Multivariate time series forecasting is fundamental to web-scale systems. However, frequency-domain forecasters face two structural challenges: (i) frequency bias, where low-amplitude yet informative temporal cues are often submerged in noise and neglected during training; (ii) spectral degradation, where standard neural transformations distort high-amplitude periodic structures, thereby weakening the predictive signal. To address both issues, we propose GFMixer, a decoupled dual-path architecture. GFMixer first applies a Temporal Gradient Block (TGB) to capture low-amplitude information through adaptive selection based on temporal-geometric evidence. Subsequently, a Fourier-Aware Attention Block (FAB) represents high-amplitude, multi-frequency information to mitigate spectral degradation. Finally, both information streams are integrated via time-aligned residual connections within a Gradient Aggregation Block (GAB) for the final forecasting task. Extensive evaluations across seven standard benchmarks (ETT, Weather, Electricity, and Traffic) demonstrate GFMixer's superiority, securing 37 first-place rankings and the lowest average MSE overall. Beyond standalone performance, GFMixer serves as a versatile plug-and-play module that consistently enhances mainstream backbones. Code is available at: https://github.com/superlin30/GFMixer.
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With the rapid proliferation of short-video platforms and content-driven social networks, sequential recommendation models capable of accurately capturing user interests have become increasingly crucial. Among these, Transformer-based sequential recommendation models have gained widespread adoption due to their superior ability. The positional encoding (PE) in Transformer architectures serves to incorporate positional information into sequences. However, relying solely on original absolute positional information may be insufficient for sequential recommendation models. In contrast, the dwell time after interactions (i.e., the time intervals between consecutive user interactions) provides a more accurate reflection of users' emotional responses and evolving interests. Despite its significance, this aspect has often been overlooked in existing works. To fully utilize this information, our work introduces an adaptive PE method, termed TSAPE (Temporal-Series-Aware Positional Encoding). This approach introduces an innovative modeling of the sequence of time intervals between user interactions, rather than the numerical values of the intervals themselves, thereby capturing real-time feedback on user interests and integrating it with conventional PE mechanisms. Furthermore, we employ multiple layers of one-dimensional convolutional networks and attention mechanisms to endow the features with adaptive capabilities across various time interval scenarios. This enables TSAPE to more accurately capture sequential positional information at any given moment. By enhancing the sequential order information of interactions, TSAPE significantly improves the accuracy of next-item recommendations. We seamlessly integrated our method into several Transformer-based sequential recommendation models and conducted comparisons with state-of-the-art sequential recommendation approaches and widely-used PE methods. The results demonstrate that the integration of TSAPE consistently outperforms the original backbone models and other SOTA methods. The SASRec model integrated with TSAPE achieves an average improvement of 15.61% across three evaluation metrics on four benchmark datasets. Our code has been made publicly available at https://github.com/rongbo-qi/TSAPE_Rec.
Modeling multiscale patterns is crucial for long-term time series forecasting (TSF). However, redundancy and noise in time series, together with semantic gaps between non-adjacent scales, make the efficient alignment and integration of multi-scale temporal dependencies challenging. To address this, we propose SEMixer, a lightweight multiscale model designed for long-term TSF. SEMixer features two key components: a Random Attention Mechanism (RAM) and a Multiscale Progressive Mixing Chain (MPMC). RAM captures diverse time-patch interactions during training and aggregates them via dropout ensemble at inference, enhancing patch-level semantics and enabling MLP-Mixer to better model multi-scale dependencies. MPMC further stacks RAM and MLP-Mixer in a memory-efficient manner, achieving more effective temporal mixing. It addresses semantic gaps across scales and facilitates better multiscale modeling and forecasting performance. We not only validate the effectiveness of SEMixer on 10 public datasets, but also on the 2025 CCF AlOps Challenge based on 21GB real wireless network data, where SEMixer achieves third place. The code is available at https://github.com/Meteor-Stars/SEMixer.
