Decomposition module (ATCD) to dynamically extract trend and seasonal components. It further integrates a Hybrid Frequency-Time Decomposition module (HFTD) to further decompose Series into frequency-domain and time-domain. These components are coupled with multi-scale Mamba-based KarmaBlock to efficiently process global and local information in a coordinated manner. Experiments on eight real-world datasets from diverse domains well demonstrated that KARMA significantly outperforms mainstream baseline methods in both predictive accuracy and computational efficiency. Code and full results are available at this repository: https://github.com/yedadasd/KARMA

We present TimeFound, an encoder-decoder transformer-based time series foundation model for out-of-the-box zero-shot forecasting. To handle time series data from various domains, TimeFound employs a multi-resolution patching strategy to capture complex temporal patterns at multiple scales. We pre-train our model with two sizes (200M and 710M parameters) on a large time-series corpus comprising both real-world and synthetic datasets. Over a collection of unseen datasets across diverse domains and forecasting horizons, our empirical evaluations suggest that TimeFound can achieve superior or competitive zero-shot forecasting performance, compared to state-of-the-art time series foundation models.

Source separation involves the ill-posed problem of retrieving a set of source signals that have been observed through a mixing operator. Solving this problem requires prior knowledge, which is commonly incorporated by imposing regularity conditions on the source signals, or implicitly learned through supervised or unsupervised methods from existing data. While data-driven methods have shown great promise in source separation, they often require large amounts of data, which rarely exists in planetary space missions. To address this challenge, we propose an unsupervised source separation scheme for domains with limited data access that involves solving an optimization problem in the wavelet scattering covariance representation spacex2014an interpretable, low-dimensional representation of stationary processes. We present a real-data example in which we remove transient, thermally-induced microtiltsx2014known as glitchesx2014from data recorded by a seismometer during NASA's InSight mission on Mars. Thanks to the wavelet scattering covariances' ability to capture non-Gaussian properties of stochastic processes, we are able to separate glitches using only a few glitch-free data snippets.

[This paper was initially published in PHME conference in 2016, selected for further publication in International Journal of Prognostics and Health Management.] This paper describes an Autoregressive Partially-hidden Markov model (ARPHMM) for fault detection and prognostics of equipments based on sensors' data. It is a particular dynamic Bayesian network that allows to represent the dynamics of a system by means of a Hidden Markov Model (HMM) and an autoregressive (AR) process. The Markov chain assumes that the system is switching back and forth between internal states while the AR process ensures a temporal coherence on sensor measurements. A sound learning procedure of standard ARHMM based on maximum likelihood allows to iteratively estimate all parameters simultaneously. This paper suggests a modification of the learning procedure considering that one may have prior knowledge about the structure which becomes partially hidden. The integration of the prior is based on the Theory of Weighted Distributions which is compatible with the Expectation-Maximization algorithm in the sense that the convergence properties are still satisfied. We show how to apply this model to estimate the remaining useful life based on health indicators. The autoregressive parameters can indeed be used for prediction while the latent structure can be used to get information about the degradation level. The interest of the proposed method for prognostics and health assessment is demonstrated on CMAPSS datasets.

Time series data, characterized by its intrinsic long and short-range dependencies, poses a unique challenge across analytical applications. While Transformer-based models excel at capturing long-range dependencies, they face limitations in noise sensitivity, computational efficiency, and overfitting with smaller datasets. In response, we introduce a novel Time Series Lightweight Adaptive Network (TSLANet), as a universal convolutional model for diverse time series tasks. Specifically, we propose an Adaptive Spectral Block, harnessing Fourier analysis to enhance feature representation and to capture both long-term and short-term interactions while mitigating noise via adaptive thresholding. Additionally, we introduce an Interactive Convolution Block and leverage self-supervised learning to refine the capacity of TSLANet for decoding complex temporal patterns and improve its robustness on different datasets. Our comprehensive experiments demonstrate that TSLANet outperforms state-of-the-art models in various tasks spanning classification, forecasting, and anomaly detection, showcasing its resilience and adaptability across a spectrum of noise levels and data sizes. The code is available at https://github.com/emadeldeen24/TSLANet

Early warning signals have been proposed to forecast the possibility of a critical transition, such as the eutrophication of a lake, the collapse of a coral reef, or the end of a glacial period. Because such transitions often unfold on temporal and spatial scales that can be difficult to approach by experimental manipulation, research has often relied on historical observations as a source of natural experiments. Here we examine a critical difference between selecting systems for study based on the fact that we have observed a critical transition and those systems for which we wish to forecast the approach of a transition. This difference arises by conditionally selecting systems known to experience a transition of some sort and failing to account for the bias this introduces -- a statistical error often known as the Prosecutor's Fallacy. By analysing simulated systems that have experienced transitions purely by chance, we reveal an elevated rate of false positives in common warning signal statistics. We further demonstrate a model-based approach that is less subject to this bias than these more commonly used summary statistics. We note that experimental studies with replicates avoid this pitfall entirely.

Conventional uncertainty-aware temporal difference (TD) learning methods often rely on simplistic assumptions, typically including a zero-mean Gaussian distribution for TD errors. Such oversimplification can lead to inaccurate error representations and compromised uncertainty estimation. In this paper, we introduce a novel framework for generalized Gaussian error modeling in deep reinforcement learning, applicable to both discrete and continuous control settings. Our framework enhances the flexibility of error distribution modeling by incorporating additional higher-order moment, particularly kurtosis, thereby improving the estimation and mitigation of data-dependent noise, i.e., aleatoric uncertainty. We examine the influence of the shape parameter of the generalized Gaussian distribution (GGD) on aleatoric uncertainty and provide a closed-form expression that demonstrates an inverse relationship between uncertainty and the shape parameter. Additionally, we propose a theoretically grounded weighting scheme to fully leverage the GGD. To address epistemic uncertainty, we enhance the batch inverse variance weighting by incorporating bias reduction and kurtosis considerations, resulting in improved robustness. Extensive experimental evaluations using policy gradient algorithms demonstrate the consistent efficacy of our method, showcasing significant performance improvements.

Explaining predictions based on multivariate time series data carries the additional difficulty of handling not only multiple features, but also time dependencies. It matters not only what happened, but also when, and the same feature could have a very different impact on a prediction depending on this time information. Previous work has used perturbation-based saliency methods to tackle this issue, perturbing an input using a trainable mask to discover which features at which times are driving the predictions. However these methods introduce fixed perturbations, inspired from similar methods on static data, while there seems to be little motivation to do so on temporal data. In this work, we aim to explain predictions by learning not only masks, but also associated perturbations. We empirically show that learning these perturbations significantly improves the quality of these explanations on time series data.

Time series data and their time-frequency representation from gravitational-wave interferometers present multiple opportunities for the use of artificial intelligence methods associated with signal and image processing. Closely connected with this is the real-time aspect associated with gravitational-wave interferometers and the astrophysical observations they perform; the discovery potential of these instruments can be significantly enhanced when data processing can be achieved in O(1s) timescales. In this work, we introduce a novel signal and noise identification tool based on the YOLO (You Only Look Once) object detection framework. For its application into gravitational waves, we will refer to it as GW-YOLO. This tool can provide scene identification capabilities and essential information regarding whether an observed transient is any combination of noise and signal. Additionally, it supplies detailed time-frequency coordinates of the detected objects in the form of pixel masks, an essential property that can be used to understand and characterize astrophysical sources, as well as instrumental noise. The simultaneous identification of noise and signal, combined with precise pixel-level localization, represents a significant advancement in gravitational-wave data analysis. Our approach yields a 50\% detection efficiency for binary black hole signals at a signal-to-noise ratio (SNR) of 15 when such signals overlap with transient noise artifacts. When noise artifacts overlap with binary neutron star signals, our algorithm attains 50\% detection efficiency at an SNR of 30. This presents the first quantitative assessment of the ability to detect astrophysical events overlapping with realistic, instrument noise present in gravitational-wave interferometers.

How neuronal circuits achieve credit assignment remains a central unsolved question in systems neuroscience. Various studies have suggested plausible solutions for back-propagating error signals through multi-layer networks. These purely functionally motivated models assume distinct neuronal compartments to represent local error signals that determine the sign of synaptic plasticity. However, this explicit error modulation is inconsistent with phenomenological plasticity models in which the sign depends primarily on postsynaptic activity. Here we show how a plausible microcircuit model and Hebbian learning rule derived within an adaptive control theory framework can resolve this discrepancy. Assuming errors are encoded in top-down dis-inhibitory synaptic afferents, we show that error-modulated learning emerges naturally at the circuit level when recurrent inhibition explicitly influences Hebbian plasticity. The same learning rule accounts for experimentally observed plasticity in the absence of inhibition and performs comparably to back-propagation of error (BP) on several non-linearly separable benchmarks. Our findings bridge the gap between functional and experimentally observed plasticity rules and make concrete predictions on inhibitory modulation of excitatory plasticity.

The growing popularity of wearable sensors has generated large quantities of temporal physiological and activity data. Ability to analyze this data offers new opportunities for real-time health monitoring and forecasting. However, temporal physiological data presents many analytic challenges: the data is noisy, contains many missing values, and each series has a different length. Most methods proposed for time series analysis and classification do not handle datasets with these characteristics nor do they offer interpretability and explainability, a critical requirement in the health domain. We propose an unsupervised method for learning representations of time series based on common patterns identified within them. The patterns are, interpretable, variable in length, and extracted using Byte Pair Encoding compression technique. In this way the method can capture both long-term and short-term dependencies present in the data. We show that this method applies to both univariate and multivariate time series and beats state-of-the-art approaches on a real world dataset collected from wearable sensors.

We investigate causal computations taking sequences of inputs to sequences of outputs where the nth output depends on the first n inputs only. We model these in category theory via a construction taking a Cartesian category C to another category St(C) with a novel trace-like operation called "delayed trace", which misses yanking and dinaturality axioms of the usual trace. The delayed trace operation provides a feedback mechanism in St(C) with an implicit guardedness guarantee. When C is equipped with a Cartesian differential operator, we construct a differential operator for St(C) using an abstract version of backpropagation through time, a technique from machine learning based on unrolling of functions. This obtains a swath of properties for backpropagation through time, including a chain rule and Schwartz theorem. Our differential operator is also able to compute the derivative of a stateful network without requiring the network to be unrolled.

Deep neural networks have shown promise for music audio signal processing applications, often surpassing prior approaches, particularly as end-to-end models in the waveform domain. Yet results to date have tended to be constrained by low sample rates, noise, narrow domains of signal types, and/or lack of parameterized controls (i.e. "knobs"), making their suitability for professional audio engineering workflows still lacking. This work expands on prior research published on modeling nonlinear time-dependent signal processing effects associated with music production by means of a deep neural network, one which includes the ability to emulate the parameterized settings you would see on an analog piece of equipment, with the goal of eventually producing commercially viable, high quality audio, i.e. 44.1 kHz sampling rate at 16-bit resolution. The results in this paper highlight progress in modeling these effects through architecture and optimization changes, towards increasing computational efficiency, lowering signal-to-noise ratio, and extending to a larger variety of nonlinear audio effects. Toward these ends, the strategies employed involved a three-pronged approach: model speed, model accuracy, and model generalizability. Most of the presented methods provide marginal or no increase in output accuracy over the original model, with the exception of dataset manipulation. We found that limiting the audio content of the dataset, for example using datasets of just a single instrument, provided a significant improvement in model accuracy over models trained on more general datasets.

Recently, channel-independent methods have achieved state-of-the-art performance in multivariate time series (MTS) forecasting. Despite reducing overfitting risks, these methods miss potential opportunities in utilizing channel dependence for accurate predictions. We argue that there exist locally stationary lead-lag relationships between variates, i.e., some lagged variates may follow the leading indicators within a short time period. Exploiting such channel dependence is beneficial since leading indicators offer advance information that can be used to reduce the forecasting difficulty of the lagged variates. In this paper, we propose a new method named LIFT that first efficiently estimates leading indicators and their leading steps at each time step and then judiciously allows the lagged variates to utilize the advance information from leading indicators. LIFT plays as a plugin that can be seamlessly collaborated with arbitrary time series forecasting methods. Extensive experiments on six real-world datasets demonstrate that LIFT improves the state-of-the-art methods by 5.5% in average forecasting performance. Our code is available at https://github.com/SJTU-Quant/LIFT.

Missing instances in time series data impose a significant challenge to deep learning models, particularly in regression tasks. In the Earth Observation field, satellite failure or cloud occlusion frequently results in missing time-steps, introducing uncertainties in the predicted output and causing a decline in predictive performance. While many studies address missing time-steps through data augmentation to improve model robustness, the uncertainty arising at the input level is commonly overlooked. To address this gap, we introduce Monte Carlo Temporal Dropout (MC-TD), a method that explicitly accounts for input-level uncertainty by randomly dropping time-steps during inference using a predefined dropout ratio, thereby simulating the effect of missing data. To bypass the need for costly searches for the optimal dropout ratio, we extend this approach with Monte Carlo Concrete Temporal Dropout (MC-ConcTD), a method that learns the optimal dropout distribution directly. Both MC-TD and MC-ConcTD are applied during inference, leveraging Monte Carlo sampling for uncertainty quantification. Experiments on three EO time-series datasets demonstrate that MC-ConcTD improves predictive performance and uncertainty calibration compared to existing approaches. Additionally, we highlight the advantages of adaptive dropout tuning over manual selection, making uncertainty quantification more robust and accessible for EO applications.

Mechanical defects in real situations affect observation values and cause abnormalities in multivariate time series, such as sensor values or network data. To perceive abnormalities in such data, it is crucial to understand the temporal context and interrelation between variables simultaneously. The anomaly detection task for time series, especially for unlabeled data, has been a challenging problem, and we address it by applying a suitable data degradation scheme to self-supervised model training. We define four types of synthetic outliers and propose the degradation scheme in which a portion of input data is replaced with one of the synthetic outliers. Inspired by the self-attention mechanism, we design a Transformer-based architecture to recognize the temporal context and detect unnatural sequences with high efficiency. Our model converts multivariate data points into temporal representations with relative position bias and yields anomaly scores from these representations. Our method, AnomalyBERT, shows a great capability of detecting anomalies contained in complex time series and surpasses previous state-of-the-art methods on five real-world benchmarks. Our code is available at https://github.com/Jhryu30/AnomalyBERT.

Multivariate time series forecasting is an important machine learning problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. Temporal data arise in these real-world applications often involves a mixture of long-term and short-term patterns, for which traditional approaches such as Autoregressive models and Gaussian Process may fail. In this paper, we proposed a novel deep learning framework, namely Long- and Short-term Time-series network (LSTNet), to address this open challenge. LSTNet uses the Convolution Neural Network (CNN) and the Recurrent Neural Network (RNN) to extract short-term local dependency patterns among variables and to discover long-term patterns for time series trends. Furthermore, we leverage traditional autoregressive model to tackle the scale insensitive problem of the neural network model. In our evaluation on real-world data with complex mixtures of repetitive patterns, LSTNet achieved significant performance improvements over that of several state-of-the-art baseline methods. All the data and experiment codes are available online.

Earth system models suffer from various structural and parametric errors in their representation of nonlinear, multi-scale processes, leading to uncertainties in their long-term projections. The effects of many of these errors (particularly those due to fast physics) can be quantified in short-term simulations, e.g., as differences between the predicted and observed states (analysis increments). With the increase in the availability of high-quality observations and simulations, learning nudging from these increments to correct model errors has become an active research area. However, most studies focus on using neural networks, which while powerful, are hard to interpret, are data-hungry, and poorly generalize out-of-distribution. Here, we show the capabilities of Model Error Discovery with Interpretability and Data Assimilation (MEDIDA), a general, data-efficient framework that uses sparsity-promoting equation-discovery techniques to learn model errors from analysis increments. Using two-layer quasi-geostrophic turbulence as the test case, MEDIDA is shown to successfully discover various linear and nonlinear structural/parametric errors when full observations are available. Discovery from spatially sparse observations is found to require highly accurate interpolation schemes. While NNs have shown success as interpolators in recent studies, here, they are found inadequate due to their inability to accurately represent small scales, a phenomenon known as spectral bias. We show that a general remedy, adding a random Fourier feature layer to the NN, resolves this issue enabling MEDIDA to successfully discover model errors from sparse observations. These promising results suggest that with further development, MEDIDA could be scaled up to models of the Earth system and real observations.

