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Deep Learning · Generative Models and Autoencoders

Edgardo Solano Carrillo, Sreerag Vadakkemeppully Naveenachandran, Julia Niebling

Score-based generative modeling through differential equations has driven breakthroughs in high-fidelity image synthesis, offering modular model design and efficient sampling. However, this success has not been widely translated to timeseries forecasting yet. This gap stems from the sequential nature of time series, in contrast to the unordered structure of images. Here, we extend the theoretical formulation used for images to explicitly address sequential structures. We propose a diffusion-based forecasting framework (TEDM) that adapts score estimation to temporal settings and elucidates its design space. Such a design allows empirical computation of noise and signal scaling directly from data, avoiding external schedules. Notably, this reduces sampling complexity to linear in the forecast horizon. Without elaborate preprocessing, TEDM sets new state-of-the-art results on multiple forecasting benchmarks. These results illustrate the growing potential of diffusion models beyond vision. TEDM generates low-latency forecasts using a lightweight architecture, making it ideal for real-time deployment.

Applications · Time Series

Ruirui Wang, Yanke Li, Manuel Günther, Diego Paez-Granados

Healthcare data, such as Intensive Care Unit (ICU) records, comprise heterogeneous multivariate time series sampled at irregular intervals with pervasive missingness. However, clinical applications demand predictive models that are both accurate and interpretable. We present our Graph Attention-based Relational Learning for Intensive Care (GARLIC) model, a novel neural network architecture that imputes missing data through a learnable exponential-decay encoder, captures inter-sensor dependencies via time-lagged summary graphs, and fuses global patterns with cross-dimensional sequential attention. All attention weights and graph edges are learned end-to-end to serve as built-in observation-, signal-, and edge-level explanations. To reconcile auxiliary reconstruction and primary classification objectives, we developed an alternating decoupled optimization scheme that stabilizes training. On three ICU benchmarks (PhysioNet 2012 \& 2019, MIMIC-III), GARLIC sets the new state of the art in outcome prediction, significantly improving AUROC and AUPRC over best-performing baselines at comparable computational cost. Ablation studies confirm the contribution of each module, and feature-removal trials validate the fidelity of importance attribution through a monotonic performance drop (full > top 50\% > random 50\% > bottom 50\%). Real-time case studies demonstrate actionable risk warnings with transparent explanations, marking a significant advance toward accurate, explainable deep learning for irregularly sampled ICU time series data. Moreover, we demonstrated GARLIC's superiority in data imputation and classification on various time-series datasets beyond the ICU domain, showing its generalizability and applicability to broader tasks.

Applications · Time Series

Roberto Neglia, Andrea Cini, Michael Bronstein, Filippo Maria Bianchi

Conformal prediction offers a powerful framework for building distribution-free prediction intervals for exchangeable data. Existing methods that extend conformal prediction to sequential data rely on fitting a relatively complex model to capture temporal dependencies. However, these methods can fail if the sample size is small and often require expensive retraining when the underlying data distribution changes. To overcome these limitations, we propose Reservoir Conformal Prediction (ResCP), a novel training-free conformal prediction method for time series. Our approach leverages the efficiency and representation learning capabilities of reservoir computing to dynamically reweight conformity scores. In particular, we compute similarity scores among reservoir states and use them to adaptively reweight the observed residuals at each step. With this approach, ResCP enables us to account for local temporal dynamics when modeling the error distribution without compromising computational scalability. We prove that, under reasonable assumptions, ResCP achieves asymptotic conditional coverage, and we empirically demonstrate its effectiveness across diverse forecasting tasks.