Time series data are prone to noise in various domains, and training samples may contain low-predictability patterns that deviate from the normal data distribution, leading to training instability or convergence to poor local minima. Therefore, mitigating the adverse effects of low-predictability samples is crucial for time series analysis tasks such as time series forecasting (TSF) and time series classification (TSC). While many deep learning models have achieved promising performance, few consider how to identify and penalize low-predictability samples to improve model performance from the training perspective. To fill this gap, we propose a general Amortized Predictability-aware Training Framework (APTF) for both TSF and TSC. APTF introduces two key designs that enable the model to focus on high-predictability samples while still learning appropriately from low-predictability ones: (i) a Hierarchical Predictability-aware Loss (HPL) that dynamically identifies low-predictability samples and progressively expands their loss penalty as training evolves, and (ii) an amortization model that mitigates predictability estimation errors caused by model bias, further enhancing HPL's effectiveness. The code is available at https://github.com/Meteor-Stars/APTF.
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 in signal processing, we propose a predictability-aware compression–decompression framework to reduce runtime, decrease communication cost, and maintain prediction accuracy across diverse predictors. The core idea involves using a circular seasonal key matrix with orthogonality to capture underlying time series predictability during compression and to mitigate reconstruction errors during decompression by introducing more realistic data assumptions. Theoretical analyses show that the proposed framework is both time-efficient and accuracy-preserving 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.
Time series anomaly detection (TSAD) has been a long-standing pillar problem in Web-scale systems and online infrastructures, such as service reliability monitoring, system fault diagnosis, and performance optimization. Large language models (LLMs) have demonstrated unprecedented capabilities in time series analysis, the potential of multimodal LLMs (MLLMs), particularly vision-language models, in TSAD remains largely under-explored. One natural way for humans to detect time series anomalies is through visualization and textual description. It motivates our research question: Can multimodal LLMs perform time series anomaly detection? Existing studies often oversimplify the problem by treating point-wise anomalies as special cases of range-wise ones or by aggregating point anomalies to approximate range-wise scenarios. They limit our understanding for realistic scenarios such as multi-granular anomalies and irregular time series. To address the gap, we build a VisualTimeAnomaly benchmark to comprehensively investigate zero-shot capabilities of MLLMs for TSAD, progressively from point-, range-, to variate-wise anomalies, and extends to irregular sampling conditions. Our study reveals several key insights. 1) MLLMs and traditional TSAD methods are complementary: MLLMs excel at coarse-grained anomalies while traditional methods are effective at fine-grained anomalies. 2) MLLMs are resilient to irregular time series. 3) Input time series modality changing from text to image makes information focus shift from quantitative variations to qualitative patterns while significantly reducing hallucinations. Built on the findings, we propose a MLLMs-based multi-agent framework TSAD-Agents to achieve automatic TSAD. Our framework comprises scanning, planning, detection, and checking agents that synergistically collaborate to reason, plan, and self-reflect to enable automatic TSAD. These agents adaptively invoke tools such as traditional methods and MLLMs and dynamically switch between text and image modalities to optimize detection performance.
Accurate multivariate time series forecasting (MTSF) is critical for intelligent web services in Web of Things. When confronted with unseen multivariate time series (MTS), the industry typically invests significant time and resources in training multiple models to identify the optimal model for deployment. This paper proposes a novel, efficient, and scalable MTSF model selection method that directly selects suitable MTSF methods based on data characteristics without extensive model training. Model selection is a core component of AutoML, which has made significant progress in recent years. However, existing methods incur high operational costs and cannot be directly applied to MTSF tasks. Moreover, there is a lack of a comprehensive and cohesive public time series library for MTSF model selection. To address these challenges, we compile the first large heterogeneous labeled MTSF model selection dataset, called the ModelPile, which covers 41 mainstream datasets across 11 domains. We then propose AutoMTSF, a large model-enabled model selection method that transforms the MTSF model selection problem into a time series classification problem and utilizes the ModelPile to unlock large-scale multi-dataset training. AutoMTSF first uses the pre-trained large model to encode raw MTS. Given the coarse-grained limitations of large model encoding, Recursive Temporal Pattern Feature (RTPF) is proposed to capture both fine-grained and global temporal feature evolution, thereby effectively mapping data characteristics to the MTSF method space. Experiments comparing AutoMTSF with 2 baselines, 17 MTSF methods, and 4 large time series models show that AutoMTSF outperforms state-of-the-art methods while maintaining comparable execution time. This work represents a critical step in validating the accuracy and efficiency of large model-enabled classification for MTSF.
