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Applications · Time Series

Abdelhakim Benechehab, Vasilii Feofanov, Giuseppe Paolo, Albert Thomas, Maurizio Filippone, Balázs Kégl

Pre-trained foundation models (FMs) have shown exceptional performance in univariate time series forecasting tasks. However, several practical challenges persist, including managing intricate dependencies among features and quantifying uncertainty in predictions. This study aims to tackle these critical limitations by introducing **adapters**—feature-space transformations that facilitate the effective use of pre-trained univariate time series FMs for multivariate tasks. Adapters operate by projecting multivariate inputs into a suitable latent space and applying the FM independently to each dimension. Inspired by the literature on representation learning and partially stochastic Bayesian neural networks, we present a range of adapters and optimization/inference strategies. Experiments conducted on both synthetic and real-world datasets confirm the efficacy of adapters, demonstrating substantial enhancements in forecasting accuracy and uncertainty quantification compared to baseline methods. Our framework, **AdaPTS**, positions adapters as a modular, scalable, and effective solution for leveraging time series FMs in multivariate contexts, thereby promoting their wider adoption in real-world applications. We release the code at https://github.com/abenechehab/AdaPTS.

General Machine Learning · Sequential, Network, and Time Series Modeling

Daoyu Wang, Mingyue Cheng, Zhiding Liu, Qi Liu

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 \textbf{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 \url{https://github.com/Melmaphother/TimeDART}.

Applications · Time Series

Hao Li, Yu-Hao Huang, Chang Xu, Viktor Schlegel, Renhe Jiang, Riza Batista-Navarro, Goran Nenadic, Jiang Bian

Time-series Generation (TSG) is a prominent research area with broad applications in simulations, data augmentation, and counterfactual analysis. While existing methods have shown promise in unconditional single-domain TSG, real-world applications demand for cross-domain approaches capable of controlled generation tailored to domain-specific constraints and instance-level requirements. In this paper, we argue that text can provide semantic insights, domain information and instance-specific temporal patterns, to guide and improve TSG. We introduce ``Text-Controlled TSG'', a task focused on generating realistic time series by incorporating textual descriptions.To address data scarcity in this setting, we propose a novel LLM-based Multi-Agent framework that synthesizes diverse, realistic text-to-TS datasets. Furthermore, we introduce Bridge, a hybrid text-controlled TSG framework that integrates semantic prototypes with text description for supporting domain-level guidance. This approach achieves state-of-the-art generation fidelity on 11 of 12 datasets, and improves controllability by up to 12% on MSE and 6% MAE compared to no text input generation, highlighting its potential for generating tailored time-series data.

Applications · Time Series

Hyeongwon Jang, Changhun Kim, Eunho Yang

Recent explainable artificial intelligence (XAI) methods for time series primarily estimate point-wise attribution magnitudes, while overlooking the directional impact on predictions, leading to suboptimal identification of significant points. Our analysis shows that conventional Integrated Gradients (IG) effectively capture critical points with both positive and negative impacts on predictions. However, current evaluation metrics fail to assess this capability, as they inadvertently cancel out opposing feature contributions. To address this limitation, we propose novel evaluation metrics—Cumulative Prediction Difference (CPD) and Cumulative Prediction Preservation(CPP)—to systematically assess whether attribution methods accurately identify significant positive and negative points in time series XAI. Under these metrics, conventional IG outperforms recent counterparts. However, directly applying IG to time series data may lead to suboptimal outcomes, as generated paths ignore temporal relationships and introduce out-of-distribution samples. To overcome these challenges, we introduce TIMING, which enhances IG by incorporating temporal awareness while maintaining its theoretical properties. Extensive experiments on synthetic and real-world time series benchmarks demonstrate that TIMING outperforms existing timeseries XAI baselines. Our code is available at https://github.com/drumpt/TIMING.