Applications · Time Series

Xiannan Huang, Shuhan Qiu, Jiayuan Du, Chao Yang

Time series forecasting is of significant importance across various domains. However, it faces significant challenges due to distribution shift. This issue becomes particularly pronounced in online deployment scenarios where data arrives sequentially, requiring models to adapt continually to evolving patterns. Current time series online learning methods focus on two main aspects: selecting suitable parameters to update (e.g., final layer weights or adapter modules) and devising suitable update strategies (e.g., using recent batches, replay buffers, or averaged gradients). We challenge the conventional parameter selection approach, proposing that distribution shifts stem from changes in underlying latent factors influencing the data. Consequently, updating the feature representations of these latent factors may be more effective. To address the critical problem of delayed feedback in multi-step forecasting (where true values arrive much later than predictions), we introduce ADAPT-Z (Automatic Delta Adjustment via Persistent Tracking in Z-space). ADAPT-Z utilizes an adapter module that leverages current feature representations combined with historical gradient information to enable robust parameter updates despite the delay. Extensive experiments demonstrate that our method consistently outperforms standard base models without adaptation and surpasses state-of-the-art online learning approaches across multiple datasets.

Applications · Time Series

Roussel Nzoyem, Nawid Keshtmand, Enrique Crespo Fernandez, Idriss TSAYEM, Raul Santos-Rodriguez, David Barton, Tom Deakin

We introduce WARP (**W**eight-space **A**daptive **R**ecurrent **P**rediction), a simple yet powerful model that unifies weight-space learning with linear recurrence to redefine sequence modeling. Unlike conventional recurrent neural networks (RNNs) which collapse temporal dynamics into fixed-dimensional hidden states, WARP explicitly parametrizes its hidden state as the weights and biases of a distinct auxiliary neural network, and uses input differences to drive its recurrence. This brain-inspired formulation enables efficient gradient-free adaptation of the auxiliary network at test-time, in-context learning abilities, and seamless integration of domain-specific physical priors. Empirical validation shows that WARP matches or surpasses state-of-the-art baselines on diverse classification tasks, featuring in the top three in 4 out of 6 real-world challenging datasets. Furthermore, extensive experiments across sequential image completion, multivariate time series forecasting, and dynamical system reconstruction demonstrate its expressiveness and generalization capabilities. Remarkably, a physics-informed variant of our model outperforms the next best model by more than 10x. Ablation studies confirm the architectural necessity of key components, solidifying weight-space linear RNNs as a transformative paradigm for adaptive machine intelligence.

General Machine Learning · Representation Learning

Hedi Zisling, Ilan Naiman, Nimrod Berman, Supasorn Suwajanakorn, Omri Azencot

Unsupervised representation learning, particularly sequential disentanglement, aims to separate static and dynamic factors of variation in data without relying on labels. This remains a challenging problem, as existing approaches based on variational autoencoders and generative adversarial networks often rely on multiple loss terms, complicating the optimization process. Furthermore, sequential disentanglement methods face challenges when applied to real-world data, and there is currently no established evaluation protocol for assessing their performance in such settings. Recently, diffusion models have emerged as state-of-the-art generative models, but no theoretical formalization exists for their application to sequential disentanglement. In this work, we introduce the Diffusion Sequential Disentanglement Autoencoder (DiffSDA), a novel, modal-agnostic framework effective across diverse real-world data modalities, including time series, video, and audio. DiffSDA leverages a new probabilistic modeling, latent diffusion, and efficient samplers, while incorporating a challenging evaluation protocol for rigorous testing. Our experiments on diverse real-world benchmarks demonstrate that DiffSDA outperforms recent state-of-the-art methods in sequential disentanglement.

Applications · Time Series

Akash Pandey, Payal Mohapatra, Wei Chen, Qi Zhu, Sinan Keten

Identifying the extent to which every temporal segment influences a model’s predictions is essential for explaining model decisions and increasing transparency. While post-hoc explainable methods based on gradients and feature-based attributions have been popular, they suffer from reference state sensitivity and struggle to generalize across time-series datasets, as they treat time points independently and ignore sequential dependencies. Another perspective on explainable time-series classification is through interpretable components of the model, for instance, leveraging self-attention mechanisms to estimate temporal attribution; however, recent findings indicate that these attention weights often fail to provide faithful measures of temporal importance. In this work, we advance this perspective and present a novel explainability-driven deep learning framework, TimeSliver, which jointly utilizes raw time-series data and its symbolic abstraction to construct a representation that maintains the original temporal structure. Each element in this representation linearly encodes the contribution of each temporal segment to the final prediction, allowing us to assign a meaningful importance score to every time point. For time-series classification, TimeSliver outperforms other temporal attribution methods by 11\% on 7 distinct synthetic and real-world multivariate time-series datasets. TimeSliver also achieves predictive performance within 2\% of state-of-the-art baselines across 26 UEA benchmark datasets, positioning it as a strong and explainable framework for general time-series classification.