In real-world web applications, especially those involving sensor networks and Internet of Things (IoT) devices, time series data are often incomplete due to network delays, device failures or logging constraints. Such missing data can severely affect downstream tasks including anomaly detection, recommendation, and A/B testing, making imputation a critical step for reliable web analytics. Diffusion models have recently achieved strong performance for time series imputation. As relevant research progresses, the spectral nature of time series has received increasing attention. However, most ''frequency-aware'' diffusion variants modify either the input or network architecture, but the variance schedule in the forward process remains unchanged, injecting noise with the same variance into every frequency bin. This limitation prevents diffusion from adapting to real data, where spectral energy varies irregularly across frequencies rather than following a simple high–low split. To address these issues, we propose Frequency-Shaped Diffusion (FSDI), which replaces the uniform variance schedule with a data-driven schedule in the frequency domain. Frequency bin variances are estimated from the spectral energy distribution of the data, allocated as inverses of that energy, and then Parseval-calibrated so the total noise energy exactly matches standard diffusion, preserving training stability and ensuring fair comparison. Experiments on real-world datasets demonstrate that FSDI achieves state-of-the-art performance. All code have been made publicly at https://github.com/decisionintelligence/FSDI.
Federated domain generalization (FDG) for time-series classification (TSC) poses a critical challenge for modern intelligent web services, which rely on edge-collected time-series signals from diverse mobile applications and web devices (e.g., wearables sensors) to support decision-making. The source heterogeneity and temporal dynamics give rise to out-of-distribution (OOD) patterns, which hinder the model's ability to generalize to previously unseen users and devices. In this work, we propose Federated Generalization via Diversity Generation (FedDiG), a diffusion-based FDG framework that captures intra-client distribution shifts from a frequency-domain perspective and employs cross-frequency sampling to synthesize time-series data with diverse spectral patterns. Specifically, FedDiG first performs frequency-proxy representation learning on clients to serve as diffusion conditions. The server then aggregates client-side frequency proxies to construct a global proxy pool and applies class-wise mixup to create novel frequency features. These features guide a global diffusion model to produce diverse data, enabling the simulation of previously unseen patterns and thereby enhancing model training. Extensive experiments on four cross-domain time-series benchmarks demonstrate that FedDiG significantly outperforms state-of-the-art federated learning and FDG baselines, particularly under small-data regimes and large-scale client scenarios, achieving robust generalization to unseen domains in federated settings. This work bridges distribution-diversity synthesis and FDG for time-series to support robust, scalable web applications fed by edge-collected signals, delivering web-scale generalization across heterogeneous web, mobile, and IoT clients.
Web service administrators must ensure the stability of multiple systems by promptly detecting anomalies in Key Performance Indicators (KPIs). Achieving the goal of ''train once, infer across scenarios'' remains a fundamental challenge for time series anomaly detection models. Beyond improving zero-shot generalization, such models must also flexibly handle sequences of varying lengths during inference—ranging from one hour to one week—without retraining. Conventional approaches rely on sliding-window encoding and self-supervised learning, which restrict inference to fixed length inputs. Large Language Models (LLMs) have demonstrated remarkable zero-shot capabilities across general domains. However, when applied to time series data, they face inherent limitations due to context length. To address this issue, we propose ViTs, a Vision-Language Model (VLM)-based framework that converts time series curves into visual representations. By rescaling time series images, temporal dependencies are preserved while maintaining a consistent input size, thereby enabling efficient processing of arbitrarily long sequences without context constraints. Training VLMs for this purpose introduces unique challenges, primarily due to the scarcity of aligned time series image–text data. To overcome this, we employ an evolutionary algorithm to automatically generate thousands of high-quality image–text pairs and design a three-stage training pipeline consisting of: (1) time series knowledge injection, (2) anomaly detection enhancement, and (3) anomaly reasoning refinement. Extensive experiments demonstrate that ViTs substantially enhance the ability of VLMs to understand and detect anomalies in time series data. All datasets and code will be publicly released at: https://github.com/Uni-WangZexin/ViTs.
