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

Tianyu Liu, kai sun, Fuchun Sun, Yu Luo, Yuanlong Zhang

Temporal sequences, even after stationarization, often exhibit leptokurtic distributions with fat tails and persistent distribution shifts. These properties destabilize feature dynamics, amplify model variance, and hinder model convergence in time series forecasting. To address this, we propose Morphing-Flow (MoF), a framework that combines a spline-based transform layer (Flow) and a test-time-trained method (Morph), which adaptively normalizes non-stationary, fat-tailed distributions while preserving critical extreme features. MoF ensures that inputs remain within a network’s effective activation space—a structured, normal-like distribution—even under distributional drift. Experiments across eight datasets show that MoF achieves state-of-the-art performance: With a simple linear backbone architecture, it matches the performance of state-of-the-art models on datasets such as Electricity and ETTh2. When paired with a patch-based Mamba architecture, MoF outperforms its closest competitor by 6.3% on average and reduces forecasting errors in fat-tailed datasets such as Exchange by 21.7%. Moreover, MoF acts as a plug-and-play module, boosting performance in existing models without architectural changes.

Applications · Time Series

Feifei Kou, Jiahao Wang, Lei Shi, Yuhan Yao, Yawen Li, Suguo Zhu, Zhongbao Zhang, Junping Du

Long-term time series forecasting has been widely studied, yet two aspects remain insufficiently explored: the interaction learning between different frequency components and the exploitation of periodic characteristics inherent in timestamps. To address the above issues, we propose **CFPT**, a novel method that empowering time series forecasting through **C**ross-**F**requency Interaction (CFI) and **P**eriodic-Aware **T**imestamp Modeling (PTM). To learn cross-frequency interactions, we design the CFI branch to process signals in frequency domain and captures their interactions through a feature fusion mechanism. Furthermore, to enhance prediction performance by leveraging timestamp periodicity, we develop the PTM branch which transforms timestamp sequences into 2D periodic tensors and utilizes 2D convolution to capture both intra-period dependencies and inter-period correlations of time series based on timestamp patterns. Extensive experiments on multiple real-world benchmarks demonstrate that CFPT achieves state-of-the-art performance in long-term forecasting tasks. The code is publicly available at this repository: https://github.com/BUPT-SN/CFPT.

Deep Learning · Sequential Models, Time series

Jaeho Kim, Seulki Lee

Unsupervised domain adaptation (UDA) for time series data remains a critical challenge in deep learning, with traditional pseudo-labeling strategies failing to capture temporal patterns and channel-wise shifts between domains, producing sub-optimal pseudo labels. As such, we introduce TransPL, a novel approach that addresses these limitations by modeling the joint distribution $P(X,y)$ of the source domain through code transition matrices, where the codes are derived from vector quantization (VQ) of time series patches. Our method constructs class- and channel-wise code transition matrices from the source domain and employs Bayes' rule for target domain adaptation, generating pseudo-labels based on channel-wise weighted class-conditional likelihoods. TransPL offers three key advantages: explicit modeling of temporal transitions and channel-wise shifts between different domains, versatility towards different UDA scenarios (e.g., weakly-supervised UDA), and explainable pseudo-label generation. We validate TransPL's effectiveness through extensive analysis on four time series UDA benchmarks and confirm that it consistently outperforms state-of-the-art pseudo-labeling methods by a strong margin (6.1\% accuracy improvement, 4.9\% F1 improvement), while providing interpretable insights into the domain adaptation process through its learned code transition matrices.

Probabilistic Methods · Structure Learning

Carles Balsells-Rodas, Xavier Sumba, Tanmayee Narendra, Ruibo Tu, Gabriele Schweikert, Hedvig Kjellström, Yingzhen Li

Causal discovery, i.e., inferring underlying causal relationships from observational data, is highly challenging for AI systems. In a time series modeling context, traditional causal discovery methods mainly consider constrained scenarios with fully observed variables and/or data from stationary time-series. We develop a causal discovery approach to handle a wide class of nonstationary time series that are _conditionally stationary_, where the nonstationary behaviour is modeled as stationarity conditioned on a set of latent state variables. Named State-Dependent Causal Inference (SDCI), our approach is able to recover the underlying causal dependencies, with provable identifiablity for the state-dependent causal structures. Empirical experiments on nonlinear particle interaction data and gene regulatory networks demonstrate SDCI's superior performance over baseline causal discovery methods. Improved results over non-causal RNNs on modeling NBA player movements demonstrate the potential of our method and motivate the use of causality-driven methods for forecasting.