Electrocardiography (ECG) signals are often degraded by noise, which complicates diagnosis in clinical and wearable settings. This study proposes a diffusion-based framework for ECG noise quantification via reconstruction-based anomaly detection, addressing annotation inconsistencies and the limited generalizability of conventional methods. We introduce a distributional evaluation using the Wasserstein-1 distance (W_1), comparing the reconstruction error distributions between clean and noisy ECGs to mitigate inconsistent annotations. Our final model achieved robust noise quantification using only three reverse diffusion steps. The model recorded a macro-average W_1 score of 1.308 across the benchmarks, outperforming the next-best method by over 48%. External validations demonstrated strong generalizability, supporting the exclusion of low-quality segments to enhance diagnostic accuracy and enable timely clinical responses to signal degradation. The proposed method enhances clinical decision-making, diagnostic accuracy, and real-time ECG monitoring capabilities, supporting future advancements in clinical and wearable ECG applications.

While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear continuous operator. This universal approximation theorem is suggestive of the potential application of neural networks in learning nonlinear operators from data. However, the theorem guarantees only a small approximation error for a sufficient large network, and does not consider the important optimization and generalization errors. To realize this theorem in practice, we propose deep operator networks (DeepONets) to learn operators accurately and efficiently from a relatively small dataset. A DeepONet consists of two sub-networks, one for encoding the input function at a fixed number of sensors x_i, i=1,dots,m (branch net), and another for encoding the locations for the output functions (trunk net). We perform systematic simulations for identifying two types of operators, i.e., dynamic systems and partial differential equations, and demonstrate that DeepONet significantly reduces the generalization error compared to the fully-connected networks. We also derive theoretically the dependence of the approximation error in terms of the number of sensors (where the input function is defined) as well as the input function type, and we verify the theorem with computational results. More importantly, we observe high-order error convergence in our computational tests, namely polynomial rates (from half order to fourth order) and even exponential convergence with respect to the training dataset size.

Differentiable programming techniques are widely used in the community and are responsible for the machine learning renaissance of the past several decades. While these methods are powerful, they have limits. In this short report, we discuss a common chaos based failure mode which appears in a variety of differentiable circumstances, ranging from recurrent neural networks and numerical physics simulation to training learned optimizers. We trace this failure to the spectrum of the Jacobian of the system under study, and provide criteria for when a practitioner might expect this failure to spoil their differentiation based optimization algorithms.

Time series foundation models have shown impressive performance on a variety of tasks, across a wide range of domains, even in zero-shot settings. However, most of these models are designed to handle short univariate time series as an input. This limits their practical use, especially in domains such as healthcare with copious amounts of long and multivariate data with strong temporal and intra-variate dependencies. Our study bridges this gap by cataloging and systematically comparing various context expansion techniques from both language and time series domains, and introducing a novel compressive memory mechanism to allow encoder-only TSFMs to effectively model intra-variate dependencies. We demonstrate the benefits of our approach by imbuing MOMENT, a recent family of multi-task time series foundation models, with the multivariate context.

The realization that complex systems such as ecological communities can collapse or shift regimes suddenly and without rapid external forcing poses a serious challenge to our understanding and management of the natural world. The potential to identify early warning signals that would allow researchers and managers to predict such events before they happen has therefore been an invaluable discovery that offers a way forward in spite of such seemingly unpredictable behavior. Research into early warning signals has demonstrated that it is possible to define and detect such early warning signals in advance of a transition in certain contexts. Here we describe the pattern emerging as research continues to explore just how far we can generalize these results. A core of examples emerges that shares three properties: the phenomenon of rapid regime shifts, a pattern of 'critical slowing down' that can be used to detect the approaching shift, and a mechanism of bifurcation driving the sudden change. As research has expanded beyond these core examples, it is becoming clear that not all systems that show regime shifts exhibit critical slowing down, or vice versa. Even when systems exhibit critical slowing down, statistical detection is a challenge. We review the literature that explores these edge cases and highlight the need for (a) new early warning behaviors that can be used in cases where rapid shifts do not exhibit critical slowing down, (b) the development of methods to identify which behavior might be an appropriate signal when encountering a novel system; bearing in mind that a positive indication for some systems is a negative indication in others, and (c) statistical methods that can distinguish between signatures of early warning behaviors and noise.

Diagnosis of bearing faults is paramount to reducing maintenance costs and operational breakdowns. Bearing faults are primary contributors to machine vibrations, and analyzing their signal morphology offers insights into their health status. Unfortunately, existing approaches are optimized for controlled environments, neglecting realistic conditions such as time-varying rotational speeds and the vibration's non-stationary nature. This paper presents a fusion of time-frequency analysis and deep learning techniques to diagnose bearing faults under time-varying speeds and varying noise levels. First, we formulate the bearing fault-induced vibrations and discuss the link between their non-stationarity and the bearing's inherent and operational parameters. We also elucidate quadratic time-frequency distributions and validate their effectiveness in resolving distinctive dynamic patterns associated with different bearing faults. Based on this, we design a time-frequency convolutional neural network (TF-CNN) to diagnose various faults in rolling-element bearings. Our experimental findings undeniably demonstrate the superior performance of TF-CNN in comparison to recently developed techniques. They also assert its versatility in capturing fault-relevant non-stationary features that couple with speed changes and show its exceptional resilience to noise, consistently surpassing competing methods across various signal-to-noise ratios and performance metrics. Altogether, the TF-CNN achieves substantial accuracy improvements up to 15%, in severe noise conditions.

Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning and statistics due to the presence of non-uniform intervals between observations. However, there has been significant progress within the machine learning community over the last decade on developing specialized models and architectures for learning from irregularly sampled univariate and multivariate time series data. In this survey, we first describe several axes along which approaches to learning from irregularly sampled time series differ including what data representations they are based on, what modeling primitives they leverage to deal with the fundamental problem of irregular sampling, and what inference tasks they are designed to perform. We then survey the recent literature organized primarily along the axis of modeling primitives. We describe approaches based on temporal discretization, interpolation, recurrence, attention and structural invariance. We discuss similarities and differences between approaches and highlight primary strengths and weaknesses.

Fast and scalable alignment of time series is a fundamental challenge in many domains. The standard solution, Dynamic Time Warping (DTW), struggles with poor scalability and sensitivity to noise. We introduce TimePoint, a self-supervised method that dramatically accelerates DTW-based alignment while typically improving alignment accuracy by learning keypoints and descriptors from synthetic data. Inspired by 2D keypoint detection but carefully adapted to the unique challenges of 1D signals, TimePoint leverages efficient 1D diffeomorphisms, which effectively model nonlinear time warping, to generate realistic training data. This approach, along with fully convolutional and wavelet convolutional architectures, enables the extraction of informative keypoints and descriptors. Applying DTW to these sparse representations yield major speedups and typically higher alignment accuracy than standard DTW applied to the full signals. TimePoint demonstrates strong generalization to real-world time series when trained solely on synthetic data, and further improves with fine-tuning on real data. Extensive experiments demonstrate that TimePoint consistently achieves faster and more accurate alignments than standard DTW, making it a scalable solution for time-series analysis. Our code is available at https://github.com/BGU-CS-VIL/TimePoint

We discover that common diffusion noise schedules do not enforce the last timestep to have zero signal-to-noise ratio (SNR), and some implementations of diffusion samplers do not start from the last timestep. Such designs are flawed and do not reflect the fact that the model is given pure Gaussian noise at inference, creating a discrepancy between training and inference. We show that the flawed design causes real problems in existing implementations. In Stable Diffusion, it severely limits the model to only generate images with medium brightness and prevents it from generating very bright and dark samples. We propose a few simple fixes: (1) rescale the noise schedule to enforce zero terminal SNR; (2) train the model with v prediction; (3) change the sampler to always start from the last timestep; (4) rescale classifier-free guidance to prevent over-exposure. These simple changes ensure the diffusion process is congruent between training and inference and allow the model to generate samples more faithful to the original data distribution.

Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence, an extension of weak convergence that compares a statistic or process to a sequence of evolving processes. Relative weak convergence retains the essential consequences of classical weak convergence and coincides with it under stationarity. Crucially, it applies in general non-stationary settings where classical weak convergence fails. We establish concrete relative CLTs for random vectors and empirical processes, along with sequential, weighted, and bootstrap variants, that parallel the state-of-the-art in stationary settings. Our framework and results offer simple, plug-in replacements for classical CLTs whenever stationarity is untenable, as illustrated by applications in nonparametric trend estimation and hypothesis testing.

Shallow water environments create a challenging channel for communications. In this paper, we focus on the challenges posed by the frequency-selective signal distortion called the Doppler effect. We explore the design and performance of machine learning (ML) based demodulation methods --- (1) Deep Belief Network-feed forward Neural Network (DBN-NN) and (2) Deep Belief Network-Convolutional Neural Network (DBN-CNN) in the physical layer of Shallow Water Acoustic Communication (SWAC). The proposed method comprises of a ML based feature extraction method and classification technique. First, the feature extraction converts the received signals to feature images. Next, the classification model correlates the images to a corresponding binary representative. An analysis of the ML based proposed demodulation shows that despite the presence of instantaneous frequencies, the performance of the algorithm shows an invariance with a small 2dB error margin in terms of bit error rate (BER).

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the observations. This paper provides a selective review of recent advancements in deep neural network-based approaches for SSMs, and presents a unified perspective for discrete time deep state space models and continuous time ones such as latent neural Ordinary Differential and Stochastic Differential Equations. It starts with an overview of the classical maximum likelihood based approach for learning SSMs, reviews variational autoencoder as a general learning pipeline for neural network-based approaches in the presence of latent variables, and discusses in detail representative deep learning models that fall under the SSM framework. Very recent developments, where SSMs are used as standalone architectural modules for improving efficiency in sequence modeling, are also examined. Finally, examples involving mixed frequency and irregularly-spaced time series data are presented to demonstrate the advantage of SSMs in these settings.

Time-series forecasting is one of the most active research topics in artificial intelligence. Applications in real-world time series should consider two factors for achieving reliable predictions: modeling dynamic dependencies among multiple variables and adjusting the model's intrinsic hyperparameters. A still open gap in that literature is that statistical and ensemble learning approaches systematically present lower predictive performance than deep learning methods. They generally disregard the data sequence aspect entangled with multivariate data represented in more than one time series. Conversely, this work presents a novel neural network architecture for time-series forecasting that combines the power of graph evolution with deep recurrent learning on distinct data distributions; we named our method Recurrent Graph Evolution Neural Network (ReGENN). The idea is to infer multiple multivariate relationships between co-occurring time-series by assuming that the temporal data depends not only on inner variables and intra-temporal relationships (i.e., observations from itself) but also on outer variables and inter-temporal relationships (i.e., observations from other-selves). An extensive set of experiments was conducted comparing ReGENN with dozens of ensemble methods and classical statistical ones, showing sound improvement of up to 64.87% over the competing algorithms. Furthermore, we present an analysis of the intermediate weights arising from ReGENN, showing that by looking at inter and intra-temporal relationships simultaneously, time-series forecasting is majorly improved if paying attention to how multiple multivariate data synchronously evolve.

In time series editing, we aim to modify some properties of a given time series without altering others. For example, when analyzing a hospital patient's blood pressure, we may add a sudden early drop and observe how it impacts their future while preserving other conditions. Existing diffusion-based editors rely on rigid, predefined attribute vectors as conditions and produce all-or-nothing edits through sampling. This attribute- and sampling-based approach limits flexibility in condition format and lacks customizable control over editing strength. To overcome these limitations, we introduce Instruction-based Time Series Editing, where users specify intended edits using natural language. This allows users to express a wider range of edits in a more accessible format. We then introduce InstructTime, the first instruction-based time series editor. InstructTime takes in time series and instructions, embeds them into a shared multi-modal representation space, then decodes their embeddings to generate edited time series. By learning a structured multi-modal representation space, we can easily interpolate between embeddings to achieve varying degrees of edit. To handle local and global edits together, we propose multi-resolution encoders. In our experiments, we use synthetic and real datasets and find that InstructTime is a state-of-the-art time series editor: InstructTime achieves high-quality edits with controllable strength, can generalize to unseen instructions, and can be easily adapted to unseen conditions through few-shot learning.

The ever-increasing sensor service, though opening a precious path and providing a deluge of earth system data for deep-learning-oriented earth science, sadly introduce a daunting obstacle to their industrial level deployment. Concretely, earth science systems rely heavily on the extensive deployment of sensors, however, the data collection from sensors is constrained by complex geographical and social factors, making it challenging to achieve comprehensive coverage and uniform deployment. To alleviate the obstacle, traditional approaches to sensor deployment utilize specific algorithms to design and deploy sensors. These methods dynamically adjust the activation times of sensors to optimize the detection process across each sub-region. Regrettably, formulating an activation strategy generally based on historical observations and geographic characteristics, which make the methods and resultant models were neither simple nor practical. Worse still, the complex technical design may ultimately lead to a model with weak generalizability. In this paper, we introduce for the first time the concept of spatio-temporal data dynamic sparse training and are committed to adaptively, dynamically filtering important sensor distributions. To our knowledge, this is the first proposal (termed DynST) of an industry-level deployment optimization concept at the data level. However, due to the existence of the temporal dimension, pruning of spatio-temporal data may lead to conflicts at different timestamps. To achieve this goal, we employ dynamic merge technology, along with ingenious dimensional mapping to mitigate potential impacts caused by the temporal aspect. During the training process, DynST utilize iterative pruning and sparse training, repeatedly identifying and dynamically removing sensor perception areas that contribute the least to future predictions.

This study introduces PV-RNN, a novel variational RNN inspired by the predictive-coding ideas. The model learns to extract the probabilistic structures hidden in fluctuating temporal patterns by dynamically changing the stochasticity of its latent states. Its architecture attempts to address two major concerns of variational Bayes RNNs: how can latent variables learn meaningful representations and how can the inference model transfer future observations to the latent variables. PV-RNN does both by introducing adaptive vectors mirroring the training data, whose values can then be adapted differently during evaluation. Moreover, prediction errors during backpropagation, rather than external inputs during the forward computation, are used to convey information to the network about the external data. For testing, we introduce error regression for predicting unseen sequences as inspired by predictive coding that leverages those mechanisms. The model introduces a weighting parameter, the meta-prior, to balance the optimization pressure placed on two terms of a lower bound on the marginal likelihood of the sequential data. We test the model on two datasets with probabilistic structures and show that with high values of the meta-prior the network develops deterministic chaos through which the data's randomness is imitated. For low values, the model behaves as a random process. The network performs best on intermediate values, and is able to capture the latent probabilistic structure with good generalization. Analyzing the meta-prior's impact on the network allows to precisely study the theoretical value and practical benefits of incorporating stochastic dynamics in our model. We demonstrate better prediction performance on a robot imitation task with our model using error regression compared to a standard variational Bayes model lacking such a procedure.

We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect Y can be written as a function of the cause X and a noise source N independent of X, which may be scaled by a positive function g over the cause, i.e., Y = f(X) + g(X)N. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of Y given X as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

The 100 MW cryogenic liquid oxygen/hydrogen multi-injector combustor BKD operated by the DLR Institute of Space Propulsion is a research platform that allows the study of thermoacoustic instabilities under realistic conditions, representative of small upper stage rocket engines. We use data from BKD experimental campaigns in which the static chamber pressure and fuel-oxidizer ratio are varied such that the first tangential mode of the combustor is excited under some conditions. We train an autoregressive Bayesian neural network model to forecast the amplitude of the dynamic pressure time series, inputting multiple sensor measurements (injector pressure/ temperature measurements, static chamber pressure, high-frequency dynamic pressure measurements, high-frequency OH* chemiluminescence measurements) and future flow rate control signals. The Bayesian nature of our algorithms allows us to work with a dataset whose size is restricted by the expense of each experimental run, without making overconfident extrapolations. We find that the networks are able to accurately forecast the evolution of the pressure amplitude and anticipate instability events on unseen experimental runs 500 milliseconds in advance. We compare the predictive accuracy of multiple models using different combinations of sensor inputs. We find that the high-frequency dynamic pressure signal is particularly informative. We also use the technique of integrated gradients to interpret the influence of different sensor inputs on the model prediction. The negative log-likelihood of data points in the test dataset indicates that predictive uncertainties are well-characterized by our Bayesian model and simulating a sensor failure event results as expected in a dramatic increase in the epistemic component of the uncertainty.