Generative modeling offers a promising solution to data scarcity and privacy challenges in time series analysis. However, the structural complexity of time series, characterized by multi-scale temporal patterns and heterogeneous components, remains insufficiently addressed. In this work, we propose a structure-disentangled multiscale generation framework for time series. Our approach encodes sequences into discrete tokens at multiple temporal resolutions and performs autoregressive generation in a coarse-to-fine manner, thereby preserving hierarchical dependencies. To tackle structural heterogeneity, we introduce a dual-path VQ-VAE that disentangles trend and seasonal components, enabling the learning of semantically consistent latent representations. Additionally, we present a guidance-based reconstruction strategy, where coarse seasonal signals are utilized as priors to guide the reconstruction of fine-grained seasonal patterns. Experiments on six datasets show that our approach produces higher-quality time series than existing methods. Notably, our model achieves strong performance with a significantly reduced parameter count and exhibits superior capability in generating high-quality long-term sequences. Our implementation is available at https://github.com/decisionintelligence/TimeMAR.
The World Wide Web increasingly relies on intelligent services that require accurate time series forecasting, from urban mobility platforms to adaptive web-based decision systems. In practice, building effective forecasting models typically requires abundant high-quality data, which may not always be available in all cities due to sensing limitations or data sparsity. To address this challenge, transfer learning methods aim to transfer knowledge from data-rich source cities to data-scarce target cities. However, source and target data distributions are often not identical: while some patterns from source cities may be beneficial, others can be irrelevant or even misleading. Existing transfer learning methods generally train the target model using all available source data without explicitly distinguishing between useful and non-useful knowledge, which may hinder performance. In this work, we propose xRAG4TS, a novel framework that integrates Retrieval-Augmented Generation (RAG) with Large Language Models (LLMs) for cross-city time series forecasting. xRAG4TS introduces a Cross-City Selective Retriever Module that filters semantically relevant historical patterns and documents from data-rich source cities, and incorporates them as structured prompts in an LLM Inference Module to guide forecasting in data-scarce target cities. By enabling selective, interpretable, and context-aware knowledge transfer, our method enhances robustness and scalability in web-oriented spatio-temporal applications. Extensive experiments on real-world cross-city datasets demonstrate that xRAG4TS significantly outperforms state-of-the-art baselines, highlighting its potential for powering adaptive and trustworthy web services under severe data scarcity.
Influence maximization (IM) aims to select a small set of seed nodes whose activation triggers a maximal cascade. Existing methods typically assume access to the network topology or a reliable surrogate, which is often unavailable in practice due to noisy, privacy-protected, or partially observed links. These settings pose two challenges: (1) the lack of explicit topology removes a key inductive constraint for diffusion modeling, undermining influence estimation, and (2) nonlinear, temporally dependent node interactions yield complex multivariate time series that hinder topology inference. We propose DynaFLUX, an end-to-end generative framework for IM under hidden topology. DynaFLUX learns a compact surrogate of latent dynamics directly from observed time series, and jointly optimizes a seed-selection policy via reinforcement learning. A self-attention pointer network captures long-range dependencies for seed generation, while an influence-prediction module infers a surrogate topology and uses Monte Carlo diffusion to provide policy-gradient rewards. Experiments show that DynaFLUX accurately identifies influential spreaders and consistently outperforms state-of-the-art baselines in unseen topology scenarios.
Social media engagement prediction is a central challenge in computational social science, particularly for understanding how users interact with misinformation. Existing approaches often treat engagement as a homogeneous time-series signal, overlooking the heterogeneous social mechanisms and platform designs that shape how misinformation spreads. In this work, we ask: ''Can neural architectures discover social exchange principles from behavioral data alone?'' We introduce Dreams (Disentangled Representations and Episodic Adaptive Modeling for Social media misinformation engagements), a social exchange theory-guided framework that models misinformation engagement as a dynamic process of social exchange. Rather than treating engagement as a static outcome, Dreams models it as a sequence-to-sequence adaptation problem, where each action reflects an evolving negotiation between user effort and social reward conditioned by platform context. It integrates adaptive mechanisms to learn how emotional and contextual signals propagate through time and across platforms. On a cross-platform dataset spanning 7 platforms and 2.37M posts collected between 2021 and 2025, Dreams achieves state-of-the-art performance in predicting misinformation engagements, reaching a mean absolute percentage error of 19.25%. This is a 43.6% improvement over the strongest baseline. Beyond predictive gains, the model reveals consistent cross-platform patterns that align with social exchange principles, suggesting that integrating behavioral theory can enhance empirical modeling of online misinformation engagement. The source code is available at: https://github.com/ltian678/DREAMS.