Deep Learning · Sequential Models, Time series

Harry Amad, Nicolás Astorga, Mihaela van der Schaar

Digital twins are models of real-world systems that can simulate their dynamics in response to potential actions. In complex settings, the state and action variables, and available data and knowledge relevant to a system can constantly change, requiring digital twins to continuously update with these changes to remain relevant. Current approaches struggle in this regard, as they require fixed, well-defined modelling environments, and they cannot adapt to novel variables without re-designs, or incorporate new information without re-training. To address this, we frame digital twinning as an in-context learning problem using large language models, enabling seamless updates to the twin at inference time. We develop CALM-DT, a Context-Adaptive Language Model-based Digital Twin that can accurately simulate across diverse state-action spaces using in-context learning alone by utilising fine-tuned encoders for sample retrieval. We empirically demonstrate CALM-DT's competitive performance with existing digital twin approaches, and its unique ability to adapt to changes in its modelling environment without parameter updates.

Deep Learning · Sequential Models, Time series

Yu Chen, Nathalia Céspedes, Payam Barnaghi

Time-series forecasting is crucial across various domains, including finance, healthcare, and energy. Transformer models, originally developed for natural language processing, have demonstrated significant potential in addressing challenges associated with time-series data. These models utilize different tokenization strategies, point-wise, patch-wise, and variate-wise, to represent time-series data, each resulting in different scope of attention maps. Despite the emergence of sophisticated architectures, simpler transformers consistently outperform their more complex counterparts in widely used benchmarks. This study examines why point-wise transformers are generally less effective, why intra- and inter-variate attention mechanisms yield similar outcomes, and which architectural components drive the success of simpler models. By analyzing mutual information and evaluating models on synthetic datasets, we demonstrate that intra-variate dependencies are the primary contributors to prediction performance on benchmarks, while inter-variate dependencies have a minor impact. Additionally, techniques such as Z-score normalization and skip connections are also crucial. However, these results are largely influenced by the self-dependent and stationary nature of benchmark datasets. By validating our findings on real-world healthcare data, we provide insights for designing more effective transformers for practical applications.

Deep Learning · Sequential Models, Time series

Jiaqi Yan, Changping Wang, De Ma, Huajin Tang, Qian Zheng, Gang Pan

Spiking Neural Networks (SNNs) are considered promising energy-efficient models due to their dynamic capability to process spatial-temporal spike information. Existing work has demonstrated that SNNs exhibit temporal heterogeneity, which leads to diverse outputs of SNNs at different time steps and has the potential to enhance their performance. Although SNNs obtained by direct training methods achieve state-of-the-art performance, current methods introduce limited temporal heterogeneity through the dynamics of spiking neurons or network structures. They lack the improvement of temporal heterogeneity through the lens of the gradient. In this paper, we first conclude that the diversity of the temporal logit gradients in current methods is limited. This leads to insufficient temporal heterogeneity and results in temporally miscalibrated SNNs with degraded performance. Based on the above analysis, we propose a Temporal Model Calibration (TMC) method, which can be seen as a logit gradient rescaling mechanism across time steps. Experimental results show that our method can improve the temporal logit gradient diversity and generate temporally calibrated SNNs with enhanced performance. In particular, our method achieves state-of-the-art accuracy on ImageNet, DVSCIFAR10, and N-Caltech101. Codes are available at https://github.com/zju-bmi-lab/TMC.