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

We show via a combination of mathematical arguments and empirical evidence that data distributions sampled from diffusion models satisfy a Concentration of Measure Property saying that any Lipschitz 1-dimensional projection of a random vector is not too far from its mean with high probability. This implies that such models are quite restrictive and gives an explanation for a fact previously observed in the literature that conventional diffusion models cannot capture "heavy-tailed" data (i.e. data x for which the norm |x|_2 does not possess a sub-Gaussian tail) well. We then proceed to train a generalized linear model using stochastic gradient descent (SGD) on the diffusion-generated data for a multiclass classification task and observe empirically that a Gaussian universality result holds for the test error. In other words, the test error depends only on the first and second order statistics of the diffusion-generated data in the linear setting. Results of such forms are desirable because they allow one to assume the data itself is Gaussian for analyzing performance of the trained classifier. Finally, we note that current approaches to proving universality do not apply to this case as the covariance matrices of the data tend to have vanishing minimum singular values for the diffusion-generated data, while the current proofs assume that this is not the case (see Subsection 3.4 for more details). This leaves extending previous mathematical universality results as an intriguing open question.

Numerical simulation of non-linear partial differential equations plays a crucial role in modeling physical science and engineering phenomena, such as weather, climate, and aerodynamics. Recent Machine Learning (ML) models trained on low-resolution spatio-temporal signals have shown new promises in capturing important dynamics in high-resolution signals, under the condition that the models can effectively recover the missing details. However, this study shows that significant information is often lost in the low-resolution down-sampled features. To address such issues, we propose a new approach, namely Temporal Stencil Modeling (TSM), which combines the strengths of advanced time-series sequence modeling (with the HiPPO features) and state-of-the-art neural PDE solvers (with learnable stencil modeling). TSM aims to recover the lost information from the PDE trajectories and can be regarded as a temporal generalization of classic finite volume methods such as WENO. Our experimental results show that TSM achieves the new state-of-the-art simulation accuracy for 2-D incompressible Navier-Stokes turbulent flows: it significantly outperforms the previously reported best results by 19.9% in terms of the highly-correlated duration time and reduces the inference latency into 80%. We also show a strong generalization ability of the proposed method to various out-of-distribution turbulent flow settings. Our code is available at "https://github.com/Edward-Sun/TSM-PDE".

Test-time adaptation (TTA) methods, which generally rely on the model's predictions (e.g., entropy minimization) to adapt the source pretrained model to the unlabeled target domain, suffer from noisy signals originating from 1) incorrect or 2) open-set predictions. Long-term stable adaptation is hampered by such noisy signals, so training models without such error accumulation is crucial for practical TTA. To address these issues, including open-set TTA, we propose a simple yet effective sample selection method inspired by the following crucial empirical finding. While entropy minimization compels the model to increase the probability of its predicted label (i.e., confidence values), we found that noisy samples rather show decreased confidence values. To be more specific, entropy minimization attempts to raise the confidence values of an individual sample's prediction, but individual confidence values may rise or fall due to the influence of signals from numerous other predictions (i.e., wisdom of crowds). Due to this fact, noisy signals misaligned with such 'wisdom of crowds', generally found in the correct signals, fail to raise the individual confidence values of wrong samples, despite attempts to increase them. Based on such findings, we filter out the samples whose confidence values are lower in the adapted model than in the original model, as they are likely to be noisy. Our method is widely applicable to existing TTA methods and improves their long-term adaptation performance in both image classification (e.g., 49.4% reduced error rates with TENT) and semantic segmentation (e.g., 11.7% gain in mIoU with TENT).

Masked time series modeling has recently gained much attention as a self-supervised representation learning strategy for time series. Inspired by masked image modeling in computer vision, recent works first patchify and partially mask out time series, and then train Transformers to capture the dependencies between patches by predicting masked patches from unmasked patches. However, we argue that capturing such patch dependencies might not be an optimal strategy for time series representation learning; rather, learning to embed patches independently results in better time series representations. Specifically, we propose to use 1) the simple patch reconstruction task, which autoencode each patch without looking at other patches, and 2) the simple patch-wise MLP that embeds each patch independently. In addition, we introduce complementary contrastive learning to hierarchically capture adjacent time series information efficiently. Our proposed method improves time series forecasting and classification performance compared to state-of-the-art Transformer-based models, while it is more efficient in terms of the number of parameters and training/inference time. Code is available at this repository: https://github.com/seunghan96/pits.

Noise plagues many numerical datasets, where the recorded values in the data may fail to match the true underlying values due to reasons including: erroneous sensors, data entry/processing mistakes, or imperfect human estimates. We consider general regression settings with covariates and a potentially corrupted response whose observed values may contain errors. By accounting for various uncertainties, we introduced veracity scores that distinguish between genuine errors and natural data fluctuations, conditioned on the available covariate information in the dataset. We propose a simple yet efficient filtering procedure for eliminating potential errors, and establish theoretical guarantees for our method. We also contribute a new error detection benchmark involving 5 regression datasets with real-world numerical errors (for which the true values are also known). In this benchmark and additional simulation studies, our method identifies incorrect values with better precision/recall than other approaches.

In recent years, microservices have gained widespread adoption in IT operations due to their scalability, maintenance, and flexibility. However, it becomes challenging for site reliability engineers (SREs) to pinpoint the root cause due to the complex relationships in microservices when facing system malfunctions. Previous research employed structured learning methods (e.g., PC-algorithm) to establish causal relationships and derive root causes from causal graphs. Nevertheless, they ignored the temporal order of time series data and failed to leverage the rich information inherent in the temporal relationships. For instance, in cases where there is a sudden spike in CPU utilization, it can lead to an increase in latency for other microservices. However, in this scenario, the anomaly in CPU utilization occurs before the latency increase, rather than simultaneously. As a result, the PC-algorithm fails to capture such characteristics. To address these challenges, we propose RUN, a novel approach for root cause analysis using neural Granger causal discovery with contrastive learning. RUN enhances the backbone encoder by integrating contextual information from time series, and leverages a time series forecasting model to conduct neural Granger causal discovery. In addition, RUN incorporates Pagerank with a personalization vector to efficiently recommend the top-k root causes. Extensive experiments conducted on the synthetic and real-world microservice-based datasets demonstrate that RUN noticeably outperforms the state-of-the-art root cause analysis methods. Moreover, we provide an analysis scenario for the sock-shop case to showcase the practicality and efficacy of RUN in microservice-based applications. Our code is publicly available at https://github.com/zmlin1998/RUN.

With the rapid deployment of SCADA systems, how to effectively analyze industrial signals and detect abnormal states is an urgent need for the industry. Due to the significant heterogeneity of these signals, which we summarize as the M5 problem, previous works only focus on small sub-problems and employ specialized models, failing to utilize the synergies between modalities and the powerful scaling law. However, we argue that the M5 signals can be modeled in a unified manner due to the intrinsic similarity. As a result, we propose FISHER, a Foundation model for multi-modal Industrial Signal compreHEnsive Representation. To support arbitrary sampling rates, FISHER considers the increment of sampling rate as the concatenation of sub-band information. Specifically, FISHER takes the STFT sub-band as the modeling unit and adopts a teacher student SSL framework for pre-training. We also develop the RMIS benchmark, which evaluates the representations of M5 industrial signals on multiple health management tasks. Compared with top SSL models, FISHER showcases versatile and outstanding capabilities with a general performance gain up to 5.03%, along with much more efficient scaling curves. We also investigate the scaling law on downstream tasks and derive potential avenues for future works. FISHER is now open-sourced on https://github.com/jianganbai/FISHER

We address causal reasoning in multivariate time series data generated by stochastic processes. Existing approaches are largely restricted to static settings, ignoring the continuity and emission of variations across time. In contrast, we propose a learning paradigm that directly establishes causation between events in the course of time. We present two key lemmas to compute causal contributions and frame them as reinforcement learning problems. Our approach offers formal and computational tools for uncovering and quantifying causal relationships in diffusion processes, subsuming various important settings such as discrete-time Markov decision processes. Finally, in fairly intricate experiments and through sheer learning, our framework reveals and quantifies causal links, which otherwise seem inexplicable.

Traditional time-series forecasting often focuses only on minimizing prediction errors, ignoring the specific requirements of real-world applications that employ them. This paper presents a new training methodology, which allows a forecasting model to dynamically adjust its focus based on the importance of forecast ranges specified by the end application. Unlike previous methods that fix these ranges beforehand, our training approach breaks down predictions over the entire signal range into smaller segments, which are then dynamically weighted and combined to produce accurate forecasts. We tested our method on standard datasets, including a new dataset from wireless communication, and found that not only it improves prediction accuracy but also improves the performance of end application employing the forecasting model. This research provides a basis for creating forecasting systems that better connect prediction and decision-making in various practical applications.

Data Drift is the phenomenon where the generating model behind the data changes over time. Due to data drift, any model built on the past training data becomes less relevant and inaccurate over time. Thus, detecting and controlling for data drift is critical in machine learning models. Hierarchical Temporal Memory (HTM) is a machine learning model developed by Jeff Hawkins, inspired by how the human brain processes information. It is a biologically inspired model of memory that is similar in structure to the neocortex, and whose performance is claimed to be comparable to state of the art models in detecting anomalies in time series data. Another unique benefit of HTMs is its independence from training and testing cycle; all the learning takes place online with streaming data and no separate training and testing cycle is required. In sequential learning paradigm, Sequential Probability Ratio Test (SPRT) offers some unique benefit for online learning and inference. This paper proposes a novel hybrid framework combining HTM and SPRT for real-time data drift detection and anomaly identification. Unlike existing data drift methods, our approach eliminates frequent retraining and ensures low false positive rates. HTMs currently work with one dimensional or univariate data. In a second study, we also propose an application of HTM in multidimensional supervised scenario for anomaly detection by combining the outputs of multiple HTM columns, one for each dimension of the data, through a neural network. Experimental evaluations demonstrate that the proposed method outperforms conventional drift detection techniques like the Kolmogorov-Smirnov (KS) test, Wasserstein distance, and Population Stability Index (PSI) in terms of accuracy, adaptability, and computational efficiency. Our experiments also provide insights into optimizing hyperparameters for real-time deployment in domains such as Telecom.

Multivariate time series forecasting is essential in domains such as finance, transportation, climate, and energy. However, existing patch-based methods typically adopt fixed-length segmentation, overlooking the heterogeneity of local temporal dynamics and the decoding heterogeneity of forecasting. Such designs lose details in information-dense regions, introduce redundancy in stable segments, and fail to capture the distinct complexities of short-term and long-term horizons. We propose TimeMosaic, a forecasting framework that aims to address temporal heterogeneity. TimeMosaic employs adaptive patch embedding to dynamically adjust granularity according to local information density, balancing motif reuse with structural clarity while preserving temporal continuity. In addition, it introduces segment-wise decoding that treats each prediction horizon as a related subtask and adapts to horizon-specific difficulty and information requirements, rather than applying a single uniform decoder. Extensive evaluations on benchmark datasets demonstrate that TimeMosaic delivers consistent improvements over existing methods, and our model trained on the large-scale corpus with 321 billion observations achieves performance competitive with state-of-the-art TSFMs.

This paper focuses on solving a fault detection problem using multivariate time series of vibration signals collected from planetary gearboxes in a test rig. Various traditional machine learning and deep learning methods have been proposed for multivariate time-series classification, including distance-based, functional data-oriented, feature-driven, and convolution kernel-based methods. Recent studies have shown using convolution kernel-based methods like ROCKET, and 1D convolutional neural networks with ResNet and FCN, have robust performance for multivariate time-series data classification. We propose an ensemble of three convolution kernel-based methods and show its efficacy on this fault detection problem by outperforming other approaches and achieving an accuracy of more than 98.8\%.

Interpreting time series models is uniquely challenging because it requires identifying both the location of time series signals that drive model predictions and their matching to an interpretable temporal pattern. While explainers from other modalities can be applied to time series, their inductive biases do not transfer well to the inherently challenging interpretation of time series. We present TimeX, a time series consistency model for training explainers. TimeX trains an interpretable surrogate to mimic the behavior of a pretrained time series model. It addresses the issue of model faithfulness by introducing model behavior consistency, a novel formulation that preserves relations in the latent space induced by the pretrained model with relations in the latent space induced by TimeX. TimeX provides discrete attribution maps and, unlike existing interpretability methods, it learns a latent space of explanations that can be used in various ways, such as to provide landmarks to visually aggregate similar explanations and easily recognize temporal patterns. We evaluate TimeX on eight synthetic and real-world datasets and compare its performance against state-of-the-art interpretability methods. We also conduct case studies using physiological time series. Quantitative evaluations demonstrate that TimeX achieves the highest or second-highest performance in every metric compared to baselines across all datasets. Through case studies, we show that the novel components of TimeX show potential for training faithful, interpretable models that capture the behavior of pretrained time series models.

Electrocardiograms (ECG) are widely employed as a diagnostic tool for monitoring electrical signals originating from a heart. Recent machine learning research efforts have focused on the application of screening various diseases using ECG signals. However, adapting to the application of screening disease is challenging in that labeled ECG data are limited. Achieving general representation through self-supervised learning (SSL) is a well-known approach to overcome the scarcity of labeled data; however, a naive application of SSL to ECG data, without considering the spatial-temporal relationships inherent in ECG signals, may yield suboptimal results. In this paper, we introduce ST-MEM (Spatio-Temporal Masked Electrocardiogram Modeling), designed to learn spatio-temporal features by reconstructing masked 12-lead ECG data. ST-MEM outperforms other SSL baseline methods in various experimental settings for arrhythmia classification tasks. Moreover, we demonstrate that ST-MEM is adaptable to various lead combinations. Through quantitative and qualitative analysis, we show a spatio-temporal relationship within ECG data. Our code is available at https://github.com/bakqui/ST-MEM.

Large-scale pre-trained models (PTMs) such as BERT and GPT have recently achieved great success in Natural Language Processing and Computer Vision domains. However, the development of PTMs on healthcare time-series data is lagging behind.This underscores the limitations of the existing transformer-based architectures, particularly their scalability to handle large-scale time series and ability to capture long-term temporal dependencies. In this study, we present Timely Generative Pre-trained Transformer (TimelyGPT). TimelyGPT employs an extrapolatable position (xPos) embedding to encode trend and periodic patterns into time-series representations. It also integrates recurrent attention and temporal convolution modules to effectively capture global-local temporal dependencies. We evaluated TimelyGPT on two large-scale healthcare time series datasets corresponding to continuous biosignals and irregularly-sampled time series, respectively. Our experiments show that during pre-training, TimelyGPT excels in learning time-series representations from continuously monitored biosignals and irregularly-sampled time series data commonly observed in longitudinal electronic health records (EHRs). In forecasting continuous biosignals, TimelyGPT achieves accurate extrapolation up to 6,000 timesteps of body temperature during the sleep stage transition, given a short look-up window (i.e., prompt) containing only 2,000 timesteps. For irregularly-sampled time series, TimelyGPT with a proposed time-specific inference demonstrates high top recall scores in predicting future diagnoses using early diagnostic records, effectively handling irregular intervals between clinical records. Together, we envision TimelyGPT to be useful in a broad spectrum of health domains, including long-term patient health state forecasting and patient risk trajectory prediction.

Not all positive pairs are beneficial to time series contrastive learning. In this paper, we study two types of bad positive pairs that can impair the quality of time series representation learned through contrastive learning: the noisy positive pair and the faulty positive pair. We observe that, with the presence of noisy positive pairs, the model tends to simply learn the pattern of noise (Noisy Alignment). Meanwhile, when faulty positive pairs arise, the model wastes considerable amount of effort aligning non-representative patterns (Faulty Alignment). To address this problem, we propose a Dynamic Bad Pair Mining (DBPM) algorithm, which reliably identifies and suppresses bad positive pairs in time series contrastive learning. Specifically, DBPM utilizes a memory module to dynamically track the training behavior of each positive pair along training process. This allows us to identify potential bad positive pairs at each epoch based on their historical training behaviors. The identified bad pairs are subsequently down-weighted through a transformation module, thereby mitigating their negative impact on the representation learning process. DBPM is a simple algorithm designed as a lightweight plug-in without learnable parameters to enhance the performance of existing state-of-the-art methods. Through extensive experiments conducted on four large-scale, real-world time series datasets, we demonstrate DBPM's efficacy in mitigating the adverse effects of bad positive pairs.