Deep Learning · Sequential Models, Time series

Vincent Herrmann, Róbert Csordás, Jürgen Schmidhuber

Detecting when a neural sequence model does "interesting" computation is an open problem. The next token prediction loss is a poor indicator: Low loss can stem from trivially predictable sequences that are uninteresting, while high loss may reflect unpredictable but also irrelevant information that can be ignored by the model. We propose a better metric: measuring the model's ability to predict its own future hidden states. We show empirically that this metric–in contrast to the next token prediction loss–correlates with the intuitive interestingness of the task. To measure predictability, we introduce the architecture-agnostic "prediction of hidden states" (PHi) layer that serves as an information bottleneck on the main pathway of the network (e.g., the residual stream in Transformers). We propose a novel learned predictive prior that enables us to measure the novel information gained in each computation step, which serves as our metric. We show empirically that our metric predicts the description length of formal languages learned in-context, the complexity of mathematical reasoning problems, and the correctness of self-generated reasoning chains.

General Machine Learning · Sequential, Network, and Time Series Modeling

Dong Huang, Pengkun Yang

Correlation analysis is a fundamental step in uncovering meaningful insights from complex datasets. In this paper, we study the problem of detecting correlations between two random graphs following the Gaussian Wigner model with unlabeled vertices. Specifically, the task is formulated as a hypothesis testing problem: under the null hypothesis, the two graphs are independent, while under the alternative hypothesis, they are edge-correlated through a latent vertex permutation, yet maintain the same marginal distributions as under the null. We focus on the scenario where two induced subgraphs, each with a fixed number of vertices, are sampled. We determine the optimal rate for the sample size required for correlation detection, derived through an analysis of the conditional second moment. Additionally, we propose an efficient approximate algorithm that significantly reduces running time.

Deep Learning · Sequential Models, Time series

Yitian Zhang, Liheng Ma, Antonios Valkanas, Boris Oreshkin, Mark Coates

Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a space of real-valued measurement functions, enabling a linear operator representation. Despite the advantage of linearity, the operator is generally infinite-dimensional. Therefore, the objective is to learn measurement functions that yield a tractable finite-dimensional Koopman operator approximation. In this work, we establish a connection between Koopman operator approximation and linear Recurrent Neural Networks (RNNs), which have recently demonstrated remarkable success in sequence modeling. We show that by considering an extended state consisting of lagged observations, we can establish an equivalence between a structured Koopman operator and linear RNN updates. Building on this connection, we present SKOLR, which integrates a learnable spectral decomposition of the input signal with a multilayer perceptron (MLP) as the measurement functions and implements a structured Koopman operator via a highly parallel linear RNN stack. Numerical experiments on various forecasting benchmarks and dynamical systems show that this streamlined, Koopman-theory-based design delivers exceptional performance. Our code is available at: https://github.com/networkslab/SKOLR.

Deep Learning · Sequential Models, Time series

Shurui Gui, Xiner Li, Shuiwang Ji

We consider learning underlying laws of dynamical systems governed by ordinary differential equations (ODE). A key challenge is how to discover intrinsic dynamics across multiple environments while circumventing environment-specific mechanisms. Unlike prior work, we tackle more complex environments where changes extend beyond function coefficients to entirely different function forms. For example, we demonstrate the discovery of ideal pendulum's natural motion $\alpha^2 \sin{\theta_t}$ by observing pendulum dynamics in different environments, such as the damped environment $\alpha^2 \sin(\theta_t) - \rho \omega_t$ and powered environment $\alpha^2 \sin(\theta_t) + \rho \frac{\omega_t}{\left|\omega_t\right|}$. Here, we formulate this problem as an *invariant function learning* task and propose a new method, known as **D**isentanglement of **I**nvariant **F**unctions (DIF), that is grounded in causal analysis. We propose a causal graph and design an encoder-decoder hypernetwork that explicitly disentangles invariant functions from environment-specific dynamics. The discovery of invariant functions is guaranteed by our information-based principle that enforces the independence between extracted invariant functions and environments. Quantitative comparisons with meta-learning and invariant learning baselines on three ODE systems demonstrate the effectiveness and efficiency of our method. Furthermore, symbolic regression explanation results highlight the ability of our framework to uncover intrinsic laws.

