Rongyao Cai

Rongyao Cai, Yuxi Wan, Kexin Zhang et al.

Diffusion models learn data distributions indirectly through denoising, making the difficulty of generative modeling closely tied to the dependency structure of data. For time series, strong temporal dependence forces the noise / score estimator to recover highly entangled cross-time relationships, leading to the curse of entanglement. We mitigate this burden by changing the topology of the diffusion space: the Discrete Fourier Transform (DFT) decomposes temporal dependencies into spectral modes, diagonalizing second-order dependency structure and better aligning the data manifold with isotropic Gaussian noise and homogeneous diffusion dynamics. However, existing frequency-aware diffusion methods mainly use the DFT to design estimator blocks under temporal DDPM/SDE frameworks, while frequency-native diffusion paths face a mathematical barrier from complex-valued dynamics. We propose PaCoDi (Parallel Complex Diffusion), a frequency-native diffusion framework that constructs the diffusion path in the spectral domain while replacing the complex-valued estimator with parallel real-valued estimators for real and imaginary components. Theoretically, we prove the statistical orthogonality of spectral Gaussian noise, establish quadrature forward transitions and conditional reverse factorization, and extend discrete PaCoDi to continuous-time spectral SDEs through a Spectral Wiener Process. We further introduce a Mean Field Theory approximation with an Interactive Correction Branch to handle marginal coupling, and exploit Hermitian symmetry to reduce 50% attention FLOPs without information loss. Extensive experiments on unconditional and conditional time series generation demonstrate superior generative quality and computational efficiency against 5 SOTA baselines in 5 benchmarks, respectively. Code is available at https://github.com/RongyaoCai/PaCoDi.

Kexin Zhang, Qingsong Wen, Chaoli Zhang et al.

Self-supervised learning (SSL) has recently achieved impressive performance on various time series tasks. The most prominent advantage of SSL is that it reduces the dependence on labeled data. Based on the pre-training and fine-tuning strategy, even a small amount of labeled data can achieve high performance. Compared with many published self-supervised surveys on computer vision and natural language processing, a comprehensive survey for time series SSL is still missing. To fill this gap, we review current state-of-the-art SSL methods for time series data in this article. To this end, we first comprehensively review existing surveys related to SSL and time series, and then provide a new taxonomy of existing time series SSL methods by summarizing them from three perspectives: generative-based, contrastive-based, and adversarial-based. These methods are further divided into ten subcategories with detailed reviews and discussions about their key intuitions, main frameworks, advantages and disadvantages. To facilitate the experiments and validation of time series SSL methods, we also summarize datasets commonly used in time series forecasting, classification, anomaly detection, and clustering tasks. Finally, we present the future directions of SSL for time series analysis.

Siqiao Xue, Zhaoyang Zhu, Wei Zhang et al.

Time series forecasting is critical across finance, healthcare, and cloud computing, yet progress is constrained by a fundamental bottleneck: the scarcity of large-scale, high-quality benchmarks. To address this gap, we introduce \textsc{QuitoBench}, a regime-balanced benchmark for time series forecasting with coverage across eight trend$\times$seasonality$\times$forecastability (TSF) regimes, designed to capture forecasting-relevant properties rather than application-defined domain labels. The benchmark is built upon \textsc{Quito}, a billion-scale time series corpus of application traffic from Alipay spanning nine business domains. Benchmarking 10 models from deep learning, foundation models, and statistical baselines across 232,200 evaluation instances, we report four key findings: (i) a context-length crossover where deep learning models lead at short context ($L=96$) but foundation models dominate at long context ($L \ge 576$); (ii) forecastability is the dominant difficulty driver, producing a $3.64 \times$ MAE gap across regimes; (iii) deep learning models match or surpass foundation models at $59 \times$ fewer parameters; and (iv) scaling the amount of training data provides substantially greater benefit than scaling model size for both model families. These findings are validated by strong cross-benchmark and cross-metric consistency. Our open-source release enables reproducible, regime-aware evaluation for time series forecasting research.

Rongyao Cai, Yuxi Wan, Kexin Zhang et al.

Optimizing time series models via point-wise loss functions (e.g., MSE) relying on a flawed point-wise independent and identically distributed (i.i.d.) assumption that disregards the causal temporal structure, an issue with growing awareness yet lacking formal theoretical grounding. Focusing on the core independence issue under covariance stationarity, this paper aims to provide a first-principles analysis of the Expectation of Optimization Bias (EOB), formalizing it information-theoretically as the discrepancy between the true joint distribution and its flawed i.i.d. counterpart. Our analysis reveals a fundamental paradigm paradox: the more deterministic and structured the time series, the more severe the bias by point-wise loss function. We derive the first closed-form quantification for the non-deterministic EOB across linear and non-linear systems, and prove EOB is an intrinsic data property, governed exclusively by sequence length and our proposed Structural Signal-to-Noise Ratio (SSNR). This theoretical diagnosis motivates our principled debiasing program that eliminates the bias through sequence length reduction and structural orthogonalization. We present a concrete solution that simultaneously achieves both principles via DFT or DWT. Furthermore, a novel harmonized $\ell_p$ norm framework is proposed to rectify gradient pathologies of high-variance series. Extensive experiments validate EOB Theory's generality and the superior performance of debiasing program.

Changning Wu, Gao Wu, Rongyao Cai et al.

Multi-scale decomposition architectures have emerged as predominant methodologies in time series forecasting. However, real-world time series exhibit noise interference across different scales, while heterogeneous information distribution among frequency components at varying scales leads to suboptimal multi-scale representation. Inspired by Kolmogorov-Arnold Networks (KAN) and Parseval's theorem, we propose a KAN based adaptive Frequency Selection learning architecture (KFS) to address these challenges. This framework tackles prediction challenges stemming from cross-scale noise interference and complex pattern modeling through its FreK module, which performs energy-distribution-based dominant frequency selection in the spectral domain. Simultaneously, KAN enables sophisticated pattern representation while timestamp embedding alignment synchronizes temporal representations across scales. The feature mixing module then fuses scale-specific patterns with aligned temporal features. Extensive experiments across multiple real-world time series datasets demonstrate that KT achieves state-of-the-art performance as a simple yet effective architecture.

Rongyao Cai, Ming Jin, Qingsong Wen et al.

Domain shift poses a fundamental challenge in time series analysis, where models trained on source domain often fail dramatically when applied in target domain with different yet similar distributions. While current unsupervised domain adaptation (UDA) methods attempt to align cross-domain feature distributions, they typically treat features as indivisible entities, ignoring their intrinsic compositions that govern domain adaptation. We introduce DARSD, a novel UDA framework with theoretical explainability that explicitly realizes UDA tasks from the perspective of representation space decomposition. Our core insight is that effective domain adaptation requires not just alignment, but principled disentanglement of transferable knowledge from mixed representations. DARSD consists of three synergistic components: (I) An adversarial learnable common invariant basis that projects original features into a domain-invariant subspace while preserving semantic content; (II) A prototypical pseudo-labeling mechanism that dynamically separates target features based on confidence, hindering error accumulation; (III) A hybrid contrastive optimization strategy that simultaneously enforces feature clustering and consistency while mitigating emerging distribution gaps. Comprehensive experiments conducted on four benchmarks (WISDM, HAR, HHAR, and MFD) demonstrate DARSD's superiority against 12 UDA algorithms, achieving optimal performance in 35 out of 53 scenarios and ranking first across all benchmarks.