Time series are the primary data type used to record dynamic system measurements and generated in great volume by both physical sensors and online processes (virtual sensors). Time series analytics is therefore crucial to unlocking the wealth of information implicit in available data. With the recent advancements in graph neural networks (GNNs), there has been a surge in GNN-based approaches for time series analysis. These approaches can explicitly model inter-temporal and inter-variable relationships, which traditional and other deep neural network-based methods struggle to do. In this survey, we provide a comprehensive review of graph neural networks for time series analysis (GNN4TS), encompassing four fundamental dimensions: forecasting, classification, anomaly detection, and imputation. Our aim is to guide designers and practitioners to understand, build applications, and advance research of GNN4TS. At first, we provide a comprehensive task-oriented taxonomy of GNN4TS. Then, we present and discuss representative research works and introduce mainstream applications of GNN4TS. A comprehensive discussion of potential future research directions completes the survey. This survey, for the first time, brings together a vast array of knowledge on GNN-based time series research, highlighting foundations, practical applications, and opportunities of graph neural networks for time series analysis.

Practitioners frequently aim to infer an unobserved population trajectory using sample snapshots at multiple time points. For instance, in single-cell sequencing, scientists would like to learn how gene expression evolves over time. But sequencing any cell destroys that cell. So we cannot access any cell's full trajectory, but we can access snapshot samples from many cells. Stochastic differential equations are commonly used to analyze systems with full individual-trajectory access; since here we have only sample snapshots, these methods are inapplicable. The deep learning community has recently explored using Schr\"odinger bridges (SBs) and their extensions to estimate these dynamics. However, these methods either (1) interpolate between just two time points or (2) require a single fixed reference dynamic within the SB, which is often just set to be Brownian motion. But learning piecewise from adjacent time points can fail to capture long-term dependencies. And practitioners are typically able to specify a model class for the reference dynamic but not the exact values of the parameters within it. So we propose a new method that (1) learns the unobserved trajectories from sample snapshots across multiple time points and (2) requires specification only of a class of reference dynamics, not a single fixed one. In particular, we suggest an iterative projection method inspired by Schr\"odinger bridges; we alternate between learning a piecewise SB on the unobserved trajectories and using the learned SB to refine our best guess for the dynamics within the reference class. We demonstrate the advantages of our method via a well-known simulated parametric model from ecology, simulated and real data from systems biology, and real motion-capture data.

In physics and engineering literature, the distribution of the excursion-above-zero time distribution (exceedance distribution) for a stationary Gaussian process has been approximated by a stationary switching process with independently distributed switching times. The approach matched the covariance of the clipped Gaussian process with the one for the stationary switching process and the distribution of the latter was used as the so-called independent interval approximation (IIA). The approach successfully assessed the persistency exponent for many physically important processes but left an unanswered question when such an approach leads to a mathematically meaningful and proper exceedance distribution. Here we address this question by proposing an alternative matching of the expected values of the clipped Slepian process and the corresponding switched process initiated at the origin. The method has allowed resolving the mathematical correctness of the matching method for a large subclass of the Gaussian processes with monotonic covariance, for which we provide a sufficient condition for the validity of the IIA. Within this class, the IIA produces a valid distribution for the excursion time and is represented in an explicit stochastic form that connects directly to the covariance of the underlying Gaussian process. We compare the excursion level distributions as well as the corresponding persistency exponents obtained through the IIA method with numerically computed exact distributions, and the simulated distribution for several important Gaussian models. We also argue that for stationary Gaussian processes with a non-monotonic covariance, the IIA fails and should not be used.

We present a self-supervised, time-to-event (TTE) foundation model called MOTOR (Many Outcome Time Oriented Representations) which is pretrained on timestamped sequences of events in electronic health records (EHR) and health insurance claims. TTE models are used for estimating the probability distribution of the time until a specific event occurs, which is an important task in medical settings. TTE models provide many advantages over classification using fixed time horizons, including naturally handling censored observations, but are challenging to train with limited labeled data. MOTOR addresses this challenge by pretraining on up to 55M patient records (9B clinical events). We evaluate MOTOR's transfer learning performance on 19 tasks, across 3 patient databases (a private EHR system, MIMIC-IV, and Merative claims data). Task-specific models adapted from MOTOR improve time-dependent C statistics by 4.6% over state-of-the-art, improve label efficiency by up to 95% ,and are more robust to temporal distributional shifts. We further evaluate cross-site portability by adapting our MOTOR foundation model for six prediction tasks on the MIMIC-IV dataset, where it outperforms all baselines. MOTOR is the first foundation model for medical TTE predictions and we release a 143M parameter pretrained model for research use at [redacted URL].

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to learning the transfer operator or the generator of the system, which in turn can be used for numerous tasks, such as forecasting and interpreting the system dynamics. We show that the search for a good representation can be cast as an optimization problem over neural networks. Our approach is supported by recent results in statistical learning theory, highlighting the role of approximation error and metric distortion in the learning problem. The objective function we propose is associated with projection operators from the representation space to the data space, overcomes metric distortion, and can be empirically estimated from data. In the discrete-time setting, we further derive a relaxed objective function that is differentiable and numerically well-conditioned. We compare our method against state-of-the-art approaches on different datasets, showing better performance across the board.

Missing values, irregularly collected samples, and multi-resolution signals commonly occur in multivariate time series data, making predictive tasks difficult. These challenges are especially prevalent in the healthcare domain, where patients' vital signs and electronic records are collected at different frequencies and have occasionally missing information due to the imperfections in equipment or patient circumstances. Researchers have handled each of these issues differently, often handling missing data through mean value imputation and then using sequence models over the multivariate signals while ignoring the different resolution of signals. We propose a unified model named Multi-resolution Flexible Irregular Time series Network (Multi-FIT). The building block for Multi-FIT is the FIT network. The FIT network creates an informative dense representation at each time step using signal information such as last observed value, time difference since the last observed time stamp and overall mean for the signal. Vertical FIT (FIT-V) is a variant of FIT which also models the relationship between different temporal signals while creating the informative dense representations for the signal. The multi-FIT model uses multiple FIT networks for sets of signals with different resolutions, further facilitating the construction of flexible representations. Our model has three main contributions: a.) it does not impute values but rather creates informative representations to provide flexibility to the model for creating task-specific representations b.) it models the relationship between different signals in the form of support signals c.) it models different resolutions in parallel before merging them for the final prediction task. The FIT, FIT-V and Multi-FIT networks improve upon the state-of-the-art models for three predictive tasks, including the forecasting of patient survival.

This paper studies sequence modeling for prediction tasks with long range dependencies. We propose a new formulation for state space models (SSMs) based on learning linear dynamical systems with the spectral filtering algorithm (Hazan et al. (2017)). This gives rise to a novel sequence prediction architecture we call a spectral state space model. Spectral state space models have two primary advantages. First, they have provable robustness properties as their performance depends on neither the spectrum of the underlying dynamics nor the dimensionality of the problem. Second, these models are constructed with fixed convolutional filters that do not require learning while still outperforming SSMs in both theory and practice. The resulting models are evaluated on synthetic dynamical systems and long-range prediction tasks of various modalities. These evaluations support the theoretical benefits of spectral filtering for tasks requiring very long range memory.

Accurate uncertainty measurement is a key step to building robust and reliable machine learning systems. Conformal prediction is a distribution-free uncertainty quantification algorithm popular for its ease of implementation, statistical coverage guarantees, and versatility for underlying forecasters. However, existing conformal prediction algorithms for time series are limited to single-step prediction without considering the temporal dependency. In this paper, we propose a Copula Conformal Prediction algorithm for multivariate, multi-step Time Series forecasting, CopulaCPTS. We prove that CopulaCPTS has finite sample validity guarantee. On several synthetic and real-world multivariate time series datasets, we show that CopulaCPTS produces more calibrated and sharp confidence intervals for multi-step prediction tasks than existing techniques.

Automated analysis of complex systems based on multiple readouts remains a challenge. Change point detection algorithms are aimed to locating abrupt changes in the time series behaviour of a process. In this paper, we present a novel change point detection algorithm based on Latent Neural Stochastic Differential Equations (SDE). Our method learns a non-linear deep learning transformation of the process into a latent space and estimates a SDE that describes its evolution over time. The algorithm uses the likelihood ratio of the learned stochastic processes in different timestamps to find change points of the process. We demonstrate the detection capabilities and performance of our algorithm on synthetic and real-world datasets. The proposed method outperforms the state-of-the-art algorithms on the majority of our experiments.

Time-series causal discovery (TSCD) is a fundamental problem of machine learning. However, existing synthetic datasets cannot properly evaluate or predict the algorithms' performance on real data. This study introduces the CausalTime pipeline to generate time-series that highly resemble the real data and with ground truth causal graphs for quantitative performance evaluation. The pipeline starts from real observations in a specific scenario and produces a matching benchmark dataset. Firstly, we harness deep neural networks along with normalizing flow to accurately capture realistic dynamics. Secondly, we extract hypothesized causal graphs by performing importance analysis on the neural network or leveraging prior knowledge. Thirdly, we derive the ground truth causal graphs by splitting the causal model into causal term, residual term, and noise term. Lastly, using the fitted network and the derived causal graph, we generate corresponding versatile time-series proper for algorithm assessment. In the experiments, we validate the fidelity of the generated data through qualitative and quantitative experiments, followed by a benchmarking of existing TSCD algorithms using these generated datasets. CausalTime offers a feasible solution to evaluating TSCD algorithms in real applications and can be generalized to a wide range of fields. For easy use of the proposed approach, we also provide a user-friendly website, hosted on www.causaltime.cc.

Despite the success of physics-informed neural networks (PINNs) in approximating partial differential equations (PDEs), PINNs can sometimes fail to converge to the correct solution in problems involving complicated PDEs. This is reflected in several recent studies on characterizing the "failure modes" of PINNs, although a thorough understanding of the connection between PINN failure modes and sampling strategies is missing. In this paper, we provide a novel perspective of failure modes of PINNs by hypothesizing that training PINNs relies on successful "propagation" of solution from initial and/or boundary condition points to interior points. We show that PINNs with poor sampling strategies can get stuck at trivial solutions if there are propagation failures, characterized by highly imbalanced PDE residual fields. To mitigate propagation failures, we propose a novel Retain-Resample-Release sampling (R3) algorithm that can incrementally accumulate collocation points in regions of high PDE residuals with little to no computational overhead. We provide an extension of R3 sampling to respect the principle of causality while solving time-dependent PDEs. We theoretically analyze the behavior of R3 sampling and empirically demonstrate its efficacy and efficiency in comparison with baselines on a variety of PDE problems.

Evaluating anomaly detection algorithms in time series data is critical as inaccuracies can lead to flawed decision-making in various domains where real-time analytics and data-driven strategies are essential. Traditional performance metrics assume iid data and fail to capture the complex temporal dynamics and specific characteristics of time series anomalies, such as early and delayed detections. We introduce Proximity-Aware Time series anomaly Evaluation (PATE), a novel evaluation metric that incorporates the temporal relationship between prediction and anomaly intervals. PATE uses proximity-based weighting considering buffer zones around anomaly intervals, enabling a more detailed and informed assessment of a detection. Using these weights, PATE computes a weighted version of the area under the Precision and Recall curve. Our experiments with synthetic and real-world datasets show the superiority of PATE in providing more sensible and accurate evaluations than other evaluation metrics. We also tested several state-of-the-art anomaly detectors across various benchmark datasets using the PATE evaluation scheme. The results show that a common metric like Point-Adjusted F1 Score fails to characterize the detection performances well, and that PATE is able to provide a more fair model comparison. By introducing PATE, we redefine the understanding of model efficacy that steers future studies toward developing more effective and accurate detection models.

Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms the prior distribution back into the data distribution by slowly removing the noise. Crucially, the reverse-time SDE depends only on the time-dependent gradient field (\aka, score) of the perturbed data distribution. By leveraging advances in score-based generative modeling, we can accurately estimate these scores with neural networks, and use numerical SDE solvers to generate samples. We show that this framework encapsulates previous approaches in score-based generative modeling and diffusion probabilistic modeling, allowing for new sampling procedures and new modeling capabilities. In particular, we introduce a predictor-corrector framework to correct errors in the evolution of the discretized reverse-time SDE. We also derive an equivalent neural ODE that samples from the same distribution as the SDE, but additionally enables exact likelihood computation, and improved sampling efficiency. In addition, we provide a new way to solve inverse problems with score-based models, as demonstrated with experiments on class-conditional generation, image inpainting, and colorization. Combined with multiple architectural improvements, we achieve record-breaking performance for unconditional image generation on CIFAR-10 with an Inception score of 9.89 and FID of 2.20, a competitive likelihood of 2.99 bits/dim, and demonstrate high fidelity generation of 1024 x 1024 images for the first time from a score-based generative model.

Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix -- a canonical representation for discrete-time processes -- which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a "closed-loop" variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length ell and state-space size d, we go from O(d ell) na\"ively to O(d + ell). In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR(p) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.

Implicit Neural Spatial Representation (INSR) has emerged as an effective representation of spatially-dependent vector fields. This work explores solving time-dependent PDEs with INSR. Classical PDE solvers introduce both temporal and spatial discretizations. Common spatial discretizations include meshes and meshless point clouds, where each degree-of-freedom corresponds to a location in space. While these explicit spatial correspondences are intuitive to model and understand, these representations are not necessarily optimal for accuracy, memory usage, or adaptivity. Keeping the classical temporal discretization unchanged (e.g., explicit/implicit Euler), we explore INSR as an alternative spatial discretization, where spatial information is implicitly stored in the neural network weights. The network weights then evolve over time via time integration. Our approach does not require any training data generated by existing solvers because our approach is the solver itself. We validate our approach on various PDEs with examples involving large elastic deformations, turbulent fluids, and multi-scale phenomena. While slower to compute than traditional representations, our approach exhibits higher accuracy and lower memory consumption. Whereas classical solvers can dynamically adapt their spatial representation only by resorting to complex remeshing algorithms, our INSR approach is intrinsically adaptive. By tapping into the rich literature of classic time integrators, e.g., operator-splitting schemes, our method enables challenging simulations in contact mechanics and turbulent flows where previous neural-physics approaches struggle. Videos and codes are available on the project page: http://www.cs.columbia.edu/cg/INSR-PDE/

Recent studies have demonstrated the great power of Transformer models for time series forecasting. One of the key elements that lead to the transformer's success is the channel-independent (CI) strategy to improve the training robustness. However, the ignorance of the correlation among different channels in CI would limit the model's forecasting capacity. In this work, we design a special Transformer, i.e., Channel Aligned Robust Blend Transformer (CARD for short), that addresses key shortcomings of CI type Transformer in time series forecasting. First, CARD introduces a channel-aligned attention structure that allows it to capture both temporal correlations among signals and dynamical dependence among multiple variables over time. Second, in order to efficiently utilize the multi-scale knowledge, we design a token blend module to generate tokens with different resolutions. Third, we introduce a robust loss function for time series forecasting to alleviate the potential overfitting issue. This new loss function weights the importance of forecasting over a finite horizon based on prediction uncertainties. Our evaluation of multiple long-term and short-term forecasting datasets demonstrates that CARD significantly outperforms state-of-the-art time series forecasting methods. The code is available at the following repository:https://github.com/wxie9/CARD

We establish a new theoretical framework for learning under multi-class, instance-dependent label noise. This framework casts learning with label noise as a form of domain adaptation, in particular, domain adaptation under posterior drift. We introduce the concept of relative signal strength (RSS), a pointwise measure that quantifies the transferability from noisy to clean posterior. Using RSS, we establish nearly matching upper and lower bounds on the excess risk. Our theoretical findings support the simple Noise Ignorant Empirical Risk Minimization (NI-ERM) principle, which minimizes empirical risk while ignoring label noise. Finally, we translate this theoretical insight into practice: by using NI-ERM to fit a linear classifier on top of a self-supervised feature extractor, we achieve state-of-the-art performance on the CIFAR-N data challenge.

Time series forecasting has attracted significant attention in recent decades. Previous studies have demonstrated that the Channel-Independent (CI) strategy improves forecasting performance by treating different channels individually, while it leads to poor generalization on unseen instances and ignores potentially necessary interactions between channels. Conversely, the Channel-Dependent (CD) strategy mixes all channels with even irrelevant and indiscriminate information, which, however, results in oversmoothing issues and limits forecasting accuracy. There is a lack of channel strategy that effectively balances individual channel treatment for improved forecasting performance without overlooking essential interactions between channels. Motivated by our observation of a correlation between the time series model's performance boost against channel mixing and the intrinsic similarity on a pair of channels, we developed a novel and adaptable Channel Clustering Module (CCM). CCM dynamically groups channels characterized by intrinsic similarities and leverages cluster information instead of individual channel identities, combining the best of CD and CI worlds. Extensive experiments on real-world datasets demonstrate that CCM can (1) boost the performance of CI and CD models by an average margin of 2.4% and 7.2% on long-term and short-term forecasting, respectively; (2) enable zero-shot forecasting with mainstream time series forecasting models; (3) uncover intrinsic time series patterns among channels and improve interpretability of complex time series models.