Deep Learning · Sequential Models, Time series

Xiangyu Qu, Guojing Liu, Liang Li

Non-autoregressive Transformers (NATs) have garnered significant attention due to their efficient decoding compared to autoregressive methods. However, existing conditional dependency modeling schemes based on masked language modeling introduce a *training-inference gap* in NATs. For instance, while NATs sample target words during training to enhance input, this condition cannot be met during inference, and simply annealing the sampling rate to zero during training leads to model performance degradation. We demonstrate that this *training-inference gap* prevents NATs from fully realizing their potential. To address this, we propose an adaptive end-to-end quantization alignment training framework, which introduces a semantic consistency space to adaptively align NAT training, eliminating the need for target information and thereby bridging the *training-inference gap*.Experimental results demonstrate that our method outperforms most existing fully NAT models, delivering performance on par with Autoregressive Transformer (AT) while being 17.0 times more efficient in inference.

Applications · Chemistry, Physics, and Earth Sciences

Jan Pauls, Max Zimmer, Berkant Turan, Sassan Saatchi, Philippe CIAIS, Sebastian Pokutta, Fabian Gieseke

With the rise in global greenhouse gas emissions, accurate large-scale tree canopy height maps are essential for understanding forest structure, estimating above-ground biomass, and monitoring ecological disruptions. To this end, we present a novel approach to generate large-scale, high-resolution canopy height maps over time. Our model accurately predicts canopy height over multiple years given Sentinel 2 time series satellite data. Using GEDI LiDAR data as the ground truth for training the model, we present the first 10 m resolution temporal canopy height map of the European continent for the period 2019–2022. As part of this product, we also offer a detailed canopy height map for 2020, providing more precise estimates than previous studies. Our pipeline and the resulting temporal height map are publicly available, enabling comprehensive large-scale monitoring of forests and, hence, facilitating future research and ecological analyses. For an interactive viewer, see https://europetreemap.projects.earthengine.app/view/europeheight.

Applications · Time Series

Xiaowen Ma, Zhen-Liang Ni, Shuai Xiao, Xinghao Chen

In long-term time series forecasting, different variables often influence the target variable over distinct time intervals, a challenge known as the multi-delay issue. Traditional models typically process all variables or time points uniformly, which limits their ability to capture complex variable relationships and obtain non-trivial time representations. To address this issue, we propose TimePro, an innovative Mamba-based model that constructs variate- and time-aware hyper-states. Unlike conventional approaches that merely transfer plain states across variable or time dimensions, TimePro preserves the fine-grained temporal features of each variate token and adaptively selects the focused time points to tune the plain state. The reconstructed hyper-state can perceive both variable relationships and salient temporal information, which helps the model make accurate forecasting. In experiments, TimePro performs competitively on eight real-world long-term forecasting benchmarks with satisfactory linear complexity. Code is available at https://github.com/xwmaxwma/TimePro.

Deep Learning · Sequential Models, Time series

Matthew Faw, Rajat Sen, Yichen Zhou, Abhimanyu Das

Motivated by the recent success of time-series foundation models for zero-shot forecasting, we present a methodology for _in-context fine-tuning_ of a time-series foundation model. In particular, we design a pretrained foundation model that can be prompted (at inference time) with multiple time-series examples, in order to forecast a target time-series into the future. Our foundation model is specifically trained to utilize examples from multiple related time-series in its context window (in addition to the history of the target time-series) to help it adapt to the specific distribution of the target domain at inference time. We show that such a foundation model that uses in-context examples at inference time can obtain much better performance on popular forecasting benchmarks compared to supervised deep learning methods, statistical models, and other time series foundation models. Interestingly, our in-context fine-tuning approach even matches the performance of a foundation model that is explicitly fine-tuned on the target domain.

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

Andrea Testa, Søren Hauberg, Tamim Asfour, Leonel Rozo

Accurately modeling and predicting complex dynamical systems, particularly those involving force exchange and dissipation, is crucial for applications ranging from fluid dynamics to robotics, but presents significant challenges due to the intricate interplay of geometric constraints and energy transfer. This paper introduces Geometric Contact Flows (GFC), a novel framework leveraging Riemannian and Contact geometry as inductive biases to learn such systems. GCF constructs a latent contact Hamiltonian model encoding desirable properties like stability or energy conservation. An ensemble of contactomorphisms then adapts this model to the target dynamics while preserving these properties. This ensemble allows for uncertainty-aware geodesics that attract the system’s behavior toward the data support, enabling robust generalization and adaptation to unseen scenarios. Experiments on learning dynamics for physical systems and for controlling robots on interaction tasks demonstrate the effectiveness of our approach.