Rutherford Agbeshi Patamia, Ha Pham Thien Dinh, Ming Liu 0028, Akansel Cosgun

Reliable detection of conversational errors and user-initiated corrections is critical for effective human-robot interaction (HRI). In this study, we present a comprehensive multimodal approach leveraging temporal window processing, targeted feature engineering, and a MiniRocket + Ridge classification pipeline to address the challenges introduced by the ERR@HRI 2.0 dataset. Our methodology systematically integrates multimodal data streams, including facial expressions, acoustic features, and linguistic embeddings, to predict robot failures and user reactions. Experimental results demonstrate significant improvements over baseline models in event-level detection performance. Notably, linguistic features derived from transcript embeddings emerged as the most informative modality, substantially enhancing model performance. However, we observed challenges associated with managing false positives at the event level, suggesting avenues for future refinement in adaptive thresholding and sequential post-processing techniques. Our findings underscore the importance of careful feature selection and robust temporal modelling in developing effective real-time error detection systems for conversational robots. Our code is available online. https://github.com/Ruddy202/err-hri-2.0-armas.git.

Yuansan Liu, Sudanthi N. R. Wijewickrema, Dongting Hu, Christofer Bester, Stephen J. O'Leary, James Bailey 0001

Recent successes in diffusion probabilistic models have demonstrated their strength in modeling and generating different types of data, paving the way for their application in generative time series forecasting. However, most existing diffusion based approaches rely on sequential models and unimodal latent variables to capture global dependencies and model entire observable data, resulting in difficulties when it comes to highly stochastic time series data. In this paper, we propose a novel Stochastic Diffusion (StochDiff) model that integrates the diffusion process into time series modeling stage and utilizes the representational power of the stochastic latent spaces to capture the variability of the stochastic time series data. Specifically, the model applies diffusion module at each time step within the sequential framework and learns a step-wise, data-driven prior for generative diffusion process. These features enable the model to effectively capture complex temporal dynamics and the multi-modal nature of the highly stochastic time series data. Through extensive experiments on real-world datasets, we demonstrate the effectiveness of our proposed model for probabilistic time series forecasting, particularly in scenarios with high stochasticity. Additionally, with a real-world surgical use case, we highlight the model's potential in a medical application.

Haiqi Jiang 0003, Ying Ding 0007, Chenjie Pan, Aimin Huang, Rui Chen, Chenyou Fan

Classical time-series forecasting methods rely on learning from a fixed context window of past observations and extrapolating to a fixed number of future steps. They are therefore limited in flexibility and effectiveness in modeling tasks of varying historical lengths or future horizons, requiring re-training for each setting. We propose Contextual Meta-Adaptation (CMA), a unified scheme that captures history contexts and extrapolates future horizons with a single training. CMA integrates denoising diffusion capability which can sequentially generate a future series with maximum likelihood and remains consistent with observed history and past generations. We develop an efficient update strategy using gradient-based meta-learning for full-parameter tuning during training and LoRA adaptation at testing time. We validate our CMA scheme on in-context learning with longer observed history, ex(tend)-context learning with up to 3 times longer future horizons, and transfer-learning across different source-target domains. Our CMA outperforms existing methods by an average of 7% on six academic datasets and a significant 16% improvement on four realistic marketing datasets.