Applications · Everything Else

Gabriel Tseng, Anthony Fuller, Marlena Reil, Henry Herzog, Patrick Beukema, Favyen Bastani, James Green, Evan Shelhamer, Hannah Kerner, David Rolnick

We introduce a highly multimodal transformer to represent many remote sensing modalities - multispectral optical, synthetic aperture radar, elevation, weather, pseudo-labels, and more - across space and time. These inputs are useful for diverse remote sensing tasks, such as crop mapping and flood detection. However, learning shared representations of remote sensing data is challenging, given the diversity of relevant data modalities, and because objects of interest vary massively in scale, from small boats (1-2 pixels and fast) to glaciers (thousands of pixels and slow). We present a novel self-supervised learning algorithm that extracts multi-scale features across a flexible set of input modalities through masked modeling. Our dual global and local contrastive losses differ in their targets (deep representations vs. shallow input projections) and masking strategies (structured vs. not). Our Galileo is a single generalist model that outperforms SoTA specialist models for satellite images and pixel time series across eleven benchmarks and multiple tasks.

General Machine Learning · Sequential, Network, and Time Series Modeling

Yu-Yang Qian, Yuan-Ze Xu, Zhen-Yu Zhang, Peng Zhao, Zhi-Hua Zhou

Many real-world applications collect data in a streaming environment, where learning tasks are encountered sequentially. This necessitates *continual learning* (CL) to update models online, enabling adaptation to new tasks while preserving past knowledge to prevent catastrophic forgetting. Nowadays, with the flourish of *large pre-trained models* (LPMs), *efficiency* has become increasingly critical for CL, due to their substantial computational demands and growing parameter sizes. In this paper, we introduce TreeLoRA (K-D Tree of Low-Rank Adapters), a novel approach that constructs *layer-wise* adapters by leveraging hierarchical gradient similarity to enable efficient CL, particularly for LPMs. To reduce the computational burden of task similarity estimation, we employ *bandit* techniques to develop an algorithm based on lower confidence bounds to efficiently explore the task structure. Furthermore, we use sparse gradient updates to facilitate parameter optimization, making the approach better suited for LPMs. Theoretical analysis is provided to justify the rationale behind our approach, and experiments on both *vision transformers* (ViTs) and *large language models* (LLMs) demonstrate the effectiveness and efficiency of our approach across various domains, including vision and natural language processing tasks.

General Machine Learning · Sequential, Network, and Time Series Modeling

Srinath Dama, Kevin L Course, Prasanth B Nair

We present an operator-theoretic framework for temporal and spatio-temporal forecasting based on learning a *continuous time-shift operator*. Our operator learning paradigm offers a continuous relaxation of the discrete lag factor used in traditional autoregressive models, enabling the history of a system up to a given time to be mapped to its future values. We parametrize the time-shift operator using Khatri-Rao neural operators (KRNOs), a novel architecture based on non-stationary integral transforms with nearly linear computational scaling. Our framework naturally handles irregularly sampled observations and enables forecasting at super-resolution in both space and time. Extensive numerical studies across diverse temporal and spatio-temporal benchmarks demonstrate that our approach achieves state-of-the-art or competitive performance with leading methods.

Deep Learning · Generative Models and Autoencoders

RISHI JINKA, Venkata Sai Mothish Gonugunta, Deepak N. Subramani

Time-series forecasting finds application across domains such as finance, climate science, and energy systems. We introduce the Conditional Diffusion with Nonlinear Data Transformation Model (CN-Diff), a generative framework that employs novel nonlinear transformations and learnable conditions in the forward process for time series forecasting. A new loss formulation for training is proposed, along with a detailed derivation of both forward and reverse process. The new additions improve the diffusion model's capacity to capture complex time series patterns, thus simplifying the reverse process. Our novel condition facilitates learning an efficient prior distribution. This also reduces the gap between the true negative log-likelihood and its variational approximation. CN-Diff is shown to perform better than other leading time series models on nine real-world datasets. Ablation studies are conducted to elucidate the role of each component of CN-Diff.

Applications · Time Series

Chenxi Wang, Linxiao Yang, Zhixian Wang, Liang Sun, Yi Wang

Diffusion models, known for their generative ability, have recently been adapted to time series analysis. Most pioneering works rely on the standard isotropic diffusion, treating each time step and the entire frequency spectrum identically. However, it may not be suitable for time series, which often have more informative low-frequency components. We empirically found that direct application of standard diffusion to time series may cause gradient contradiction during training, due to the rapid decrease of low-frequency information in the diffusion process. To this end, we proposed a novel time series diffusion model, MA-TSD, which utilizes the moving average, a natural low-frequency filter, as the forward transition. Its backward process is accelerable like DDIM and can be further considered a time series super-resolution. Our experiments on various datasets demonstrated MA-TSD's superior performance in time series forecasting and super-resolution tasks.

