With rapid urbanization in the modern era, traffic signals from various sensors have been playing a significant role in monitoring the states of cities, which provides a strong foundation in ensuring safe travel, reducing traffic congestion and optimizing urban mobility. Most existing methods for traffic time series modeling often rely on the original data modality, i.e., numerical direct readings from the sensors in cities. However, this unimodal approach overlooks the semantic information existing in multimodal heterogeneous urban data in different perspectives, which hinders a comprehensive understanding of traffic signals and limits the accurate prediction of complex traffic dynamics. To address this problem, we propose a novel Multimodal framework, MTP, for urban Traffic Profiling, which learns multimodal features through numeric, visual, and textual perspectives in the frequency domain. The three branches drive a multimodal perspective of traffic signal learning for augmentation, while the frequency learning strategies delicately refine the information for extraction. Specifically, we first conduct the visual augmentation for the traffic time series, which transforms the original modality into periodicity images and frequency images for visual learning. Also, we augment descriptive texts for the traffic time series based on the specific topic, background information and item description for textual learning. To complement the numeric information, we utilize frequency multilayer perceptrons for learning on the original modality. We design a hierarchical contrastive learning on the three branches to fuse the three modalities. Finally, extensive experiments on six real-world datasets demonstrate superior performance compared with the state-of-the-art approaches.

Decoding visual information from human brain activity has seen remarkable advancements in recent research. However, the diversity in cortical parcellation and fMRI patterns across individuals has prompted the development of deep learning models tailored to each subject. The personalization limits the broader applicability of brain visual decoding in real-world scenarios. To address this issue, we introduce Wills Aligner, a novel approach designed to achieve multi-subject collaborative brain visual decoding. Wills Aligner begins by aligning the fMRI data from different subjects at the anatomical level. It then employs delicate mixture-of-brain-expert adapters and a meta-learning strategy to account for individual fMRI pattern differences. Additionally, Wills Aligner leverages the semantic relation of visual stimuli to guide the learning of inter-subject commonality, enabling visual decoding for each subject to draw insights from other subjects' data. We rigorously evaluate our Wills Aligner across various visual decoding tasks, including classification, cross-modal retrieval, and image reconstruction. The experimental results demonstrate that Wills Aligner achieves promising performance.

We propose an energy amplification technique to address the issue that existing models easily overlook low-energy components in time series forecasting. This technique comprises an energy amplification block and an energy restoration block. The energy amplification block enhances the energy of low-energy components to improve the model's learning efficiency for these components, while the energy restoration block returns the energy to its original level. Moreover, considering that the energy-amplified data typically displays two distinct energy peaks in the frequency spectrum, we integrate the energy amplification technique with a seasonal-trend forecaster to model the temporal relationships of these two peaks independently, serving as the backbone for our proposed model, Amplifier. Additionally, we propose a semi-channel interaction temporal relationship enhancement block for Amplifier, which enhances the model's ability to capture temporal relationships from the perspective of the commonality and specificity of each channel in the data. Extensive experiments on eight time series forecasting benchmarks consistently demonstrate our model's superiority in both effectiveness and efficiency compared to state-of-the-art methods.

Federated Learning (FL) addresses the growing concerns of Internet of Things (IoT) service security and privacy in edge computing environments by enabling collaborative model training without the need to centralize sensitive data. Most existing FL frameworks remain vulnerable to sophisticated threats such as source inference attacks (SIAs), which exploit model updates to infer sensitive information about participating clients, thereby compromising the integrity and security of edge services. To mitigate such attacks and ensure service security and user privacy, various defensive methods, such as RM Learning and RelaxLoss, have been proposed. However, these methods fail to provide effective privacy protection in practical FL scenarios characterized by non-IID data distributions. To address this issue, we propose FedMLU, a novel algorithm designed to counter SIAs effectively. Specifically, FedMLU combines a model alternating update strategy with the RelaxLoss algorithm to minimize the loss discrepancy among samples, thereby reducing the distinguishability exploited by SIAs. Furthermore, distinct soft labels are assigned for training each federated participant model, aiming to decrease the model's prediction confidence and enhance privacy protection. Extensive experiments on synthetic datasets and various real-world datasets demonstrate that our method achieves better defense performance and a more favorable tradeoff between privacy protection and model utility compared to the state-of-the-art RelaxLoss and two popular FL frameworks, particularly in scenarios with data heterogeneity.