Applications · Time Series

Thomas Y.L. Lin, Jerry Yao-Chieh Hu, Wan-Jiun Paul Chiou, Peter Lin

We revisit the Bayesian Black–Litterman (BL) portfolio model and remove its reliance on subjective investor views. Classical BL requires an investor “view”: a forecast vector $q$ and its uncertainty matrix $\Omega$ that describe how much a chosen portfolio should outperform the market.Our key idea is to treat $(q,\Omega)$ as latent variables and learn them from market data within a single Bayesian network.Consequently, the resulting posterior estimation admits closed-form expression, enabling fast inference and stable portfolio weights.Building on these, we propose two mechanisms to capture how features interact with returns: shared-latent parametrization and feature-influenced views; both recover classical BL and Markowitz portfolios as special cases.Empirically, on 30-year Dow-Jones and 20-year sector-ETF data, we improve Sharpe ratios by 50\% and cut turnover by 55\% relative to Markowitz and the index baselines.This work turns BL into a fully data-driven, view-free, and coherent Bayesian framework for portfolio optimization.

Applications · Time Series

Jiaming Ma, Binwu Wang, Pengkun Wang, Zhengyang Zhou, Xu Wang, Yang Wang

Recently, spatiotemporal graph convolutional networks have achieved dominant performance in spatiotemporal prediction tasks. However, most models relying on node-to-node messaging interaction exhibit sensitivity to spatiotemporal shifts, encountering out-of-distribution (OOD) challenges. To address these issues, we introduce \textbf{\underline{S}}patio-\textbf{\underline{T}}emporal \textbf{\underline{O}}OD \textbf{\underline{P}}rocessor (STOP), which employs a centralized messaging mechanism along with a message perturbation mechanism to facilitate robust spatiotemporal interactions. Specifically, the centralized messaging mechanism integrates Context-Aware Units for coarse-grained spatiotemporal feature interactions with nodes, effectively blocking traditional node-to-node messages. We also implement a message perturbation mechanism to disrupt this messaging process, compelling the model to extract generalizable contextual features from generated variant environments. Finally, we customize a spatiotemporal distributionally robust optimization approach that exposes the model to challenging environments, thereby further enhancing its generalization capabilities. Compared with 14 baselines across six datasets, STOP achieves up to \textbf{17.01\%} improvement in generalization performance and \textbf{18.44\%} improvement in inductive learning performance. The code is available at https://github.com/PoorOtterBob/STOP.

Theory · Probabilistic Methods

Lorenzo Lucchese, Mikko S. Pakkanen, Almut E. D. Veraart

The expected signature maps a collection of data streams to a lower dimensional representation, with a remarkable property: the resulting feature tensor can fully characterize the data generating distribution. This "model-free"' embedding has been successfully leveraged to build multiple domain-agnostic machine learning (ML) algorithms for time series and sequential data. The convergence results proved in this paper bridge the gap between the expected signature's empirical discrete-time estimator and its theoretical continuous-time value, allowing for a more complete probabilistic interpretation of expected signature-based ML methods. Moreover, when the data generating process is a martingale, we suggest a simple modification of the expected signature estimator with significantly lower mean squared error and empirically demonstrate how it can be effectively applied to improve predictive performance.

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

Thibaut Germain, Chrysoula Kosma, Laurent Oudre

Automatically extracting robust representations from large and complex time series data is becoming imperative for several real-world applications. Unfortunately, the potential of common neural network architectures in capturing invariant properties of time series remains relatively underexplored. For instance, convolutional layers often fail to capture underlying patterns in time series inputs that encompass strong deformations, such as trends. Indeed, invariances to some deformations may be critical for solving complex time series tasks, such as classification, while guaranteeing good generalization performance.To address these challenges, we mathematically formulate and technically design efficient and hard-coded *invariant convolutions* for specific group actions applicable to the case of time series.We construct these convolutions by considering specific sets of deformations commonly observed in time series, including *scaling*, *offset shift*, and *trend*.We further combine the proposed invariant convolutions with standard convolutions in single embedding layers, and we showcase the layer capacity to capture complex invariant time series properties in several scenarios.

