In long-term series forecasting (LTSF), it is imperative for models to adeptly discern and distill from historical time series data to forecast future states. Although Transformer-based models excel at capturing long-term dependencies in LTSF, their practical use is limited by issues like computational inefficiency, noise sensitivity, and overfitting on smaller datasets. Therefore, we introduce a novel time series lightweight interactive Mamba with an adaptive Fourier filter model (Affirm). Specifically, (i) we propose an adaptive Fourier filter block. This neural operator employs Fourier analysis to refine feature representation, reduces noise with learnable adaptive thresholds, and captures inter-frequency interactions using global and local semantic adaptive Fourier filters via element-wise multiplication. (ii) A dual interactive Mamba block is introduced to facilitate efficient intra-modal interactions at different granularities, capturing more detailed local features and broad global contextual information, providing a more comprehensive representation for LTSF. Extensive experiments on multiple benchmarks demonstrate that Affirm consistently outperforms existing SOTA methods, offering a superior balance of accuracy and efficiency, making it ideal for various challenging scenarios with noise levels and data sizes.

Learning time series representations with sparse labels presents notable challenges. The surge in unsupervised contrastive learning has garnered increasing interest due to its immense advancements in deriving meaningful representations in semi-supervised settings, typically involving a two-stage process: pretraining on large unlabeled data followed by fine-tuning with few labeled samples. However, this approach has inherent drawbacks: poor knowledge transfer, reduced generalizability, and failure to directly utilize unsupervised contrastive loss from pretraining and valuable supervised loss guided by ground truth to impact the downstream tasks. In response, we introduce a novel end-to-end semi-supervised framework, Semi4TSF, for time series forecasting (TSF). It optimizes unsupervised loss on massive unlabeled data and integrates supervised contrastive and forecasting losses on limited labeled data, enabling the model to see other unlabeled embeddings meanwhile learning useful labeled embeddings, improving generalization. The three losses are jointly to refine the encoder and forecaster. Specifically, the unsupervised learning module applies two instance-wise augmentation banks over the entire series to capture long-term dependencies, suggests a learnable Fourier layer, and fuses temporal and frequency information to uncover intricate temporal-frequency correlations through cross-domain interactions to capture nuanced representations. Extensive experiments on five benchmarks demonstrate that Semi4TSF is an effective and superior end-to-end framework that fills the gap in semi-supervised TSF.

Existing domain generalization (DG) methods for cross-person sensor-based activity recognition tasks often struggle to capture both intra- and inter-domain style diversity, leading to significant domain gaps with the target domain. In this study, we explore a novel perspective to tackle this problem, a process conceptualized as domain padding. This proposal aims to enrich the domain diversity by synthesizing intra- and inter-domain style data while maintaining robustness to class labels. We instantiate this concept using a conditional diffusion model and introduce a style-fused sampling strategy to enhance data generation diversity, termed Diversified Intra- and Inter-domain distributions via activity Style-fused Diffusion modeling (DI2SDiff). In contrast to traditional condition-guided sampling, our style-fused sampling strategy allows for the flexible use of one or more random style representations from the same class to guide data synthesis. This feature presents a notable advancement: it allows for the maximum utilization of possible combinations among existing styles to generate a broad spectrum of new style instances. We further extend DI2SDiff into DI2SDiff++ by enhancing the diversity of style guidance. Specifically, DI2SDiff++ integrates a multi-head style conditioner to provide multiple distinct, decomposed substyles and introduces a substyle-fused sampling strategy that allows cross-class substyle fusion for broader guidance. Empirical evaluations on a wide range of datasets demonstrate that our generated data achieves remarkable diversity within the domain space. Both intra- and inter-domain generated data have been proven significant and valuable, enabling DI2SDiff and DI2SDiff++ to surpass state-of-the-art DG methods in various cross-person activity recognition tasks.

Existing domain generalization (DG) methods for cross-person generalization tasks often face challenges in capturing intra- and inter-domain style diversity, resulting in domain gaps with the target domain. In this study, we explore a novel perspective to tackle this problem, a process conceptualized as domain padding. This proposal aims to enrich the domain diversity by synthesizing intra- and inter-domain style data while maintaining robustness to class labels. We instantiate this concept using a conditional diffusion model and introduce a style-fused sampling strategy to enhance data generation diversity. In contrast to traditional condition-guided sampling, our style-fused sampling strategy allows for the flexible use of one or more random styles to guide data synthesis. This feature presents a notable advancement: it allows for the maximum utilization of possible permutations and combinations among existing styles to generate a broad spectrum of new style instances. Empirical evaluations on a broad range of datasets demonstrate that our generated data achieves remarkable diversity within the domain space. Both intra- and inter-domain generated data have proven to be significant and valuable, contributing to varying degrees of performance enhancements. Notably, our approach outperforms state-of-the-art DG methods in all human activity recognition tasks.

Learning semantic-rich representations from unlabeled time series data with intricate dynamics is a notable challenge. Traditional contrastive learning techniques predominantly focus on segment-level augmentations through time slicing, a practice that, while valuable, often results in sampling bias and suboptimal performance due to the loss of global context. Furthermore, they typically disregard the vital frequency information to enrich data representations. To this end, we propose a novel self-supervised general-purpose framework called Temporal-Frequency and Contextual Consistency (TFCC). Specifically, this framework first performs two instance-level augmentation families over the entire series to capture nuanced representations alongside critical long-term dependencies. Then, TFCC advances by initiating dual cross-view forecasting tasks between the original series and its augmented counterpart in both time and frequency domains to learn robust representations. Finally, three specially designed consistency modules 'temporal, frequency, and temporal-frequency' aid in further developing discriminative representations on top of the learned robust representations. Extensive experiments on multiple benchmarks demonstrate TFCC's superiority over the state-of-the-art classification and forecasting methods and exhibit exceptional efficiency in semi-supervised and transfer learning scenarios.

While one-dimensional convolutional neural networks (1D-CNNs) have been empirically proven effective in time series classification tasks, we find that there remain undesirable outcomes that could arise in their application, motivating us to further investigate and understand their underlying mechanisms. In this work, we propose a Temporal Convolutional Explorer (TCE) to empirically explore the learning behavior of 1D-CNNs from the perspective of the frequency domain. Our TCE analysis highlights that deeper 1D-CNNs tend to distract the focus from the low-frequency components leading to the accuracy degradation phenomenon, and the disturbing convolution is the driving factor. Then, we leverage our findings to the practical application and propose a regulatory framework, which can easily be integrated into existing 1D-CNNs. It aims to rectify the suboptimal learning behavior by enabling the network to selectively bypass the specified disturbing convolutions. Finally, through comprehensive experiments on widely-used UCR, UEA, and UCI benchmarks, we demonstrate that 1) TCE's insight into 1D-CNN's learning behavior; 2) our regulatory framework enables state-of-the-art 1D-CNNs to get improved performances with less consumption of memory and computational overhead.