Early exiting has demonstrated great potential in accelerating the inference of pre-trained language models (PLMs) by enabling easy samples to exit at shallow layers, eliminating the need for executing deeper layers. However, existing early exiting methods primarily rely on class-relevant logits to formulate their exiting signals for estimating prediction certainty, neglecting the detrimental influence of class-irrelevant information in the features on prediction certainty. This leads to an overestimation of prediction certainty, causing premature exiting of samples with incorrect early predictions. To remedy this, we define an NSP score to estimate prediction certainty by considering the proportion of class-irrelevant information in the features. On this basis, we propose a novel early exiting method based on the Certainty-Aware Probability (CAP) score, which integrates insights from both logits and the NSP score to enhance prediction certainty estimation, thus enabling more reliable exiting decisions. The experimental results on the GLUE benchmark show that our method can achieve an average speed-up ratio of 2.19× across all tasks with negligible performance degradation, surpassing the state-of-the-art (SOTA) ConsistentEE by 28%, yielding a better trade-off between task performance and inference efficiency. The code is available at https://github.com/He-Jianing/NSP.git.

Recently, frequency transformation (FT) has been increasingly incorporated into deep learning models to significantly enhance state-of-the-art accuracy and efficiency in time series analysis. The advantages of FT, such as high efficiency and a global view, have been rapidly explored and exploited in various time series tasks and applications, demonstrating the promising potential of FT as a new deep learning paradigm for time series analysis. Despite the growing attention and the proliferation of research in this emerging field, there is currently a lack of a systematic review and in-depth analysis of deep learning-based time series models with FT. It is also unclear why FT can enhance time series analysis and what its limitations are in the field. To address these gaps, we present a comprehensive review that systematically investigates and summarizes the recent research advancements in deep learning-based time series analysis with FT. Specifically, we explore the primary approaches used in current models that incorporate FT, the types of neural networks that leverage FT, and the representative FT-equipped models in deep time series analysis. We propose a novel taxonomy to categorize the existing methods in this field, providing a structured overview of the diverse approaches employed in incorporating FT into deep learning models for time series analysis. Finally, we highlight the advantages and limitations of FT for time series modeling and identify potential future research directions that can further contribute to the community of time series analysis.

Due to the non-stationarity of time series, the distribution shift problem largely hinders the performance of time series forecasting. Existing solutions either rely on using certain statistics to specify the shift, or developing specific mechanisms for certain network architectures. However, the former would fail for the unknown shift beyond simple statistics, while the latter has limited compatibility on different forecasting models. To overcome these problems, we first propose a decoupled formulation for time series forecasting, with no reliance on fixed statistics and no restriction on forecasting architectures. This formulation regards the removing-shift procedure as a special transformation between a raw distribution and a desired target distribution and separates it from the forecasting. Such a formulation is further formalized into a bi-level optimization problem, to enable the joint learning of the transformation (outer loop) and forecasting (inner loop). Moreover, the special requirements of expressiveness and bi-direction for the transformation motivate us to propose instance normalization flow (IN-Flow), a novel invertible network for time series transformation. Different from the classic ''normalizing flow'' models, IN-Flow does not aim for normalizing input to the prior distribution (e.g., Gaussian distribution) for generation, but creatively transforms time series distribution by stacking normalization layers and flow-based invertible networks, which is thus named ''normalization'' flow. Finally, we have conducted extensive experiments on both synthetic data and real-world data, which demonstrate the superiority of our method.

The recent boom of large pre-trained models witnesses remarkable success in developing foundation models (FMs) for time series forecasting. Despite impressive performance across diverse downstream forecasting tasks, existing time series FMs possess massive network architectures and require substantial pre-training on large-scale datasets, which significantly hinders their deployment in resource-constrained environments. In response to this growing tension between versatility and affordability, we propose **SEMPO**, a novel lightweight foundation model that requires pretraining on relatively small-scale data, yet exhibits strong general time series forecasting. Concretely, SEMPO comprises two key modules: 1) _energy-aware **S**p**E**ctral decomposition module_, that substantially improves the utilization of pre-training data by modeling not only the high-energy frequency signals but also the low-energy yet informative frequency signals that are ignored in current methods; and 2) _**M**ixture-of-**P**r**O**mpts enabled Transformer_, that learns heterogeneous temporal patterns through small dataset-specific prompts and adaptively routes time series tokens to prompt-based experts for parameter-efficient model adaptation across different datasets and domains. Equipped with these modules, SEMPO significantly reduces both pre-training data scale and model size, while achieving strong generalization. Extensive experiments on two large-scale benchmarks covering 16 datasets demonstrate the superior performance of SEMPO in both zero-shot and few-shot forecasting scenarios compared with state-of-the-art methods. Code and data are available at https://github.com/mala-lab/SEMPO.