Time series analysis is of immense importance in extensive applications, such as weather forecasting, anomaly detection, and action recognition. This paper focuses on temporal variation modeling, which is the common key problem of extensive analysis tasks. Previous methods attempt to accomplish this directly from the 1D time series, which is extremely challenging due to the intricate temporal patterns. Based on the observation of multi-periodicity in time series, we ravel out the complex temporal variations into the multiple intraperiod- and interperiod-variations. To tackle the limitations of 1D time series in representation capability, we extend the analysis of temporal variations into the 2D space by transforming the 1D time series into a set of 2D tensors based on multiple periods. This transformation can embed the intraperiod- and interperiod-variations into the columns and rows of the 2D tensors respectively, making the 2D-variations to be easily modeled by 2D kernels. Technically, we propose the TimesNet with TimesBlock as a task-general backbone for time series analysis. TimesBlock can discover the multi-periodicity adaptively and extract the complex temporal variations from transformed 2D tensors by a parameter-efficient inception block. Our proposed TimesNet achieves consistent state-of-the-art in five mainstream time series analysis tasks, including short- and long-term forecasting, imputation, classification, and anomaly detection. Code is available at this repository: https://github.com/thuml/TimesNet.

Independence testing is a fundamental and classical statistical problem that has been extensively studied in the batch setting when one fixes the sample size before collecting data. However, practitioners often prefer procedures that adapt to the complexity of a problem at hand instead of setting sample size in advance. Ideally, such procedures should (a) allow stopping earlier on easy tasks (and later on harder tasks), hence making better use of available resources, and (b) continuously monitor the data and efficiently incorporate statistical evidence after collecting new data, while controlling the false alarm rate. It is well known that classical batch tests are not tailored for streaming data settings: valid inference after data peeking requires correcting for multiple testing but such corrections generally result in low power. Following the principle of testing by betting, we design sequential kernelized independence tests (SKITs) that overcome such shortcomings. We exemplify our broad framework using bets inspired by kernelized dependence measures, e.g, the Hilbert-Schmidt independence criterion. Our test is valid under non-i.i.d. time-varying settings, for which there exist no batch tests. We demonstrate the power of our approaches on both simulated and real data.

We introduce MOMENT, a family of open-source foundation models for general-purpose time-series analysis. Pre-training large models on time-series data is challenging due to (1) the absence of a large and cohesive public time-series repository, and (2) diverse time-series characteristics which make multi-dataset training onerous. Additionally, (3) experimental benchmarks to evaluate these models, especially in scenarios with limited resources, time, and supervision, are still in their nascent stages. To address these challenges, we compile a large and diverse collection of public time-series, called the Time-series Pile, and systematically tackle time-series-specific challenges to unlock large-scale multi-dataset pre-training. Finally, we build on recent work to design a benchmark to evaluate time-series foundation models on diverse tasks and datasets in limited supervision settings. Experiments on this benchmark demonstrate the effectiveness of our pre-trained models with minimal data and task-specific fine-tuning. Finally, we present several interesting empirical observations about large pre-trained time-series models. Our code is available anonymously at anonymous.4open.science/r/BETT-773F/.

In this paper, we introduce TimeGPT, the first foundation model for time series, capable of generating accurate predictions for diverse datasets not seen during training. We evaluate our pre-trained model against established statistical, machine learning, and deep learning methods, demonstrating that TimeGPT zero-shot inference excels in performance, efficiency, and simplicity. Our study provides compelling evidence that insights from other domains of artificial intelligence can be effectively applied to time series analysis. We conclude that large-scale time series models offer an exciting opportunity to democratize access to precise predictions and reduce uncertainty by leveraging the capabilities of contemporary advancements in deep learning.

This paper presents OLinear, a linear-based multivariate time series forecasting model that operates in an orthogonally transformed domain. Recent forecasting models typically adopt the temporal forecast (TF) paradigm, which directly encode and decode time series in the time domain. However, the entangled step-wise dependencies in series data can hinder the performance of TF. To address this, some forecasters conduct encoding and decoding in the transformed domain using fixed, dataset-independent bases (e.g., sine and cosine signals in the Fourier transform). In contrast, we utilize OrthoTrans, a data-adaptive transformation based on an orthogonal matrix that diagonalizes the series' temporal Pearson correlation matrix. This approach enables more effective encoding and decoding in the decorrelated feature domain and can serve as a plug-in module to enhance existing forecasters. To enhance the representation learning for multivariate time series, we introduce a customized linear layer, NormLin, which employs a normalized weight matrix to capture multivariate dependencies. Empirically, the NormLin module shows a surprising performance advantage over multi-head self-attention, while requiring nearly half the FLOPs. Extensive experiments on 24 benchmarks and 140 forecasting tasks demonstrate that OLinear consistently achieves state-of-the-art performance with high efficiency. Notably, as a plug-in replacement for self-attention, the NormLin module consistently enhances Transformer-based forecasters. The code and datasets are available at https://anonymous.4open.science/r/OLinear

This work explores the in-context learning capabilities of State Space Models (SSMs) and presents, to the best of our knowledge, the first theoretical explanation of a possible underlying mechanism. We introduce a novel weight construction for SSMs, enabling them to predict the next state of any dynamical system after observing previous states without parameter fine-tuning. This is accomplished by extending the HiPPO framework to demonstrate that continuous SSMs can approximate the derivative of any input signal. Specifically, we find an explicit weight construction for continuous SSMs and provide an asymptotic error bound on the derivative approximation. The discretization of this continuous SSM subsequently yields a discrete SSM that predicts the next state. Finally, we demonstrate the effectiveness of our parameterization empirically. This work should be an initial step toward understanding how sequence models based on SSMs learn in context.

When sound waves hit an object, they induce vibrations that produce high-frequency and subtle visual changes, which can be used for recovering the sound. Early studies always encounter trade-offs related to sampling rate, bandwidth, field of view, and the simplicity of the optical path. Recent advances in event camera hardware show good potential for its application in visual sound recovery, because of its superior ability in capturing high-frequency signals. However, existing event-based vibration recovery methods are still sub-optimal for sound recovery. In this work, we propose a novel pipeline for non-contact sound recovery, fully utilizing spatial-temporal information from the event stream. We first generate a large training set using a novel simulation pipeline. Then we designed a network that leverages the sparsity of events to capture spatial information and uses Mamba to model long-term temporal information. Lastly, we train a spatial aggregation block to aggregate information from different locations to further improve signal quality. To capture event signals caused by sound waves, we also designed an imaging system using a laser matrix to enhance the gradient and collected multiple data sequences for testing. Experimental results on synthetic and real-world data demonstrate the effectiveness of our method.

Deep learning approaches have demonstrated success in modeling analog audio effects. Nevertheless, challenges remain in modeling more complex effects that involve time-varying nonlinear elements, such as dynamic range compressors. Existing neural network approaches for modeling compression either ignore the device parameters, do not attain sufficient accuracy, or otherwise require large noncausal models prohibiting real-time operation. In this work, we propose a modification to temporal convolutional networks (TCNs) enabling greater efficiency without sacrificing performance. By utilizing very sparse convolutional kernels through rapidly growing dilations, our model attains a significant receptive field using fewer layers, reducing computation. Through a detailed evaluation we demonstrate our efficient and causal approach achieves state-of-the-art performance in modeling the analog LA-2A, is capable of real-time operation on CPU, and only requires 10 minutes of training data.

Self-supervised learning has garnered increasing attention in time series analysis for benefiting various downstream tasks and reducing reliance on labeled data. Despite its effectiveness, existing methods often struggle to comprehensively capture both long-term dynamic evolution and subtle local patterns in a unified manner. In this work, we propose TimeDART, a novel self-supervised time series pre-training framework that unifies two powerful generative paradigms to learn more transferable representations. Specifically, we first employ a causal Transformer encoder, accompanied by a patch-based embedding strategy, to model the evolving trends from left to right. Building on this global modeling, we further introduce a denoising diffusion process to capture fine-grained local patterns through forward diffusion and reverse denoising. Finally, we optimize the model in an autoregressive manner. As a result, TimeDART effectively accounts for both global and local sequence features in a coherent way. We conduct extensive experiments on public datasets for time series forecasting and classification. The experimental results demonstrate that TimeDART consistently outperforms previous compared methods, validating the effectiveness of our approach. Our code is available at https://github.com/Melmaphother/TimeDART.

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are often best described using continuous-time stochastic processes. Unfortunately, most existing structure learning approaches assume that the underlying process evolves in discrete-time and/or observations occur at regular time intervals. These mismatched assumptions can often lead to incorrect learned structures and models. In this work, we introduce a novel structure learning method, SCOTCH, which combines neural stochastic differential equations (SDE) with variational inference to infer a posterior distribution over possible structures. This continuous-time approach can naturally handle both learning from and predicting observations at arbitrary time points. Theoretically, we establish sufficient conditions for an SDE and SCOTCH to be structurally identifiable, and prove its consistency under infinite data limits. Empirically, we demonstrate that our approach leads to improved structure learning performance on both synthetic and real-world datasets compared to relevant baselines under regular and irregular sampling intervals.

In practical scenarios, time series forecasting necessitates not only accuracy but also efficiency. Consequently, the exploration of model architectures remains a perennially trending topic in research. To address these challenges, we propose a novel backbone architecture named Time Evidence Fusion Network (TEFN) from the perspective of information fusion. Specifically, we introduce the Basic Probability Assignment (BPA) Module based on evidence theory to capture the uncertainty of multivariate time series data from both channel and time dimensions. Additionally, we develop a novel multi-source information fusion method to effectively integrate the two distinct dimensions from BPA output, leading to improved forecasting accuracy. Lastly, we conduct extensive experiments to demonstrate that TEFN achieves performance comparable to state-of-the-art methods while maintaining significantly lower complexity and reduced training time. Also, our experiments show that TEFN exhibits high robustness, with minimal error fluctuations during hyperparameter selection. Furthermore, due to the fact that BPA is derived from fuzzy theory, TEFN offers a high degree of interpretability. Therefore, the proposed TEFN balances accuracy, efficiency, stability, and interpretability, making it a desirable solution for time series forecasting.

In this paper, we introduce RaVAEn, a lightweight, unsupervised approach for change detection in satellite data based on Variational Auto-Encoders (VAEs) with the specific purpose of on-board deployment. Applications such as disaster management enormously benefit from the rapid availability of satellite observations. Traditionally, data analysis is performed on the ground after all data is transferred - downlinked - to a ground station. Constraint on the downlink capabilities therefore affects any downstream application. In contrast, RaVAEn pre-processes the sampled data directly on the satellite and flags changed areas to prioritise for downlink, shortening the response time. We verified the efficacy of our system on a dataset composed of time series of catastrophic events - which we plan to release alongside this publication - demonstrating that RaVAEn outperforms pixel-wise baselines. Finally we tested our approach on resource-limited hardware for assessing computational and memory limitations.

A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo & Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called `stochastic interpolants' to bridge any two arbitrary probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient. Upon consideration of the time evolution of an individual sample, this viewpoint immediately leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score of the interpolant density. We show that minimization of these quadratic objectives leads to control of the likelihood for generative models built upon stochastic dynamics, while likelihood control for deterministic dynamics is more stringent. We also discuss connections with other methods such as score-based diffusion models, stochastic localization processes, probabilistic denoising techniques, and rectifying flows. In addition, we demonstrate that stochastic interpolants recover the Schr\"odinger bridge between the two target densities when explicitly optimizing over the interpolant. Finally, algorithmic aspects are discussed and the approach is illustrated on numerical examples.

We provide a new theoretical framework for the variable-step deferred correction (DC) methods based on the well-known BDF2 formula. By using the discrete orthogonal convolution kernels, some high-order BDF2-DC methods are proven to be stable on arbitrary time grids according to the recent definition of stability (SINUM, 60: 2253-2272). It significantly relaxes the existing step-ratio restrictions for the BDF2-DC methods (BIT, 62: 1789-1822). The associated sharp error estimates are established by taking the numerical effects of the starting approximations into account, and they suggest that the BDF2-DC methods have no aftereffect, that is, the lower-order starting scheme for the BDF2 scheme will not cause a loss in the accuracy of the high-order BDF2-DC methods. Extensive tests on the graded and random time meshes are presented to support the new theory.

We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems modulated via nonlinear interlinked gates. The resulting models represent dynamical systems with varying (i.e., liquid) time-constants coupled to their hidden state, with outputs being computed by numerical differential equation solvers. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations, and give rise to improved performance on time-series prediction tasks. To demonstrate these properties, we first take a theoretical approach to find bounds over their dynamics and compute their expressive power by the trajectory length measure in latent trajectory space. We then conduct a series of time-series prediction experiments to manifest the approximation capability of Liquid Time-Constant Networks (LTCs) compared to classical and modern RNNs. Code and data are available at https://github.com/raminmh/liquid_time_constant_networks

Understanding when the noise in stochastic gradient descent (SGD) affects generalization of deep neural networks remains a challenge, complicated by the fact that networks can operate in distinct training regimes. Here we study how the magnitude of this noise T affects performance as the size of the training set P and the scale of initialization alpha are varied. For gradient descent, alpha is a key parameter that controls if the network is `lazy'(alphagg1) or instead learns features (alphall1). For classification of MNIST and CIFAR10 images, our central results are: (i) obtaining phase diagrams for performance in the (alpha,T) plane. They show that SGD noise can be detrimental or instead useful depending on the training regime. Moreover, although increasing T or decreasing alpha both allow the net to escape the lazy regime, these changes can have opposite effects on performance. (ii) Most importantly, we find that the characteristic temperature T_c where the noise of SGD starts affecting the trained model (and eventually performance) is a power law of P. We relate this finding with the observation that key dynamical quantities, such as the total variation of weights during training, depend on both T and P as power laws. These results indicate that a key effect of SGD noise occurs late in training by affecting the stopping process whereby all data are fitted. Indeed, we argue that due to SGD noise, nets must develop a stronger `signal', i.e. larger informative weights, to fit the data, leading to a longer training time. A stronger signal and a longer training time are also required when the size of the training set P increases. We confirm these views in the perceptron model, where signal and noise can be precisely measured. Interestingly, exponents characterizing the effect of SGD depend on the density of data near the decision boundary, as we explain.

A central problem in learning from sequential data is representing cumulative history in an incremental fashion as more data is processed. We introduce a general framework (HiPPO) for the online compression of continuous signals and discrete time series by projection onto polynomial bases. Given a measure that specifies the importance of each time step in the past, HiPPO produces an optimal solution to a natural online function approximation problem. As special cases, our framework yields a short derivation of the recent Legendre Memory Unit (LMU) from first principles, and generalizes the ubiquitous gating mechanism of recurrent neural networks such as GRUs. This formal framework yields a new memory update mechanism (HiPPO-LegS) that scales through time to remember all history, avoiding priors on the timescale. HiPPO-LegS enjoys the theoretical benefits of timescale robustness, fast updates, and bounded gradients. By incorporating the memory dynamics into recurrent neural networks, HiPPO RNNs can empirically capture complex temporal dependencies. On the benchmark permuted MNIST dataset, HiPPO-LegS sets a new state-of-the-art accuracy of 98.3%. Finally, on a novel trajectory classification task testing robustness to out-of-distribution timescales and missing data, HiPPO-LegS outperforms RNN and neural ODE baselines by 25-40% accuracy.

Multivariate time series forecasting tasks are usually conducted in a channel-dependent (CD) way since it can incorporate more variable-relevant information. However, it may also involve a lot of irrelevant variables, and this even leads to worse performance than the channel-independent (CI) strategy. This paper combines the strengths of both strategies and proposes the Deep Graph Clustering Transformer (DGCformer) for multivariate time series forecasting. Specifically, it first groups these relevant variables by a graph convolutional network integrated with an autoencoder, and a former-latter masked self-attention mechanism is then considered with the CD strategy being applied to each group of variables while the CI one for different groups. Extensive experimental results on eight datasets demonstrate the superiority of our method against state-of-the-art models, and our code will be publicly available upon acceptance.