Deep Learning · Generative Models and Autoencoders

Grigoriy Ksenofontov, Aleksandr Korotin

The Schrödinger Bridge (SB) is a powerful framework for solving generative modeling tasks such as unpaired domain translation. Most SB-related research focuses on continuous data space $\mathbb{R}^{D}$ and leaves open theoretical and algorithmic questions about applying SB methods to discrete data, e.g, on finite spaces $\mathbb{S}^{D}$. Notable examples of such sets $\mathbb{S}$ are codebooks of vector-quantized (VQ) representations of modern autoencoders, tokens in texts, categories of atoms in molecules, etc. In this paper, we provide a theoretical and algorithmic foundation for solving SB in discrete spaces using the recently introduced Iterative Markovian Fitting (IMF) procedure. Specifically, we theoretically justify the convergence of discrete-time IMF (D-IMF) to SB in discrete spaces. This enables us to develop a practical computational algorithm for SB, which we call Categorical Schrödinger Bridge Matching (CSBM). We show the performance of CSBM via a series of experiments with synthetic data and VQ representations of images. The code of CSBM is available at [this repository](https://github.com/gregkseno/csbm).

General Machine Learning · Sequential, Network, and Time Series Modeling

Samidha Verma, Arushi Goyal, Ananya Mathur, Ankit Anand, Sayan Ranu

Graph Edit Distance (GED) is a widely used metric for measuring similarity between two graphs. Computing the optimal GED is NP-hard, leading to the development of various neural and non-neural heuristics. While neural methods have achieved improved approximation quality compared to non-neural approaches, they face significant challenges: (1) They require large amounts of ground truth data, which is itself NP-hard to compute. (2) They operate as black boxes, offering limited interpretability. (3) They lack cross-domain generalization, necessitating expensive retraining for each new dataset. We address these limitations with GRAIL, introducing a paradigm shift in this domain. Instead of training a neural model to predict GED, GRAIL employs a novel combination of large language models (LLMs) and automated prompt tuning to generate a *program* that is used to compute GED. This shift from predicting GED to generating programs imparts various advantages, including end-to-end interpretability and an autonomous self-evolutionary learning mechanism without ground-truth supervision. Extensive experiments on seven datasets confirm that GRAIL not only surpasses state-of-the-art GED approximation methods in prediction quality but also achieves robust cross-domain generalization across diverse graph distributions.

Deep Learning · Sequential Models, Time series

Mehmet Yiğit Balık, Maksim Sinelnikov, Priscilla Ong, Harri Lähdesmäki

High-dimensional time-series datasets are common in domains such as healthcare and economics. Variational autoencoder (VAE) models, where latent variables are modeled with a Gaussian process (GP) prior, have become a prominent model class to analyze such correlated datasets. However, their applications are challenged by the inherent cubic time complexity that requires specific GP approximation techniques, as well as the general challenge of modeling both shared and individual-specific correlations across time. Though inducing points enhance GP prior VAE scalability, optimizing them remains challenging, especially since discrete covariates resist gradient‑based methods. In this work, we propose a scalable basis function approximation technique for GP prior VAEs that mitigates these challenges and results in linear time complexity, with a global parametrization that eliminates the need for amortized variational inference and the associated amortization gap, making it well-suited for conditional generation tasks where accuracy and efficiency are crucial. Empirical evaluations on synthetic and real-world benchmark datasets demonstrate that our approach not only improves scalability and interpretability but also drastically enhances predictive performance.