Applications · Time Series

Michal Wilinski, Mononito Goswami, Willa Potosnak, Nina Żukowska, Artur Dubrawski

Time series foundation models (TSFMs) promise to be powerful tools for a wide range of applications. However, their internal representations and learned concepts are still not well understood. In this study, we investigate the structure and redundancy of representations across various TSFMs, examining the self-similarity of model layers within and across different model sizes. This analysis reveals block-like redundancy in the representations, which can be utilized for informed pruning to improve inference speed and efficiency. We also explore the concepts learned by these models, such as periodicity and trends. We demonstrate how conceptual priors can be derived from TSFM representations and leveraged to steer its outputs toward concept-informed predictions. Our work bridges representational analysis from language and vision models to TSFMs, offering new methods for building more computationally efficient and transparent TSFMs.

Applications · Time Series

Peer Nagy, Sascha Frey, Kang Li, Bidipta Sarkar, Svitlana Vyetrenko, Stefan Zohren, Anisoara Calinescu, Jakob Foerster

While financial data presents one of the most challenging and interesting sequence modelling tasks due to high noise, heavy tails, and strategic interactions, progress in this area has been hindered by the lack of consensus on quantitative evaluation paradigms. To address this, we present **LOB-Bench**, a benchmark, implemented in python, designed to evaluate the quality and realism of generative message-by-order data for limit order books (LOB) in the LOBSTER format. Our framework measures distributional differences in conditional and unconditional statistics between generated and real LOB data, supporting flexible multivariate statistical evaluation. The benchmark also includes features commonly used LOB statistics such as spread, order book volumes, order imbalance, and message inter-arrival times, along with scores from a trained discriminator network. Lastly, LOB-Bench contains "market impact metrics", i.e. the cross-correlations and price response functions for specific events in the data. We benchmark generative autoregressive state-space models, a (C)GAN, as well as a parametric LOB model and find that the autoregressive GenAI approach beats traditional model classes.

Deep Learning · Sequential Models, Time series

Abrar Majeedi, Viswanatha Reddy Gajjala, Satya Sai Srinath Namburi GNVV, Nada Elkordi, Yin Li

Real-world time series are often governed by complex nonlinear dynamics. Understanding these underlying dynamics is crucial for precise future prediction. While deep learning has achieved major success in time series forecasting, many existing approaches do not explicitly model the dynamics. To bridge this gap, we introduce DeepEDM, a framework that integrates nonlinear dynamical systems modeling with deep neural networks. Inspired by empirical dynamic modeling (EDM) and rooted in Takens' theorem, DeepEDM presents a novel deep model that learns a latent space from time-delayed embeddings, and employs kernel regression to approximate the underlying dynamics, while leveraging efficient implementation of softmax attention and allowing for accurate prediction of future time steps. To evaluate our method, we conduct comprehensive experiments on synthetic data of nonlinear dynamical systems as well as real-world time series across domains. Our results show that DeepEDM is robust to input noise, and outperforms state-of-the-art methods in forecasting accuracy. Our code is available at: https://abrarmajeedi.github.io/deep_edm.

Applications · Time Series

Yue Jiang, Yile Chen, Xiucheng Li, Qin Chao, SHUAI LIU, Gao Cong

Time series forecasting fundamentally relies on accurately modeling complex interdependencies and shared patterns within time series data. Recent advancements, such as Spatio-Temporal Graph Neural Networks (STGNNs) and Time Series Foundation Models (TSFMs), have demonstrated promising results by effectively capturing intricate spatial and temporal dependencies across diverse real-world datasets. However, these models typically require large volumes of training data and often struggle in data-scarce scenarios. To address this limitation, we propose a framework named Few-shot Spatio-Temporal Large Language Models (FSTLLM), aimed at enhancing model robustness and predictive performance in few-shot settings. FSTLLM leverages the contextual knowledge embedded in Large Language Models (LLMs) to provide reasonable and accurate predictions. In addition, it supports the seamless integration of existing forecasting models to further boost their predicative capabilities. Experimental results on real-world datasets demonstrate the adaptability and consistently superior performance of FSTLLM over major baseline models by a significant margin. Our code is available at: https://github.com/JIANGYUE61610306/FSTLLM.