The goal of the change-point detection is to discover changes of time series distribution. One of the state of the art approaches of the change-point detection are based on direct density ratio estimation. In this work we show how existing algorithms can be generalized using various binary classification and regression models. In particular, we show that the Gradient Boosting over Decision Trees and Neural Networks can be used for this purpose. The algorithms are tested on several synthetic and real-world datasets. The results show that the proposed methods outperform classical RuLSIF algorithm. Discussion of cases where the proposed algorithms have advantages over existing methods are also provided.

Time series foundation models (TSFMs) have emerged as a powerful paradigm for time series analysis, driven by large-scale pretraining on diverse data corpora. However, time series inherently exhibit heterogeneous information density over time, influenced by system states and signal complexity, presenting significant modeling challenges especially in a zero-shot scenario. Current TSFMs rely on non-adaptive processing pipelines that fail to capture this dynamic nature. For example, common tokenization strategies such as fixed-size patching enforce rigid observational granularity, limiting their ability to adapt to varying information densities. Similarly, conventional positional encodings impose a uniform temporal scale, making it difficult to model diverse periodicities and trends across series. To overcome these limitations, we propose Kairos, a flexible TSFM framework that integrates a dynamic patching tokenizer and an instance-adaptive positional embedding. Kairos adaptively selects tokenization granularity and tailors positional encodings to the unique characteristics of each time series instance. Trained on a large-scale Predictability-Stratified Time Series (PreSTS) corpus comprising over 300 billion time points and adopting a multi-patch prediction strategy in the inference stage, Kairos achieves superior performance with much fewer parameters on two common zero-shot benchmarks, GIFT-Eval and the Time-Series-Library benchmark, consistently outperforming established methods across diverse tasks. The project page is at https://foundation-model-research.github.io/Kairos .

Linear time-invariant state space models (SSM) are a classical model from engineering and statistics, that have recently been shown to be very promising in machine learning through the Structured State Space sequence model (S4). A core component of S4 involves initializing the SSM state matrix to a particular matrix called a HiPPO matrix, which was empirically important for S4's ability to handle long sequences. However, the specific matrix that S4 uses was actually derived in previous work for a particular time-varying dynamical system, and the use of this matrix as a time-invariant SSM had no known mathematical interpretation. Consequently, the theoretical mechanism by which S4 models long-range dependencies actually remains unexplained. We derive a more general and intuitive formulation of the HiPPO framework, which provides a simple mathematical interpretation of S4 as a decomposition onto exponentially-warped Legendre polynomials, explaining its ability to capture long dependencies. Our generalization introduces a theoretically rich class of SSMs that also lets us derive more intuitive S4 variants for other bases such as the Fourier basis, and explains other aspects of training S4, such as how to initialize the important timescale parameter. These insights improve S4's performance to 86% on the Long Range Arena benchmark, with 96% on the most difficult Path-X task.

Many real-world systems exhibit temporal, dynamic behaviors, which are captured as time series of complex agent interactions. To perform temporal reasoning, current methods primarily encode temporal dynamics through simple sequence-based models. However, in general these models fail to efficiently capture the full spectrum of rich dynamics in the input, since the dynamics is not uniformly distributed. In particular, relevant information might be harder to extract and computing power is wasted for processing all individual timesteps, even if they contain no significant changes or no new information. Here we propose TimeGraphs, a novel approach that characterizes dynamic interactions as a hierarchical temporal graph, diverging from traditional sequential representations. Our approach models the interactions using a compact graph-based representation, enabling adaptive reasoning across diverse time scales. Adopting a self-supervised method, TimeGraphs constructs a multi-level event hierarchy from a temporal input, which is then used to efficiently reason about the unevenly distributed dynamics. This construction process is scalable and incremental to accommodate streaming data. We evaluate TimeGraphs on multiple datasets with complex, dynamic agent interactions, including a football simulator, the Resistance game, and the MOMA human activity dataset. The results demonstrate both robustness and efficiency of TimeGraphs on a range of temporal reasoning tasks. Our approach obtains state-of-the-art performance and leads to a performance increase of up to 12.2% on event prediction and recognition tasks over current approaches. Our experiments further demonstrate a wide array of capabilities including zero-shot generalization, robustness in case of data sparsity, and adaptability to streaming data flow.

Online updating of time series forecasting models aims to address the concept drifting problem by efficiently updating forecasting models based on streaming data. Many algorithms are designed for online time series forecasting, with some exploiting cross-variable dependency while others assume independence among variables. Given every data assumption has its own pros and cons in online time series modeling, we propose Online ensembling Network (OneNet). It dynamically updates and combines two models, with one focusing on modeling the dependency across the time dimension and the other on cross-variate dependency. Our method incorporates a reinforcement learning-based approach into the traditional online convex programming framework, allowing for the linear combination of the two models with dynamically adjusted weights. OneNet addresses the main shortcoming of classical online learning methods that tend to be slow in adapting to the concept drift. Empirical results show that OneNet reduces online forecasting error by more than 50% compared to the State-Of-The-Art (SOTA) method. The code is available at https://github.com/yfzhang114/OneNet.

Classification of time series data is an important task for many application domains. One of the best existing methods for this task, in terms of accuracy and computation time, is MiniROCKET. In this work, we extend this approach to provide better global temporal encodings using hyperdimensional computing (HDC) mechanisms. HDC (also known as Vector Symbolic Architectures, VSA) is a general method to explicitly represent and process information in high-dimensional vectors. It has previously been used successfully in combination with deep neural networks and other signal processing algorithms. We argue that the internal high-dimensional representation of MiniROCKET is well suited to be complemented by the algebra of HDC. This leads to a more general formulation, HDC-MiniROCKET, where the original algorithm is only a special case. We will discuss and demonstrate that HDC-MiniROCKET can systematically overcome catastrophic failures of MiniROCKET on simple synthetic datasets. These results are confirmed by experiments on the 128 datasets from the UCR time series classification benchmark. The extension with HDC can achieve considerably better results on datasets with high temporal dependence without increasing the computational effort for inference.

Most existing forecasting systems are memory-based methods, which attempt to mimic human forecasting ability by employing various memory mechanisms and have progressed in temporal modeling for memory dependency. Nevertheless, an obvious weakness of this paradigm is that it can only model limited historical dependence and can not transcend the past. In this paper, we rethink the temporal dependence of event evolution and propose a novel memory-anticipation-based paradigm to model an entire temporal structure, including the past, present, and future. Based on this idea, we present Memory-and-Anticipation Transformer (MAT), a memory-anticipation-based approach, to address the online action detection and anticipation tasks. In addition, owing to the inherent superiority of MAT, it can process online action detection and anticipation tasks in a unified manner. The proposed MAT model is tested on four challenging benchmarks TVSeries, THUMOS'14, HDD, and EPIC-Kitchens-100, for online action detection and anticipation tasks, and it significantly outperforms all existing methods. Code is available at https://github.com/Echo0125/Memory-and-Anticipation-Transformer.

Time series classification (TSC) on multivariate time series is a critical problem. We propose a novel multi-view approach integrating frequency-domain and time-domain features to provide complementary contexts for TSC. Our method fuses continuous wavelet transform spectral features with temporal convolutional or multilayer perceptron features. We leverage the Mamba state space model for efficient and scalable sequence modeling. We also introduce a novel tango scanning scheme to better model sequence relationships. Experiments on 10 standard benchmark datasets demonstrate our approach achieves an average 6.45% accuracy improvement over state-of-the-art TSC models.

Time series research has gathered lots of interests in the last decade, especially for Time Series Classification (TSC) and Time Series Forecasting (TSF). Research in TSC has greatly benefited from the University of California Riverside and University of East Anglia (UCR/UEA) Time Series Archives. On the other hand, the advancement in Time Series Forecasting relies on time series forecasting competitions such as the Makridakis competitions, NN3 and NN5 Neural Network competitions, and a few Kaggle competitions. Each year, thousands of papers proposing new algorithms for TSC and TSF have utilized these benchmarking archives. These algorithms are designed for these specific problems, but may not be useful for tasks such as predicting the heart rate of a person using photoplethysmogram (PPG) and accelerometer data. We refer to this problem as Time Series Extrinsic Regression (TSER), where we are interested in a more general methodology of predicting a single continuous value, from univariate or multivariate time series. This prediction can be from the same time series or not directly related to the predictor time series and does not necessarily need to be a future value or depend heavily on recent values. To the best of our knowledge, research into TSER has received much less attention in the time series research community and there are no models developed for general time series extrinsic regression problems. Most models are developed for a specific problem. Therefore, we aim to motivate and support the research into TSER by introducing the first TSER benchmarking archive. This archive contains 19 datasets from different domains, with varying number of dimensions, unequal length dimensions, and missing values. In this paper, we introduce the datasets in this archive and did an initial benchmark on existing models.

Time-series forecasting is crucial for numerous real-world applications including weather prediction and financial market modeling. While temporal-domain methods remain prevalent, frequency-domain approaches can effectively capture multi-scale periodic patterns, reduce sequence dependencies, and naturally denoise signals. However, existing approaches typically train model components for all frequencies under a unified training objective, often leading to mismatched learning speeds: high-frequency components converge faster and risk overfitting, while low-frequency components underfit due to insufficient training time. To deal with this challenge, we propose BEAT (Balanced frEquency Adaptive Tuning), a novel framework that dynamically monitors the training status for each frequency and adaptively adjusts their gradient updates. By recognizing convergence, overfitting, or underfitting for each frequency, BEAT dynamically reallocates learning priorities, moderating gradients for rapid learners and increasing those for slower ones, alleviating the tension between competing objectives across frequencies and synchronizing the overall learning process. Extensive experiments on seven real-world datasets demonstrate that BEAT consistently outperforms state-of-the-art approaches.

Semiconductor lasers have been rapidly evolving to meet the demands of next-generation optical networks. This imposes much more stringent requirements on the laser reliability, which are dominated by degradation mechanisms (e.g., sudden degradation) limiting the semiconductor laser lifetime. Physics-based approaches are often used to characterize the degradation behavior analytically, yet explicit domain knowledge and accurate mathematical models are required. Building such models can be very challenging due to a lack of a full understanding of the complex physical processes inducing the degradation under various operating conditions. To overcome the aforementioned limitations, we propose a new data-driven approach, extracting useful insights from the operational monitored data to predict the degradation trend without requiring any specific knowledge or using any physical model. The proposed approach is based on an unsupervised technique, a conditional variational autoencoder, and validated using vertical-cavity surface-emitting laser (VCSEL) and tunable edge emitting laser reliability data. The experimental results confirm that our model (i) achieves a good degradation prediction and generalization performance by yielding an F1 score of 95.3%, (ii) outperforms several baseline ML based anomaly detection techniques, and (iii) helps to shorten the aging tests by early predicting the failed devices before the end of the test and thereby saving costs

Error Feedback (EF) is a highly popular and immensely effective mechanism for fixing convergence issues which arise in distributed training methods (such as distributed GD or SGD) when these are enhanced with greedy communication compression techniques such as TopK. While EF was proposed almost a decade ago (Seide et al., 2014), and despite concentrated effort by the community to advance the theoretical understanding of this mechanism, there is still a lot to explore. In this work we study a modern form of error feedback called EF21 (Richtarik et al., 2021) which offers the currently best-known theoretical guarantees, under the weakest assumptions, and also works well in practice. In particular, while the theoretical communication complexity of EF21 depends on the quadratic mean of certain smoothness parameters, we improve this dependence to their arithmetic mean, which is always smaller, and can be substantially smaller, especially in heterogeneous data regimes. We take the reader on a journey of our discovery process. Starting with the idea of applying EF21 to an equivalent reformulation of the underlying problem which (unfortunately) requires (often impractical) machine cloning, we continue to the discovery of a new weighted version of EF21 which can (fortunately) be executed without any cloning, and finally circle back to an improved analysis of the original EF21 method. While this development applies to the simplest form of EF21, our approach naturally extends to more elaborate variants involving stochastic gradients and partial participation. Further, our technique improves the best-known theory of EF21 in the rare features regime (Richtarik et al., 2023). Finally, we validate our theoretical findings with suitable experiments.

Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via either Monte Carlo or expectation-maximization methods. In this work we introduce an alternative, variational inference algorithm for Markov jump processes which relies on neural ordinary differential equations, and is trainable via back-propagation. Our methodology learns neural, continuous-time representations of the observed data, that are used to approximate the initial distribution and time-dependent transition probability rates of the posterior Markov jump process. The time-independent rates of the prior process are in contrast trained akin to generative adversarial networks. We test our approach on synthetic data sampled from ground-truth Markov jump processes, experimental switching ion channel data and molecular dynamics simulations. Source code to reproduce our experiments is available online.

Neural surrogates for partial differential equations (PDEs) have become popular due to their potential to quickly simulate physics. With a few exceptions, neural surrogates generally treat the forward evolution of time-dependent PDEs as a black box by directly predicting the next state. While this is a natural and easy framework for applying neural surrogates, it can be an over-simplified and rigid framework for predicting physics. In this work, we propose an alternative framework in which neural solvers predict the temporal derivative and an ODE integrator forwards the solution in time, which has little overhead and is broadly applicable across model architectures and PDEs. We find that by simply changing the training target and introducing numerical integration during inference, neural surrogates can gain accuracy and stability. Predicting temporal derivatives also allows models to not be constrained to a specific temporal discretization, allowing for flexible time-stepping during inference or training on higher-resolution PDE data. Lastly, we investigate why this new framework can be beneficial and in what situations does it work well.

Efficient decoding to estimate error locations from outcomes of syndrome measurement is the prerequisite for quantum error correction. Decoding in presence of circuit-level noise including measurement errors should be considered in case of actual quantum computing devices. In this work, we develop a decoder for circuit-level noise that solves the error estimation problems as Ising-type optimization problems. We confirm that the threshold theorem in the surface code under the circuitlevel noise is reproduced with an error threshold of approximately 0.4%. We also demonstrate the advantage of the decoder through which the Y error detection rate can be improved compared with other matching-based decoders. Our results reveal that a lower logical error rate can be obtained using our algorithm compared with that of the minimum-weight perfect matching algorithm.

In this work, we develop a joint denoising and feedback strategy for channel state information in frequency division duplex systems. In such systems, the biggest challenge is the overhead incurred when the mobile terminal has to send the downlink channel state information or corresponding partial information to the base station, where the complete estimates can subsequently be restored. To this end, we propose a novel learning-based framework for denoising and compression of channel estimates. Unlike existing studies, we extend a recently proposed approach and show that based solely on noisy uplink data available at the base station, it is possible to learn an autoencoder neural network that generalizes to downlink data. Subsequently, half of the autoencoder can be offloaded to the mobile terminals to generate channel feedback there as efficiently as possible, without any training effort at the terminals or corresponding transfer of training data. Numerical simulations demonstrate the excellent performance of the proposed method.

Accurate detection of cardiac abnormalities from electrocardiogram recordings is regarded as essential for clinical diagnostics and decision support. Traditional deep learning models such as residual networks and transformer architectures have been applied successfully to this task, but their performance has been limited when long sequential signals are processed. Recently, state space models have been introduced as an efficient alternative. In this study, a hybrid framework named One Dimensional Convolutional Neural Network Electrocardiogram Mamba is introduced, in which convolutional feature extraction is combined with Mamba, a selective state space model designed for effective sequence modeling. The model is built upon Vision Mamba, a bidirectional variant through which the representation of temporal dependencies in electrocardiogram data is enhanced. Comprehensive experiments on the PhysioNet Computing in Cardiology Challenges of 2020 and 2021 were conducted, and superior performance compared with existing methods was achieved. Specifically, the proposed model achieved substantially higher AUPRC and AUROC scores than those reported by the best previously published algorithms on twelve lead electrocardiograms. These results demonstrate the potential of Mamba-based architectures to advance reliable ECG classification. This capability supports early diagnosis and personalized treatment, while enhancing accessibility in telemedicine and resource-constrained healthcare systems.