Chenxi Liu, Shaowen Zhou, Qianxiong Xu, Hao Miao, Cheng Long, Ziyue Li, Rui Zhao

The proliferation of edge devices has generated an unprecedented volume of time series data across different domains, motivating a variety of well-customized methods. Recently, Large Language Models (LLMs) have emerged as a new paradigm for time series analytics by leveraging the shared sequential nature of textual data and time series. However, a fundamental cross-modality gap between time series and LLMs exists, as LLMs are pre-trained on textual corpora and are not inherently optimized for time series. Many recent proposals are designed to address this issue. In this survey, we provide an up-to-date overview of LLMs-based cross-modality modeling for time series analytics. We first introduce a taxonomy that classifies existing approaches into four groups based on the type of textual data employed for time series modeling. We then summarize key cross-modality strategies, e.g., alignment and fusion, and discuss their applications across a range of downstream tasks. Furthermore, we conduct experiments on multimodal datasets from different application domains to investigate effective combinations of textual data and cross-modality strategies for enhancing time series analytics. Finally, we suggest several promising directions for future research. This survey is designed for a range of professionals, researchers, and practitioners interested in LLM-based time series modeling.

Jiaxiang Cheng, Yipeng Pang, Guoqiang Hu

Supervised time series prediction relies on directly measured target variables, but real-world use cases such as predicting remaining useful life (RUL) involve indirect supervision, where the target variable is labeled as a function of another dependent variable. Trending temporal regression techniques rely on sequential time series inputs to capture temporal patterns, requiring interpolation when dealing with sparsely and irregularly sampled covariates along the timeline. However, interpolation can introduce significant biases, particularly with highly scarce data. In this paper, we address the RUL prediction problem with data scarcity as time series regression under indirect supervision. We introduce a unified framework called parameterized static regression, which takes single data points as inputs for regression of target values, inherently handling data scarcity without requiring interpolation. The time dependency under indirect supervision is captured via a parametrical rectification (PR) process, approximating a parametric function during inference with historical posteriori estimates, following the same underlying distribution used for labeling during training. Additionally, we propose a novel batch training technique for tasks in indirect supervision to prevent overfitting and enhance efficiency. We evaluate our model on public benchmarks for RUL prediction with simulated data scarcity. Our method demonstrates competitive performance in prediction accuracy when dealing with highly scarce time series data.

Xin Wang, Shengfei Lyu, Kangyang Luo, Lishan Yang, Huanhuan Chen, Chunyan Miao

In the medical field, treatment sequences significantly influence future outcomes through complex temporal interactions. Therefore, highlighting the role of temporal treatments within the model is crucial for accurate counterfactual estimation, which is often overlooked in current methods. To address this, we employ Koopman theory, known for its capability to model complex dynamic systems, and introduce a novel model named the Counterfactual Temporal Dynamics Network via Neural Koopman Operators (CTD-NKO). This model utilizes Koopman operators to encapsulate sequential treatment data, aiming to capture the causal dynamics within the system induced by temporal interactions between treatments. Moreover, CTD-NKO implements a weighting strategy that aligns joint and marginal distributions of the system state and the current treatment to mitigate time-varying confounding bias. This deviates from the balanced representation strategy employed by existing methods, as we demonstrate that such a strategy may suffer from the potential information loss of historical treatments. These designs allow CTD-NKO to exploit treatment information more thoroughly and effectively, resulting in superior performance on both synthetic and real-world datasets.

Ruichu Cai, Kaitao Zheng, Junxian Huang, Zijian Li, Zhengming Chen, Boyan Xu, Zhifeng Hao

Time series imputation is one of the most challenging problems and has broad applications in various fields like health care and the Internet of Things. Existing methods mainly aim to model the temporally latent dependencies and the generation process from the observed time series data. In real-world scenarios, different types of missing mechanisms, like MAR (Missing At Random) and MNAR (Missing Not At Random), can occur in time series data. However, existing methods often overlook the difference among the aforementioned missing mechanisms and use a single model for time series imputation, which can easily lead to misleading results due to mechanism mismatching. In this paper, we propose a framework for the time series imputation problem by exploring Different Missing Mechanisms (DMM in short) and tailoring solutions accordingly. Specifically, we first analyze the data generation processes with temporal latent states and missing cause variables for different mechanisms. Sequentially, we model these generation processes via variational inference and estimate prior distributions of latent variables via a normalizing flow-based neural architecture. Furthermore, we establish identifiability results under the nonlinear independent component analysis framework to show that latent variables are identifiable. Experimental results show that our method surpasses existing time series imputation techniques across various datasets with different missing mechanisms, demonstrating its effectiveness in real-world applications.

