Long-term Time Series Forecasting (LTSF) tasks, which leverage the current data sequence as input to predict the future sequence, have become increasingly crucial in real-world applications such as weather forecasting and planning of electricity consumption. However, state-of-the-art LTSF models often fail to achieve prediction output alignment for the same timestamps across lagged input sequences.

Temporal non-stationarity, the phenomenon that time series distributions change over time, poses fundamental challenges to reliable time series forecasting. Intuitively, the complex time series can be decomposed into two factors, i.e., timeinvariant and time-varying components, which indicate static and dynamic patterns, respectively. Nonetheless, existing methods often conflate the time-varying and time-invariant components, and jointly learn the combined long-term patterns and short-term fluctuations, leading to suboptimal performance facing distribution shifts. To address this issue, we initiatively propose a lightweight static-dynamic decomposition framework, TimeEmb, for time series forecasting. TimeEmb innovatively separates time series into two complementary components: (1) time-invariant component, captured by a novel global embedding module that learns persistent representations across time series, and (2) time-varying component, processed by an efficient frequency-domain filtering mechanism inspired by full-spectrum analysis in signal processing. Experiments on real-world datasets demonstrate that TimeEmb outperforms state-of-the-art baselines and requires fewer computational resources. We conduct comprehensive quantitative and qualitative analyses to verify the efficacy of static-dynamic disentanglement. This lightweight framework can also improve existing time-series forecasting methods with simple integration.

Image deblurring plays a crucial role in enhancing visual clarity across various applications. Although most deep learning approaches primarily focus on sRGB images, which inherently lose critical information during the image signal processing pipeline, RAW images, being unprocessed and linear, possess superior restoration potential but remain underexplored. Deblurring RAW images presents unique challenges, particularly in handling frequency-dependent blur while maintaining computational efficiency. To address these issues, we propose Frequency Enhanced Network (FrENet), a framework specifically designed for RAW-to-RAW deblurring that operates directly in the frequency domain. We introduce a novel Adaptive Frequency Positional Modulation module, which dynamically adjusts frequency components according to their spectral positions, thereby enabling precise control over the deblurring process. Additionally, frequency domain skip connections are adopted to further preserve high-frequency details. Experimental results demonstrate that FrENet surpasses state-of-the-art deblurring methods in RAW image deblurring, achieving significantly better restoration quality while maintaining high efficiency in terms of reduced MACs. Furthermore, FrENet's adaptability enables it to be extended to sRGB images, where it delivers comparable or superior performance compared to methods specifically designed for sRGB data. The source code and pre-trained models are publicly available at https://github.com/WenlongJiao/FrENet.

Neural Processes (NPs) are meta-learning models that learn to map sets of observations to approximations of the corresponding posterior predictive distributions. By accommodating variable-sized, unstructured collections of observations and enabling probabilistic predictions at arbitrary query points, NPs provide a flexible framework for modeling functions over continuous domains. Since their introduction, numerous variants have emerged; however, early formulations shared a fundamental limitation: they compressed the observed data into finite-dimensional global representations via aggregation operations such as mean pooling. This strategy induces an intrinsic mismatch with the infinite-dimensional nature of the stochastic processes that NPs intend to model. Convolutional conditional neural processes (ConvCNPs) address this limitation by constructing infinite-dimensional functional embeddings processed through convolutional neural networks (CNNs) to enforce translation equivariance. Yet CNNs with local spatial kernels struggle to capture long-range dependencies without resorting to large kernels, which impose significant computational costs. To overcome this limitation, we propose spectral ConvCNPs (SConvCNPs), which perform global convolution in the frequency domain. Inspired by Fourier neural operators (FNOs) for learning solution operators of partial differential equations (PDEs), our approach directly parameterizes convolution kernels in the frequency domain, leveraging the relatively compact yet global Fourier representation of many natural signals. We validate the effectiveness of SConvCNPs on both synthetic and real-world datasets, demonstrating how ideas from operator learning can advance the capabilities of NPs.

While deep reinforcement learning (RL) has been demonstrated effective in solving complex control tasks, sample efficiency remains a key challenge due to the large amounts of data required for remarkable performance. Existing research explores the application of representation learning for data-efficient RL, e.g., learning predictive representations by predicting long-term future states. However, many existing methods do not fully exploit the structural information inherent in sequential state signals, which can potentially improve the quality of long-term decision-making but is difficult to discern in the time domain. To tackle this problem, we propose State Sequences Prediction via Fourier Transform (SPF), a novel method that exploits the frequency domain of state sequences to extract the underlying patterns in time series data for learning expressive representations efficiently. Specifically, we theoretically analyze the existence of structural information in state sequences, which is closely related to policy performance and signal regularity, and then propose to predict the Fourier transform of infinite-step future state sequences to extract such information. One of the appealing features of SPF is that it is simple to implement while not requiring storage of infinite-step future states as prediction targets. Experiments demonstrate that the proposed method outperforms several state-of-the-art algorithms in terms of both sample efficiency and performance.2

Here we note our problem definition of pre-training is fundamentally different from domain adaptation [S1, S2, S3, S4, S5, S6]1 in order to prevent any confusion between this work and domain adaptation methods. DA applies a model trained on a pre-training dataset (i.e., source dataset) to a different target dataset [21, 42]. In contrast, self-supervised pre-training has four key differences with domain adaptation. In contrast, domain adaptation methods usually restrict pre-training and target datasets to have the same feature space (but possible different distributions), e.g., [S22, S18, S19, S20, S13]. In summary, to support transfer learning across different time series datasets, a pre-training approach needs a capability to capture a generalizable property of time series, one that is shared across different time series datasets regardless of the specific semantic meaning of a time series signal (e.g., ECG, EMG, acceleration, vibration), conditions of data acquisition (e.g., variation across subjects and devices), sampling frequencies, etc. This work develops a self-supervised contrastive pre-training strategy that fulfills these requirements by injecting an appropriate inductive bias (called Time-Frequency Consistency, TF-C, into the model (Sec. Further, we clarify that the term'self-supervised' has different meanings in DA and in pretraining [S23, S24, S25, S26]. The'self-supervised domain adaptation' [S27, S16, S21, S15] or'unsupervised domain adaptation' [S1, S22, S28, S11, S14] means that there are no labels in the target dataset, however that still requires labels in the pre-training dataset. In contrast, 'self-supervised pretraining' [S29, S30, S31] (i.e., the problem studied here, in line with a breadth of existing literature on pre-training) indicates the setting where no labels are available in pre-training. Up to the submission of this manuscript, there is no existing contrastive augmentations in time series' frequency domain. There are two models, CoST [49] and BTSF [50], that involved frequency domain in contrastive learning, however, the proposed TF-C is fundamentally different with them in the following aspects. We take BTSF as an example while the differences also apply to CoST. Problem definitions for both papers are different. Our method is designed to produce generalizable representations that can transfer to a different time series dataset (going from pre-training to a fine-tuning dataset) for the purpose of transfer learning.