Medical time series has been playing a vital role in real-world healthcare systems as valuable information in monitoring health conditions of patients. Traditional methods towards medical time series classification rely on handcrafted feature extraction and statistical methods; with the recent advancement of artificial intelligence, the machine learning and deep learning methods have become more popular. However, existing methods often fail to fully model the complex spatial dynamics under different scales, which ignore the dynamic multi-resolution spatial and temporal joint inter-dependencies. Moreover, they are less likely to consider the special baseline wander problem as well as the multi-view characteristics of medical time series, which largely hinders their prediction performance. To address these limitations, we propose a Multi-resolution Spatiotemporal Graph Learning framework, MedGNN, for medical time series classification. Specifically, we first propose to construct multi-resolution adaptive graph structures to learn dynamic multi-scale embeddings. Then, to address the baseline wander problem, we propose Difference Attention Networks to operate self-attention mechanisms on the finite difference for temporal modeling. Moreover, to learn the multi-view characteristics, we utilize the Frequency Convolution Networks to capture complementary information of medical time series from the frequency domain. In addition, we introduce the Multi-resolution Graph Transformer architecture to model the dynamic dependencies and fuse the information from different resolutions. Finally, we have conducted extensive experiments on multiple medical real-world datasets that demonstrate the superior performance of our method. Our Code is available at this repository: https://github.com/aikunyi/MedGNN.

Due to the nonstationary nature, the distribution of real-world multivariate time series (MTS) changes over time, which is known as distribution drift. Most existing MTS forecasting models greatly suffer from distribution drift and degrade the forecasting performance over time. Existing methods address distribution drift via adapting to the latest arrived data or self-correcting per the meta knowledge derived from future data. Despite their great success in MTS forecasting, these methods hardly capture the intrinsic distribution changes, especially from a distributional perspective. Accordingly, we propose a novel framework temporal conditional variational autoencoder (TCVAE) to model the dynamic distributional dependencies over time between historical observations and future data in MTSs and infer the dependencies as a temporal conditional distribution to leverage latent variables. Specifically, a novel temporal Hawkes attention (THA) mechanism represents temporal factors that subsequently fed into feedforward networks to estimate the prior Gaussian distribution of latent variables. The representation of temporal factors further dynamically adjusts the structures of Transformer-based encoder and decoder to distribution changes by leveraging a gated attention mechanism (GAM). Moreover, we introduce conditional continuous normalization flow (CCNF) to transform the prior Gaussian to a complex and form-free distribution to facilitate flexible inference of the temporal conditional distribution. Extensive experiments conducted on six real-world MTS datasets demonstrate the TCVAE's superior robustness and effectiveness over the state-of-the-art MTS forecasting baselines. We further illustrate the TCVAE applicability through multifaceted case studies and visualization in real-world scenarios.

The nonstationary nature of real-world multivariate time series (MTS) data presents forecasting models with a formidable challenge of the time-variant distribution of time series, referred to as distribution shift. Existing studies on the distribution shift mostly adhere to adaptive normalization techniques for alleviating temporal mean and covariance shifts or time-variant modeling for capturing temporal shifts. Despite improving model generalization, these normalization-based methods often assume a time-invariant transition between outputs and inputs but disregard specific intraseries/interseries correlations, while time-variant models overlook the intrinsic causes of the distribution shift. This limits the model's expressiveness and interpretability in tackling the distribution shift for MTS forecasting. To mitigate such a dilemma, we present a unified Probabilistic Graphical Model to Jointly capture intraseries/interseries correlations and model the time-variant transitional distribution and instantiate a neural framework called JointPGM for nonstationary MTS forecasting. Specifically, JointPGM first employs multiple Fourier basis functions to learn dynamic time factors and designs two distinct learners: intraseries and interseries learners. The intraseries learner effectively captures temporal dynamics by utilizing temporal gates, while the interseries learner explicitly models spatial dynamics through multihop propagation, incorporating Gumbel-softmax sampling. These two types of series dynamics are subsequently fused into a latent variable, which is inversely employed to infer time factors, generate a final prediction, and perform the reconstruction. We validate the effectiveness and efficiency of JointPGM through extensive experiments on six highly nonstationary MTS datasets, achieving state-of-the-art (SOTA) forecasting performance of MTS forecasting.