Fan Lu, Xiaolong Xu, Haolong Xiang, Lianyong Qi, Xiaokang Zhou, Fei Dai, Wanchun Dou

Sequential recommendation generates embedding representations from historical user-item interactions to recommend the next potential interaction item. Due to the complexity and variability of historical user-item interactions, extracting effective user features is quite challenging. Recent studies have employed sequential networks such as time series networks and Transformers to capture the intricate dependencies and temporal patterns in historical user-item interactions, extracting more effective user features. However, limited by the scarcity and suboptimal quality of data, these methods struggle to capture subtle differences in user sequences, which results in diminished recommendation accuracy. To address the above issue, we propose a contrastive learning framework with LLMs-based view augmentation (CLLMRec), which effectively mines differences in behavioral sequences through sample generation. Specifically, CLLMRec utilizes LLMs (Large Language Models) to augment views and expand user behavior sequence representations, providing high-quality positive and negative samples. Subsequently, CLLMRec employs the augmented views for effective contrastive learning, capturing subtle differences in behavioral sequences to suppress interference from irrelevant noise. Experimental results on three public datasets demonstrate that the proposed method outperforms state-of-the-art baseline models, and significantly enhances recommendation performance.

Jiaxin Gao, Qinglong Cao, Yuntian Chen

Time series forecasting (TSF) is essential in various domains, and recent advancements in diffusion-based TSF models have shown considerable promise. However, these models typically adopt traditional diffusion patterns, treating TSF as a noise-based conditional generation task. This approach neglects the inherent continuous sequential nature of time series, leading to a fundamental misalignment between diffusion mechanisms and the TSF objective, thereby severely impairing performance. To bridge this misalignment, and inspired by the classic Auto-Regressive Moving Average (ARMA) theory, which views time series as continuous sequential progressions evolving from previous data points, we propose a novel Auto-Regressive Moving Diffusion (ARMD) model to first achieve the continuous sequential diffusion-based TSF. Unlike previous methods that start from white Gaussian noise, our model employs chain-based diffusion with priors, accurately modeling the evolution of time series and leveraging intermediate state information to improve forecasting accuracy and stability. Specifically, our approach reinterprets the diffusion process by considering future series as the initial state and historical series as the final state, with intermediate series generated using a sliding-based technique during the forward process. This design aligns the diffusion model's sampling procedure with the forecasting objective, resulting in an unconditional, continuous sequential diffusion TSF model. Extensive experiments conducted on seven widely used datasets demonstrate that our model achieves state-of-the-art performance, significantly outperforming existing diffusion-based TSF models.

Ruichu Cai, Haiqin Huang, Zhifan Jiang, Zijian Li, Changze Zhou, Yuequn Liu, Yuming Liu, Zhifeng Hao

Current methods for time series forecasting struggle in the online scenario, since it is difficult to preserve long-term dependency while adapting short-term changes when data are arriving sequentially. Although some recent methods solve this problem by controlling the updates of latent states, they cannot disentangle the long/short-term states, leading to the inability to effectively adapt to nonstationary. To tackle this challenge, we propose a general framework to disentangle long/short-term states for online time series forecasting. Our idea is inspired by the observations where short-term changes can be led by unknown interventions like abrupt policies in the stock market. Based on this insight, we formalize a data generation process with unknown interventions on short-term states. Under mild assumptions, we further leverage the independence of short-term states led by unknown interventions to establish the identification theory to achieve the disentanglement of long/short-term states. Built on this theory, we develop a Long Short-Term Disentanglement model (LSTD) to extract the long/short-term states with long/short term encoders, respectively. Furthermore, the LSTD model incorporates a smooth constraint to preserve the long-term dependencies and an interrupted dependency constraint to enforce the forgetting of short-term dependencies, together boosting the disentanglement of long/short-term states. Experimental results on several benchmark datasets show that our LSTD model outperforms existing methods for online time series forecasting, validating its efficacy in real-world applications.