Pseudo-Alignment is a pervasive challenge in many large language models for time series (LLM4TS) models, often causing them to underperform compared to linear models or randomly initialised backbones. However, there is limited discussion in the community for the reasons that pseudo-alignment occurs. In this work, we conduct a thorough investigation into the root causes of pseudo-alignment in LLM4TS and build a connection of pseudo-alignment to the cone effect in LLM. We demonstrate that pseudo-alignment arises from the interplay of cone effect within pretrained LLM components and the intrinsically low-dimensional manifold of time-series data. In addition, we also introduce TimeSUP, a novel technique designed to mitigate this issue and improve forecast performance in existing LLM4TS approaches. TimeSUP addresses this by increasing the time series manifold to more closely match the intrinsic dimension of language embeddings, allowing the model to distinguish temporal signals clearly while still capturing shared structures across modalities. As a result, representations for time and language tokens remain distinct yet exhibit high cosine similarity, signifying that the model preserves each modality's unique features while learning their commonalities in a unified embedding space. Empirically, TimeSUP consistently outperforms state-of-the-art LLM4TS methods and other lightweight baselines on long-term forecasting performance. Furthermore, it can be seamlessly integrated into four existing LLM4TS pipelines and delivers significant improvements in forecasting performance.
Accurate forecasting of sequential data streams is a cornerstone of modern Web services, supporting applications such as traffic management, user behavior modeling, and online anomaly prevention. However, in many Web environments, new domains emerge rapidly and labeled history data is scarce, which makes zero-shot forecasting particularly challenging. Existing time-series pre-trained models (TSPMs) show promise but they lack the ability to dynamically incorporate external knowledge, while conventional retrieval-augmented generation (RAG) methods are rarely extended beyond text. In this work, we present QuiZSF, a retrieval-augmented forecasting framework that integrates search and forecasting for time series data. The framework performs search by retrieving structurally similar sequences from a large-scale time-series database, and it performs forecasting by integrating the retrieved knowledge into the target sequence. Specifically, QuiZSF introduces a ChronoRAG Base, a hierarchical tree-structured database that enables scalable and domain-aware retrieval, a Multi-grained Series Interaction Learner that captures fine- and coarse-grained dependencies between target and retrieved sequences, and a Model Cooperation Coherer that adapts retrieved knowledge to TSPMs. This design teaches models to actively perform search, align auxiliary information across modalities, and leverage it for more accurate forecasting. Extensive experiments on five public benchmarks demonstrate that QuiZSF consistently outperforms strong baselines, ranking first in up to 87.5% of zero-shot forecasting settings while maintaining high efficiency.
Detecting data that deviates from normal behavior in dynamic graphs is an important hotspot. In the real world, anomaly detection is widely applied across various domains. However, existing anomaly detection methods typically assume static input graphs, failing to capture dynamic information in real-world scenarios. In addition, during the evolution of node representations over time, standard updating mechanisms lack the ability to selectively preserve important features. To address these issues, this paper constructs a dynamic graph anomaly detection framework (DyConAD) that enhances model perception of dynamic information through memory enhancement strategies and multi-scale similarity-based anomaly scoring mechanisms. Additionally, we also design a dynamic graph construction method that extracts time-aware shapelet and establishes spatiotemporal relationships between these shapelet. Experimental validation is conducted on four real-world datasets and three public datasets from the UCR Time Series Archive. Results demonstrate that our proposed method outperforms existing approaches across multiple datasets, achieving effective improvements in both detection accuracy and efficiency.