We consider the problem of modeling high-speed flows using machine learning methods. While most prior studies focus on low-speed fluid flows in which uniform time-stepping is practical, flows approaching and exceeding the speed of sound exhibit sudden changes such as shock waves. In such cases, it is essential to use adaptive time-stepping methods to allow a temporal resolution sufficient to resolve these phenomena while simultaneously balancing computational costs. Here, we propose a two-phase machine learning method, known as ShockCast, to model high-speed flows with adaptive time-stepping. In the first phase, we propose to employ a machine learning model to predict the timestep size. In the second phase, the predicted timestep is used as an input along with the current fluid fields to advance the system state by the predicted timestep. We explore several physically-motivated components for timestep prediction and introduce timestep conditioning strategies inspired by neural ODE and Mixture of Experts. As ShockCast is the first framework for learning high-speed flows, we evaluate our methods by generating two supersonic flow datasets, available at https://huggingface.co/datasets/divelab. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Noisy partial label learning (noisy PLL) is an important branch of weakly supervised learning. Unlike PLL where the ground-truth label must conceal in the candidate label set, noisy PLL relaxes this constraint and allows the ground-truth label may not be in the candidate label set. To address this challenging problem, most of the existing works attempt to detect noisy samples and estimate the ground-truth label for each noisy sample. However, detection errors are unavoidable. These errors can accumulate during training and continuously affect model optimization. To this end, we propose a novel framework for noisy PLL with theoretical guarantees, called ``Adjusting Label Importance Mechanism (ALIM)''. It aims to reduce the negative impact of detection errors by trading off the initial candidate set and model outputs. ALIM is a plug-in strategy that can be integrated with existing PLL approaches. Experimental results on benchmark datasets demonstrate that our method can achieve state-of-the-art performance on noisy PLL. \textcolor[rgb]{0.93,0.0,0.47}{Our code can be found in Supplementary Material}.

Spiking Neural Networks (SNNs) are a promising research direction for building power-efficient information processing systems, especially for temporal tasks such as speech recognition. In SNNs, delays refer to the time needed for one spike to travel from one neuron to another. These delays matter because they influence the spike arrival times, and it is well-known that spiking neurons respond more strongly to coincident input spikes. More formally, it has been shown theoretically that plastic delays greatly increase the expressivity in SNNs. Yet, efficient algorithms to learn these delays have been lacking. Here, we propose a new discrete-time algorithm that addresses this issue in deep feedforward SNNs using backpropagation, in an offline manner. To simulate delays between consecutive layers, we use 1D convolutions across time. The kernels contain only a few non-zero weights - one per synapse - whose positions correspond to the delays. These positions are learned together with the weights using the recently proposed Dilated Convolution with Learnable Spacings (DCLS). We evaluated our method on three datasets: the Spiking Heidelberg Dataset (SHD), the Spiking Speech Commands (SSC) and its non-spiking version Google Speech Commands v0.02 (GSC) benchmarks, which require detecting temporal patterns. We used feedforward SNNs with two or three hidden fully connected layers, and vanilla leaky integrate-and-fire neurons. We showed that fixed random delays help and that learning them helps even more. Furthermore, our method outperformed the state-of-the-art in the three datasets without using recurrent connections and with substantially fewer parameters. Our work demonstrates the potential of delay learning in developing accurate and precise models for temporal data processing. Our code is based on PyTorch / SpikingJelly and available at: https://github.com/Thvnvtos/SNN-delays

In this work we present a data-driven approach for predicting the behavior of (i.e., profiling) a given non-linear audio signal processing effect (henceforth "audio effect"). Our objective is to learn a mapping function that maps the unprocessed audio to the processed by the audio effect to be profiled, using time-domain samples. To that aim, we employ a deep auto-encoder model that is conditioned on both time-domain samples and the control parameters of the target audio effect. As a test-case study, we focus on the offline profiling of two dynamic range compression audio effects, one software-based and the other analog. Compressors were chosen because they are a widely used and important set of effects and because their parameterized nonlinear time-dependent nature makes them a challenging problem for a system aiming to profile "general" audio effects. Results from our experimental procedure show that the primary functional and auditory characteristics of the compressors can be captured, however there is still sufficient audible noise to merit further investigation before such methods are applied to real-world audio processing workflows.

In speech enhancement and source separation, signal-to-noise ratio is a ubiquitous objective measure of denoising/separation quality. A decade ago, the BSS_eval toolkit was developed to give researchers worldwide a way to evaluate the quality of their algorithms in a simple, fair, and hopefully insightful way: it attempted to account for channel variations, and to not only evaluate the total distortion in the estimated signal but also split it in terms of various factors such as remaining interference, newly added artifacts, and channel errors. In recent years, hundreds of papers have been relying on this toolkit to evaluate their proposed methods and compare them to previous works, often arguing that differences on the order of 0.1 dB proved the effectiveness of a method over others. We argue here that the signal-to-distortion ratio (SDR) implemented in the BSS_eval toolkit has generally been improperly used and abused, especially in the case of single-channel separation, resulting in misleading results. We propose to use a slightly modified definition, resulting in a simpler, more robust measure, called scale-invariant SDR (SI-SDR). We present various examples of critical failure of the original SDR that SI-SDR overcomes.

Given a dataset on actions and resulting long-term rewards, a direct estimation approach fits value functions that minimize prediction error on the training data. Temporal difference learning (TD) methods instead fit value functions by minimizing the degree of temporal inconsistency between estimates made at successive time-steps. Focusing on finite state Markov chains, we provide a crisp asymptotic theory of the statistical advantages of this approach. First, we show that an intuitive inverse trajectory pooling coefficient completely characterizes the percent reduction in mean-squared error of value estimates. Depending on problem structure, the reduction could be enormous or nonexistent. Next, we prove that there can be dramatic improvements in estimates of the difference in value-to-go for two states: TD's errors are bounded in terms of a novel measure - the problem's trajectory crossing time - which can be much smaller than the problem's time horizon.

Periodic signals play an important role in daily lives. Although conventional sequential models have shown remarkable success in various fields, they still come short in modeling periodicity; they either collapse, diverge or ignore details. In this paper, we introduce a novel framework inspired by Fourier series to generate periodic signals. We first decompose the given signals into multiple sines and cosines and then conditionally generate periodic signals with the output components. We have shown our model efficacy on three tasks: reconstruction, imputation and conditional generation. Our model outperforms baselines in all tasks and shows more stable and refined results.

The design of codes for feedback-enabled communications has been a long-standing open problem. Recent research on non-linear, deep learning-based coding schemes have demonstrated significant improvements in communication reliability over linear codes, but are still vulnerable to the presence of forward and feedback noise over the channel. In this paper, we develop a new family of non-linear feedback codes that greatly enhance robustness to channel noise. Our autoencoder-based architecture is designed to learn codes based on consecutive blocks of bits, which obtains de-noising advantages over bit-by-bit processing to help overcome the physical separation between the encoder and decoder over a noisy channel. Moreover, we develop a power control layer at the encoder to explicitly incorporate hardware constraints into the learning optimization, and prove that the resulting average power constraint is satisfied asymptotically. Numerical experiments demonstrate that our scheme outperforms state-of-the-art feedback codes by wide margins over practical forward and feedback noise regimes, and provide information-theoretic insights on the behavior of our non-linear codes. Moreover, we observe that, in a long blocklength regime, canonical error correction codes are still preferable to feedback codes when the feedback noise becomes high.

It is commonplace to encounter heterogeneous or nonstationary data, of which the underlying generating process changes across domains or over time. Such a distribution shift feature presents both challenges and opportunities for causal discovery. In this paper, we develop a framework for causal discovery from such data, called Constraint-based causal Discovery from heterogeneous/NOnstationary Data (CD-NOD), to find causal skeleton and directions and estimate the properties of mechanism changes. First, we propose an enhanced constraint-based procedure to detect variables whose local mechanisms change and recover the skeleton of the causal structure over observed variables. Second, we present a method to determine causal orientations by making use of independent changes in the data distribution implied by the underlying causal model, benefiting from information carried by changing distributions. After learning the causal structure, next, we investigate how to efficiently estimate the "driving force" of the nonstationarity of a causal mechanism. That is, we aim to extract from data a low-dimensional representation of changes. The proposed methods are nonparametric, with no hard restrictions on data distributions and causal mechanisms, and do not rely on window segmentation. Furthermore, we find that data heterogeneity benefits causal structure identification even with particular types of confounders. Finally, we show the connection between heterogeneity/nonstationarity and soft intervention in causal discovery. Experimental results on various synthetic and real-world data sets (task-fMRI and stock market data) are presented to demonstrate the efficacy of the proposed methods.

The coupling of the angular jitter of the spacecraft and their sub-assemblies with the optical bench and the telescope into the interferometric length readout will be a major noise source in the LISA mission. We refer to this noise as tilt-to-length (TTL) coupling. It will be reduced directly by realignments, and the residual noise will then be subtracted in post-processing. The success of these mitigation strategies depends on an accurate computation of the TTL coupling coefficients. We present here a thorough analysis of the accuracy of the coefficient estimation under different jitter characteristics, angular readout noise levels, and gravitational wave sources. We analyze in which cases the estimates degrade using two estimators, the common least squares estimator and the instrumental variables estimator. Our investigations show that angular readout noise leads to a bias of the least squares estimator, depending on the TTL coupling coefficients, jitter and readout noise level, while the instrumental variable estimator is not biased. We present an equation that predicts the estimation bias of the least squares method due to angular readout noise.

The progress in modelling time series and, more generally, sequences of structured data has recently revamped research in anomaly detection. The task stands for identifying abnormal behaviors in financial series, IT systems, aerospace measurements, and the medical domain, where anomaly detection may aid in isolating cases of depression and attend the elderly. Anomaly detection in time series is a complex task since anomalies are rare due to highly non-linear temporal correlations and since the definition of anomalous is sometimes subjective. Here we propose the novel use of Hyperbolic uncertainty for Anomaly Detection (HypAD). HypAD learns self-supervisedly to reconstruct the input signal. We adopt best practices from the state-of-the-art to encode the sequence by an LSTM, jointly learned with a decoder to reconstruct the signal, with the aid of GAN critics. Uncertainty is estimated end-to-end by means of a hyperbolic neural network. By using uncertainty, HypAD may assess whether it is certain about the input signal but it fails to reconstruct it because this is anomalous; or whether the reconstruction error does not necessarily imply anomaly, as the model is uncertain, e.g. a complex but regular input signal. The novel key idea is that a detectable anomaly is one where the model is certain but it predicts wrongly. HypAD outperforms the current state-of-the-art for univariate anomaly detection on established benchmarks based on data from NASA, Yahoo, Numenta, Amazon, and Twitter. It also yields state-of-the-art performance on a multivariate dataset of anomaly activities in elderly home residences, and it outperforms the baseline on SWaT. Overall, HypAD yields the lowest false alarms at the best performance rate, thanks to successfully identifying detectable anomalies.

Developing models and algorithms to predict nonstationary time series is a long standing statistical problem. It is crucial for many applications, in particular for fashion or retail industries, to make optimal inventory decisions and avoid massive wastes. By tracking thousands of fashion trends on social media with state-of-the-art computer vision approaches, we propose a new model for fashion time series forecasting. Our contribution is twofold. We first provide publicly a dataset gathering 10000 weekly fashion time series. As influence dynamics are the key of emerging trend detection, we associate with each time series an external weak signal representing behaviours of influencers. Secondly, to leverage such a dataset, we propose a new hybrid forecasting model. Our approach combines per-time-series parametric models with seasonal components and a global recurrent neural network to include sporadic external signals. This hybrid model provides state-of-the-art results on the proposed fashion dataset, on the weekly time series of the M4 competition, and illustrates the benefit of the contribution of external weak signals.

In recent years, there has been increasing interest in developing foundation models for time series data that can generalize across diverse downstream tasks. While numerous forecasting-oriented foundation models have been introduced, there is a notable scarcity of models tailored for time series classification. To address this gap, we present Mantis, a new open-source foundation model for time series classification based on the Vision Transformer (ViT) architecture that has been pre-trained using a contrastive learning approach. Our experimental results show that Mantis outperforms existing foundation models both when the backbone is frozen and when fine-tuned, while achieving the lowest calibration error. In addition, we propose several adapters to handle the multivariate setting, reducing memory requirements and modeling channel interdependence.

Modern enterprises generate vast streams of time series metrics when monitoring complex systems, known as observability data. Unlike conventional time series from domains such as weather, observability data are zero-inflated, highly stochastic, and exhibit minimal temporal structure. Despite their importance, observability datasets are underrepresented in public benchmarks due to proprietary restrictions. Existing datasets are often anonymized and normalized, removing scale information and limiting their use for tasks beyond forecasting, such as anomaly detection, root-cause analysis, and multi-modal reasoning. To address this gap, we introduce TelecomTS, a large-scale observability dataset derived from a 5G telecommunications network. TelecomTS features heterogeneous, de-anonymized covariates with explicit scale information and supports a suite of downstream tasks, including anomaly detection, root-cause analysis, and a question-answering benchmark requiring multi-modal reasoning. Benchmarking state-of-the-art time series, language, and reasoning models reveals that existing approaches struggle with the abrupt, noisy, and high-variance dynamics of observability data. Our experiments also underscore the importance of preserving covariates' absolute scale, emphasizing the need for foundation time series models that natively leverage scale information for practical observability applications.

Real-world multichannel time series prediction faces growing demands for efficiency across edge and cloud environments, making channel compression a timely and essential problem. Motivated by success of Multiple-Input Multiple-Output (MIMO) methods, we propose a predictability-aware compression-decompression framework to reduce runtime, lower communication cost, and maintain prediction accuracy across diverse predictors. The core idea involves using a circular periodicity key matrix with orthogonality to capture underlying time series predictability during compression and to mitigate reconstruction errors during decompression by relaxing oversimplified data assumptions. Theoretical and empirical analyses show that the proposed framework is both time-efficient and scalable under a large number of channels. Extensive experiments on six datasets across various predictors demonstrate that the proposed method achieves superior overall performance by jointly considering prediction accuracy and runtime, while maintaining strong compatibility with diverse predictors.

We develop a data-driven deep neural operator framework to approximate multiple output states for a diesel engine and generate real-time predictions with reasonable accuracy. As emission norms become more stringent, the need for fast and accurate models that enable analysis of system behavior have become an essential requirement for system development. The fast transient processes involved in the operation of a combustion engine make it difficult to develop accurate physics-based models for such systems. As an alternative to physics based models, we develop an operator-based regression model (DeepONet) to learn the relevant output states for a mean-value gas flow engine model using the engine operating conditions as input variables. We have adopted a mean-value model as a benchmark for comparison, simulated using Simulink. The developed approach necessitates using the initial conditions of the output states to predict the accurate sequence over the temporal domain. To this end, a sequence-to-sequence approach is embedded into the proposed framework. The accuracy of the model is evaluated by comparing the prediction output to ground truth generated from Simulink model. The maximum mathcal L_2 relative error observed was approximately 6.5%. The sensitivity of the DeepONet model is evaluated under simulated noise conditions and the model shows relatively low sensitivity to noise. The uncertainty in model prediction is further assessed by using a mean ensemble approach. The worst-case error at the (mu + 2sigma) boundary was found to be 12%. The proposed framework provides the ability to predict output states in real-time and enables data-driven learning of complex input-output operator mapping. As a result, this model can be applied during initial development stages, where accurate models may not be available.

Real-world deployment of machine learning models is challenging because data evolves over time. While no model can work when data evolves in an arbitrary fashion, if there is some pattern to these changes, we might be able to design methods to address it. This paper addresses situations when data evolves gradually. We introduce a time-varying propensity score that can detect gradual shifts in the distribution of data which allows us to selectively sample past data to update the model -- not just similar data from the past like that of a standard propensity score but also data that evolved in a similar fashion in the past. The time-varying propensity score is quite general: we demonstrate different ways of implementing it and evaluate it on a variety of problems ranging from supervised learning (e.g., image classification problems) where data undergoes a sequence of gradual shifts, to reinforcement learning tasks (e.g., robotic manipulation and continuous control) where data shifts as the policy or the task changes.

This article focuses on estimating relative transfer functions (RTFs) for beamforming applications. Traditional methods often assume that spectra are uncorrelated, an assumption that is often violated in practical scenarios due to factors such as time-domain windowing or the non-stationary nature of signals, as observed in speech. To overcome these limitations, we propose an RTF estimation technique that leverages spectral and spatial correlations through subspace analysis. Additionally, we derive Cram\'er--Rao bounds (CRBs) for the RTF estimation task, providing theoretical insights into the achievable estimation accuracy. These bounds reveal that channel estimation can be performed more accurately if the noise or the target signal exhibits spectral correlations. Experiments with both real and synthetic data show that our technique outperforms the narrowband maximum-likelihood estimator, known as covariance whitening (CW), when the target exhibits spectral correlations. Although the proposed algorithm generally achieves accuracy close to the theoretical bound, there is potential for further improvement, especially in scenarios with highly spectrally correlated noise. While channel estimation has various applications, we demonstrate the method using a minimum variance distortionless (MVDR) beamformer for multichannel speech enhancement. A free Python implementation is also provided.