Applications · Time Series

Boyuan Li, Yicheng Luo, Zhen Liu, Junhao Zheng, Jianming Lv, Qianli Ma

Irregular multivariate time series (IMTS) are characterized by irregular time intervals within variables and unaligned observations across variables, posing challenges in learning temporal and variable dependencies. Many existing IMTS models either require padded samples to learn separately from temporal and variable dimensions, or represent original samples via bipartite graphs or sets.However, the former approaches often need to handle extra padding values affecting efficiency and disrupting original sampling patterns, while the latter ones have limitations in capturing dependencies among unaligned observations.To represent and learn both dependencies from original observations in a unified form, we propose HyperIMTS, a **Hyper**graph neural network for **I**rregular **M**ultivariate **T**ime **S**eries forecasting.Observed values are converted as nodes in the hypergraph, interconnected by temporal and variable hyperedges to enable message passing among all observations.Through irregularity-aware message passing, HyperIMTS captures variable dependencies in a time-adaptive way to achieve accurate forecasting. Experiments demonstrate HyperIMTS's competitive performance among state-of-the-art models in IMTS forecasting with low computational cost.Our code is available at [https://github.com/qianlima-lab/PyOmniTS](https://github.com/qianlima-lab/PyOmniTS).

Miscellaneous Aspects of Machine Learning · Sequential, Network, and Time Series Modeling

Yan Ru Pei

We introduce Centaurus, a class of networks composed of generalized state-space model (SSM) blocks, where the SSM operations can be treated as tensor contractions during training. The optimal order of tensor contractions can then be systematically determined for every SSM block to maximize training efficiency. This allows more flexibility in designing SSM blocks beyond the depthwise-separable configuration commonly implemented. The new design choices will take inspiration from classical convolutional blocks including group convolutions, full convolutions, and bottleneck blocks. We architect the Centaurus network with a mixture of these blocks, to balance between network size and performance, as well as memory and computational efficiency during both training and inference. We show that this heterogeneous network design outperforms its homogeneous counterparts in raw audio processing tasks including keyword spotting, speech denoising, and automatic speech recognition (ASR). For ASR, Centaurus is the first network with competitive performance that can be made fully state-space based, without using any nonlinear recurrence (LSTMs), explicit convolutions (CNNs), or (surrogate) attention mechanism.

Deep Learning · Sequential Models, Time series

T. Konstantin Rusch, Daniela Rus

We propose Linear Oscillatory State-Space models (LinOSS) for efficiently learning on long sequences. Inspired by cortical dynamics of biological neural networks, we base our proposed LinOSS model on a system of forced harmonic oscillators. A stable discretization, integrated over time using fast associative parallel scans, yields the proposed state-space model. We prove that LinOSS produces stable dynamics only requiring nonnegative diagonal state matrix. This is in stark contrast to many previous state-space models relying heavily on restrictive parameterizations. Moreover, we rigorously show that LinOSS is universal, i.e., it can approximate any continuous and causal operator mapping between time-varying functions, to desired accuracy. In addition, we show that an implicit-explicit discretization of LinOSS perfectly conserves the symmetry of time reversibility of the underlying dynamics. Together, these properties enable efficient modeling of long-range interactions, while ensuring stable and accurate long-horizon forecasting. Finally, our empirical results, spanning a wide range of time-series tasks from mid-range to very long-range classification and regression, as well as long-horizon forecasting, demonstrate that our proposed LinOSS model consistently outperforms state-of-the-art sequence models. Notably, LinOSS outperforms Mamba and LRU by nearly 2x on a sequence modeling task with sequences of length 50k.

Applications · Time Series

Yuanzhao Zhang, William Gilpin

Time-series forecasting is a challenging problem that traditionally requires specialized models custom-trained for the specific task at hand. Recently, inspired by the success of large language models, foundation models pre-trained on vast amounts of time-series data from diverse domains have emerged as a promising candidate for general-purpose time-series forecasting. The defining characteristic of these foundation models is their ability to perform zero-shot learning, that is, forecasting a new system from limited context data without explicit re-training or fine-tuning. Here, we evaluate whether the zero-shot learning paradigm extends to the challenging task of forecasting chaotic systems. Across 135 distinct chaotic dynamical systems and $10^8$ timepoints, we find that foundation models produce competitive forecasts compared to custom-trained models (including NBEATS, TiDE, etc.), particularly when training data is limited. Interestingly, even after point forecasts fail, large foundation models are able to preserve the geometric and statistical properties of the chaotic attractors.We attribute this success to foundation models' ability to perform in-context learning and identify context parroting as a simple mechanism used by these models to capture the long-term behavior of chaotic dynamical systems. Our results highlight the potential of foundation models as a tool for probing nonlinear and complex systems.