Ziwei Liu, Qidong Liu, Yejing Wang, Wanyu Wang, Pengyue Jia, Maolin Wang, Zitao Liu, Yi Chang, Xiangyu Zhao

Sequential Recommender Systems (SRS) has stood out as a highly promising technique in numerous domains due to its impressive capability of capturing complex user preferences. Current SRS have employed transformer-based models to give the next-item prediction. Nevertheless, its quadratic computational complexity has often resulted in notable inefficiencies, posing a significant obstacle to real-time recommendation processes. Recently, Mamba has demonstrated its exceptional effectiveness in time series prediction, delivering substantial improvements in both efficiency and effectiveness. However, directly applying Mamba to SRS poses certain challenges. Its unidirectional structure may impede the ability to capture contextual information in user-item interactions, while its instability in state estimation may hinder the ability to capture short-term patterns in interaction sequences. To address these issues, we propose a novel framework called Selective Gated Mamba for Sequential Recommendation (SIGMA). By introducing the Partially Flipped Mamba (PF-Mamba), we construct a special bi-directional structure to address the context modeling challenge. Then, to consolidate PF-Mamba's performance, we employed an input-dependent Dense Selective Gate (DS Gate) to allocate the weights of the two directions and further filter the sequential information. Moreover, for short sequence modeling, we devise a Feature Extract GRU (FE-GRU) to capture the short-term dependencies. Experimental results demonstrate that SIGMA significantly outperforms existing baselines across five real-world datasets. Our implementation code is available in Supplementary Material to ease reproducibility.

Yaxuan Kong, Zepu Wang, Yuqi Nie, Tian Zhou, Stefan Zohren, Yuxuan Liang, Peng Sun, Qingsong Wen

Traditional recurrent neural network architectures, such as long short-term memory neural networks (LSTM), have historically held a prominent role in time series forecasting (TSF) tasks. While the recently introduced sLSTM for Natural Language Processing (NLP) introduces exponential gating and memory mixing that are beneficial for long term sequential learning, its potential short memory issue is a barrier to applying sLSTM directly in TSF. To address this, we propose a simple yet efficient algorithm named P-sLSTM, which is built upon sLSTM by incorporating patching and channel independence. These modifications substantially enhance sLSTM's performance in TSF, achieving state-of-the-art results. Furthermore, we provide theoretical justifications for our design, and conduct extensive comparative and analytical experiments to fully validate the efficiency and superior performance of our model.

Nikola Zubic, Davide Scaramuzza

State Space Models (SSMs) are powerful tools for modeling sequential data in computer vision and time series analysis domains. However, traditional SSMs are limited by fixed, one-dimensional sequential processing, which restricts their ability to model non-local interactions in high-dimensional data. While methods like Mamba and VMamba introduce selective and flexible scanning strategies, they rely on predetermined paths, which fails to efficiently capture complex dependencies. We introduce Graph-Generating State Space Models (GG-SSMs), a novel framework that overcomes these limitations by dynamically constructing graphs based on feature relationships. Using Chazelle's Minimum Spanning Tree algorithm, GG-SSMs adapt to the inherent data structure, enabling robust feature propagation across dynamically generated graphs and efficiently modeling complex dependencies. We validate GG-SSMs on 11 diverse datasets, including event-based eye-tracking, ImageNet classification, optical flow estimation, and six time series datasets. GG-SSMs achieve state-of-the-art performance across all tasks, surpassing existing methods by significant margins. Specifically, GG-SSM attains a top-1 accuracy of 84.9% on ImageNet, outperforming prior SSMs by 1%, reducing the KITTI-15 error rate to 2.77%, and improving eye-tracking detection rates by up to 0.33% with fewer parameters. These results demonstrate that dynamic scanning based on feature relationships significantly improves SSMs' representational power and efficiency, offering a versatile tool for various applications in computer vision and beyond.