Multivariate time-series data in numerous real-world applications (e.g., healthcare and industry) are informative but challenging due to the lack of labels and high dimensionality. Recent studies in self-supervised learning have shown their potential in learning rich representations without relying on labels, yet they fall short in learning disentangled embeddings and addressing issues of inductive bias (e.g., transformation-invariance). To tackle these challenges, we propose TimeDRL, a generic multivariate time-series representation learning framework with disentangled dual-level embeddings. TimeDRL is characterized by three novel features: (i) disentangled derivation of timestamp-level and instance-level embeddings from patched time-series data using a [CLS] token strategy; (ii) utilization of timestamp-predictive and instance-contrastive tasks for disentangled representation learning, with the former optimizing timestamp-level embeddings with predictive loss, and the latter optimizing instance-level embeddings with contrastive loss; and (iii) avoidance of augmentation methods to eliminate inductive biases, such as transformation-invariance from cropping and masking. Comprehensive experiments on 6 time-series forecasting datasets and 5 time-series classification datasets have shown that TimeDRL consistently surpasses existing representation learning approaches, achieving an average improvement of forecasting by 58.02% in MSE and classification by 1.48% in accuracy. Furthermore, extensive ablation studies confirmed the relative contribution of each component in TimeDRL's architecture, and semi-supervised learning evaluations demonstrated its effectiveness in real-world scenarios, even with limited labeled data. The code is available at https://github.com/blacksnail789521/TimeDRL.

In this work, we consider rather general and broad class of Markov chains, Ito chains, that look like Euler-Maryama discretization of some Stochastic Differential Equation. The chain we study is a unified framework for theoretical analysis. It comes with almost arbitrary isotropic and state-dependent noise instead of normal and state-independent one as in most related papers. Moreover, in our chain the drift and diffusion coefficient can be inexact in order to cover wide range of applications as Stochastic Gradient Langevin Dynamics, sampling, Stochastic Gradient Descent or Stochastic Gradient Boosting. We prove the bound in W_{2}-distance between the laws of our Ito chain and corresponding differential equation. These results improve or cover most of the known estimates. And for some particular cases, our analysis is the first.

While previous distribution shift detection approaches can identify if a shift has occurred, these approaches cannot localize which specific features have caused a distribution shift -- a critical step in diagnosing or fixing any underlying issue. For example, in military sensor networks, users will want to detect when one or more of the sensors has been compromised, and critically, they will want to know which specific sensors might be compromised. Thus, we first define a formalization of this problem as multiple conditional distribution hypothesis tests and propose both non-parametric and parametric statistical tests. For both efficiency and flexibility, we then propose to use a test statistic based on the density model score function (i.e. gradient with respect to the input) -- which can easily compute test statistics for all dimensions in a single forward and backward pass. Any density model could be used for computing the necessary statistics including deep density models such as normalizing flows or autoregressive models. We additionally develop methods for identifying when and where a shift occurs in multivariate time-series data and show results for multiple scenarios using realistic attack models on both simulated and real world data.

This report presents the dataset and baseline of Task 3 of the DCASE2021 Challenge on Sound Event Localization and Detection (SELD). The dataset is based on emulation of real recordings of static or moving sound events under real conditions of reverberation and ambient noise, using spatial room impulse responses captured in a variety of rooms and delivered in two spatial formats. The acoustical synthesis remains the same as in the previous iteration of the challenge, however the new dataset brings more challenging conditions of polyphony and overlapping instances of the same class. The most important difference of the new dataset is the introduction of directional interferers, meaning sound events that are localized in space but do not belong to the target classes to be detected and are not annotated. Since such interfering events are expected in every real-world scenario of SELD, the new dataset aims to promote systems that deal with this condition effectively. A modified SELDnet baseline employing the recent ACCDOA representation of SELD problems accompanies the dataset and it is shown to outperform the previous one. The new dataset is shown to be significantly more challenging for both baselines according to all considered metrics. To investigate the individual and combined effects of ambient noise, interferers, and reverberation, we study the performance of the baseline on different versions of the dataset excluding or including combinations of these factors. The results indicate that by far the most detrimental effects are caused by directional interferers.

X-ray observing facilities, such as the Chandra X-ray Observatory and the eROSITA, have detected millions of astronomical sources associated with high-energy phenomena. The arrival of photons as a function of time follows a Poisson process and can vary by orders-of-magnitude, presenting obstacles for common tasks such as source classification, physical property derivation, and anomaly detection. Previous work has either failed to directly capture the Poisson nature of the data or only focuses on Poisson rate function reconstruction. In this work, we present Poisson Process AutoDecoder (PPAD). PPAD is a neural field decoder that maps fixed-length latent features to continuous Poisson rate functions across energy band and time via unsupervised learning. PPAD reconstructs the rate function and yields a representation at the same time. We demonstrate the efficacy of PPAD via reconstruction, regression, classification and anomaly detection experiments using the Chandra Source Catalog.

We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the Random Fourier features (RFFs) associated with shift-invariant kernels. We prove that our quantized RFFs -- even in the case of 1-bit quantization -- allow a high accuracy approximation of the underlying kernels, and the approximation error decays at least polynomially fast as the dimension of the RFFs increases. We also show that the quantized RFFs can be further compressed, yielding an excellent trade-off between memory use and accuracy. Namely, the approximation error now decays exponentially as a function of the bits used. Moreover, we empirically show by testing the performance of our methods on several machine learning tasks that our method compares favorably to other state of the art quantization methods in this context.

We introduce the concept of programmable feature engineering for time series modeling and propose a feature programming framework. This framework generates large amounts of predictive features for noisy multivariate time series while allowing users to incorporate their inductive bias with minimal effort. The key motivation of our framework is to view any multivariate time series as a cumulative sum of fine-grained trajectory increments, with each increment governed by a novel spin-gas dynamical Ising model. This fine-grained perspective motivates the development of a parsimonious set of operators that summarize multivariate time series in an abstract fashion, serving as the foundation for large-scale automated feature engineering. Numerically, we validate the efficacy of our method on several synthetic and real-world noisy time series datasets.

We introduce a mathematically rigorous framework based on rough path theory to model stochastic spiking neural networks (SSNNs) as stochastic differential equations with event discontinuities (Event SDEs) and driven by c\`adl\`ag rough paths. Our formalism is general enough to allow for potential jumps to be present both in the solution trajectories as well as in the driving noise. We then identify a set of sufficient conditions ensuring the existence of pathwise gradients of solution trajectories and event times with respect to the network's parameters and show how these gradients satisfy a recursive relation. Furthermore, we introduce a general-purpose loss function defined by means of a new class of signature kernels indexed on c\`adl\`ag rough paths and use it to train SSNNs as generative models. We provide an end-to-end autodifferentiable solver for Event SDEs and make its implementation available as part of the diffrax library. Our framework is, to our knowledge, the first enabling gradient-based training of SSNNs with noise affecting both the spike timing and the network's dynamics.

Recently, denoising diffusion models have led to significant breakthroughs in the generation of images, audio and text. However, it is still an open question on how to adapt their strong modeling ability to model time series. In this paper, we propose TimeDiff, a non-autoregressive diffusion model that achieves high-quality time series prediction with the introduction of two novel conditioning mechanisms: future mixup and autoregressive initialization. Similar to teacher forcing, future mixup allows parts of the ground-truth future predictions for conditioning, while autoregressive initialization helps better initialize the model with basic time series patterns such as short-term trends. Extensive experiments are performed on nine real-world datasets. Results show that TimeDiff consistently outperforms existing time series diffusion models, and also achieves the best overall performance across a variety of the existing strong baselines (including transformers and FiLM).

Transformer-based models have significantly advanced time series forecasting, with patch-based input strategies offering efficiency and improved long-horizon modeling. Yet, existing approaches rely on temporally-agnostic patch construction, where arbitrary starting positions and fixed lengths fracture temporal coherence by splitting natural transitions across boundaries. This naive segmentation often disrupts short-term dependencies and weakens representation learning. In response, we propose EntroPE (Entropy-Guided Dynamic Patch Encoder), a novel, temporally informed framework that dynamically detects transition points via conditional entropy and dynamically places patch boundaries. This preserves temporal structure while retaining the computational benefits of patching. EntroPE consists of two key modules, namely an Entropy-based Dynamic Patcher (EDP) that applies information-theoretic criteria to locate natural temporal shifts and determine patch boundaries, and an Adaptive Patch Encoder (APE) that employs pooling and cross-attention to capture intra-patch dependencies and produce fixed-size latent representations. These embeddings are then processed by a global transformer to model inter-patch dynamics. Experiments across long-term forecasting benchmarks demonstrate that EntroPE improves both accuracy and efficiency, establishing entropy-guided dynamic patching as a promising new paradigm for time series modeling. Code is available at: https://github.com/Sachithx/EntroPE.

Discrete event sequences are ubiquitous, such as an ordered event series of process interactions in Information and Communication Technology systems. Recent years have witnessed increasing efforts in detecting anomalies with discrete-event sequences. However, it still remains an extremely difficult task due to several intrinsic challenges including data imbalance issues, the discrete property of the events, and sequential nature of the data. To address these challenges, in this paper, we propose OC4Seq, a multi-scale one-class recurrent neural network for detecting anomalies in discrete event sequences. Specifically, OC4Seq integrates the anomaly detection objective with recurrent neural networks (RNNs) to embed the discrete event sequences into latent spaces, where anomalies can be easily detected. In addition, given that an anomalous sequence could be caused by either individual events, subsequences of events, or the whole sequence, we design a multi-scale RNN framework to capture different levels of sequential patterns simultaneously. Experimental results on three benchmark datasets show that OC4Seq consistently outperforms various representative baselines by a large margin. Moreover, through both quantitative and qualitative analysis, the importance of capturing multi-scale sequential patterns for event anomaly detection is verified.

The Sequential Recommendation modeling paradigm is shifting from Transformer to Mamba architecture, which comprises two generations: Mamba1, based on the State Space Model (SSM), and Mamba2, based on State Space Duality (SSD). Although SSD offers superior computational efficiency compared to SSM, it suffers performance degradation in sequential recommendation tasks, especially in low-dimensional scenarios that are critical for these tasks. Considering that time-aware enhancement methods are commonly employed to mitigate performance loss, our analysis reveals that the performance decline of SSD can similarly be fundamentally compensated by leveraging mechanisms in time-aware methods. Thus, we propose integrating time-awareness into the SSD framework to address these performance issues. However, integrating current time-aware methods, modeled after TiSASRec, into SSD faces the following challenges: 1) the complexity of integrating these transformer-based mechanisms with the SSD architecture, and 2) the computational inefficiency caused by the need for dimensionality expansion of time-difference modeling. To overcome these challenges, we introduce a novel Time-aware Structured Masked Matrix that efficiently incorporates time-aware capabilities into SSD. Building on this, we propose Time-Aware Mamba for Recommendation (TiM4Rec), which mitigates performance degradation in low-dimensional SSD contexts while preserving computational efficiency. This marks the inaugural application of a time-aware enhancement method specifically tailored for the Mamba architecture within the domain of sequential recommendation. Extensive experiments conducted on three real-world datasets demonstrate the superiority of our approach. The code for our model is accessible at https://github.com/AlwaysFHao/TiM4Rec.

The reliability of deep time series models is often compromised by their tendency to rely on confounding factors, which may lead to misleading results. Our newly recorded, naturally confounded dataset named P2S from a real mechanical production line emphasizes this. To tackle the challenging problem of mitigating confounders in time series data, we introduce Right on Time (RioT). Our method enables interactions with model explanations across both the time and frequency domain. Feedback on explanations in both domains is then used to constrain the model, steering it away from the annotated confounding factors. The dual-domain interaction strategy is crucial for effectively addressing confounders in time series datasets. We empirically demonstrate that RioT can effectively guide models away from the wrong reasons in P2S as well as popular time series classification and forecasting datasets.

We study short-horizon forecasting of weekly terrorism incident counts using the Global Terrorism Database (GTD, 1970--2016). We build a reproducible pipeline with fixed time-based splits and evaluate a Bidirectional LSTM (BiLSTM) against strong classical anchors (seasonal-naive, linear/ARIMA) and a deep LSTM-Attention baseline. On the held-out test set, the BiLSTM attains RMSE 6.38, outperforming LSTM-Attention (9.19; +30.6\%) and a linear lag-regression baseline (+35.4\% RMSE gain), with parallel improvements in MAE and MAPE. Ablations varying temporal memory, training-history length, spatial grain, lookback size, and feature groups show that models trained on long historical data generalize best; a moderate lookback (20--30 weeks) provides strong context; and bidirectional encoding is critical for capturing both build-up and aftermath patterns within the window. Feature-group analysis indicates that short-horizon structure (lagged counts and rolling statistics) contributes most, with geographic and casualty features adding incremental lift. We release code, configs, and compact result tables, and provide a data/ethics statement documenting GTD licensing and research-only use. Overall, the study offers a transparent, baseline-beating reference for GTD incident forecasting.

Contrastive learning has shown to be effective to learn representations from time series in a self-supervised way. However, contrasting similar time series instances or values from adjacent timestamps within a time series leads to ignore their inherent correlations, which results in deteriorating the quality of learned representations. To address this issue, we propose SoftCLT, a simple yet effective soft contrastive learning strategy for time series. This is achieved by introducing instance-wise and temporal contrastive loss with soft assignments ranging from zero to one. Specifically, we define soft assignments for 1) instance-wise contrastive loss by the distance between time series on the data space, and 2) temporal contrastive loss by the difference of timestamps. SoftCLT is a plug-and-play method for time series contrastive learning that improves the quality of learned representations without bells and whistles. In experiments, we demonstrate that SoftCLT consistently improves the performance in various downstream tasks including classification, semi-supervised learning, transfer learning, and anomaly detection, showing state-of-the-art performance. Code is available at this repository: https://github.com/seunghan96/softclt.

Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in the posterior, hyperparameters, and inducing points, making accurate learning challenging. Here, we present a method to keep all such errors in check using the recently proposed dual sparse variational GP. Our method enables accurate inference for generic likelihoods and improves learning by actively building and updating a memory of past data. We demonstrate its effectiveness in several applications involving Bayesian optimization, active learning, and continual learning.

Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each task. Most inverse tasks can be formulated as inferring a posterior distribution over data (e.g., a full image) given a measurement (e.g., a masked image). This is however challenging in diffusion models since the nonlinear and iterative nature of the diffusion process renders the posterior intractable. To cope with this challenge, we propose a variational approach that by design seeks to approximate the true posterior distribution. We show that our approach naturally leads to regularization by denoising diffusion process (RED-Diff) where denoisers at different timesteps concurrently impose different structural constraints over the image. To gauge the contribution of denoisers from different timesteps, we propose a weighting mechanism based on signal-to-noise-ratio (SNR). Our approach provides a new variational perspective for solving inverse problems with diffusion models, allowing us to formulate sampling as stochastic optimization, where one can simply apply off-the-shelf solvers with lightweight iterates. Our experiments for image restoration tasks such as inpainting and superresolution demonstrate the strengths of our method compared with state-of-the-art sampling-based diffusion models.

The quality of many modern machine learning models improves as model complexity increases, an effect that has been quantified, for predictive performance, with the non-monotonic double descent learning curve. Here, we address the overarching question: is there an analogous theory of double descent for models which estimate uncertainty? We provide a partially affirmative and partially negative answer in the setting of Gaussian processes (GP). Under standard assumptions, we prove that higher model quality for optimally-tuned GPs (including uncertainty prediction) under marginal likelihood is realized for larger input dimensions, and therefore exhibits a monotone error curve. After showing that marginal likelihood does not naturally exhibit double descent in the input dimension, we highlight related forms of posterior predictive loss that do exhibit non-monotonicity. Finally, we verify empirically that our results hold for real data, beyond our considered assumptions, and we explore consequences involving synthetic covariates.

Machine learning has opened up new tools for financial fraud detection. Using a sample of annotated transactions, a machine learning classification algorithm learns to detect frauds. With growing credit card transaction volumes and rising fraud percentages there is growing interest in finding appropriate machine learning classifiers for detection. However, fraud data sets are diverse and exhibit inconsistent characteristics. As a result, a model effective on a given data set is not guaranteed to perform on another. Further, the possibility of temporal drift in data patterns and characteristics over time is high. Additionally, fraud data has massive and varying imbalance. In this work, we evaluate sampling methods as a viable pre-processing mechanism to handle imbalance and propose a data-driven classifier selection strategy for characteristic highly imbalanced fraud detection data sets. The model derived based on our selection strategy surpasses peer models, whilst working in more realistic conditions, establishing the effectiveness of the strategy.