Multimodal content, such as mixing text with images, presents significant challenges to rumor detection in social media. Existing multimodal rumor detection has focused on mixing tokens among spatial and sequential locations for unimodal representation or fusing clues of rumor veracity across modalities. However, they suffer from less discriminative unimodal representation and are vulnerable to intricate location dependencies in the time-consuming fusion of spatial and sequential tokens. This work makes the first attempt at multimodal rumor detection in the frequency domain, which efficiently transforms spatial features into the frequency spectrum and obtains highly discriminative spectrum features for multimodal representation and fusion. A novel Frequency Spectrum Representation and fUsion network (FSRU) with dual contrastive learning reveals the frequency spectrum is more effective for multimodal representation and fusion, extracting the informative components for rumor detection. FSRU involves three novel mechanisms: utilizing the Fourier transform to convert features in the spatial domain to the frequency domain, the unimodal spectrum compression, and the cross-modal spectrum co-selection module in the frequency domain. Substantial experiments show that FSRU achieves satisfactory multimodal rumor detection performance.

Contrastive Language-Image Pretraining (CLIP) has achieved remarkable success, leading to rapid advancements in multimodal studies. However, CLIP faces a notable challenge in terms of *inefficient data utilization*. It relies on a single contrastive supervision for each image-text pair during representation learning, disregarding a substantial amount of valuable information that could offer richer supervision. Additionally, the retention of non-informative tokens leads to increased computational demands and time costs, particularly in CLIP's ViT image encoder. To address these issues, we propose **M**ulti-Perspective **L**anguage-**I**mage **P**retraining (**MLIP**). In MLIP, we leverage the frequency transform's sensitivity to both high and low-frequency variations, which complements the spatial domain's sensitivity limited to low-frequency variations only. By incorporating frequency transforms and token-level alignment, we expand CILP's single supervision into multi-domain and multi-level supervision, enabling a more thorough exploration of informative image features. Additionally, we introduce a token merging method guided by comprehensive semantics from the frequency and spatial domains. This allows us to merge tokens to multi-granularity tokens with a controllable compression rate to accelerate CLIP. Extensive experiments validate the effectiveness of our design.

Given the ubiquitous presence of time series data across various domains, precise forecasting of time series holds significant importance and finds widespread real-world applications such as energy, weather, healthcare, etc. While numerous forecasters have been proposed using different network architectures, the Transformer-based models have state-of-the-art performance in time series forecasting. However, forecasters based on Transformers are still suffering from vulnerability to high-frequency signals, efficiency in computation, and bottleneck in full-spectrum utilization, which essentially are the cornerstones for accurately predicting time series with thousands of points. In this paper, we explore a novel perspective of enlightening signal processing for deep time series forecasting. Inspired by the filtering process, we introduce one simple yet effective network, namely FilterNet, built upon our proposed learnable frequency filters to extract key informative temporal patterns by selectively passing or attenuating certain components of time series signals. Concretely, we propose two kinds of learnable filters in the FilterNet: (i) Plain shaping filter, that adopts a universal frequency kernel for signal filtering and temporal modeling; (ii) Contextual shaping filter, that utilizes filtered frequencies examined in terms of its compatibility with input signals for dependency learning. Equipped with the two filters, FilterNet can approximately surrogate the linear and attention mappings widely adopted in time series literature, while enjoying superb abilities in handling high-frequency noises and utilizing the whole frequency spectrum that is beneficial for forecasting. Finally, we conduct extensive experiments on eight time series forecasting benchmarks, and experimental results have demonstrated our superior performance in terms of both effectiveness and efficiency compared with state-of-the-art methods. Our code is available at$^1$.

Multivariate time series (MTS) forecasting penetrates various aspects of our economy and society, whose roles become increasingly recognized. However, often MTS forecasting is unfair, not only degrading their practical benefits but even incurring potential risk. Unfair MTS forecasting may be attributed to disparities relating to advantaged and disadvantaged variables, which has rarely been studied in the MTS forecasting. In this work, we formulate the MTS fairness modeling problem as learning informative representations attending to both advantaged and disadvantaged variables. Accordingly, we propose a novel framework, namedFairFor, for fairness-aware MTS forecasting, i.e.,fair MTS forecasting.FairForuses adversarial learning to generate both group-irrelevant and -relevant representations for downstream forecasting.FairForfirst adopts recurrent graph convolution to capture spatio-temporal variable correlations and to group variables by leveraging a spectral relaxation of the K-means objective. Then, it utilizes a novel filtering$\&$fusion module to filter group-relevant information and generate group-irrelevant representations by orthogonality regularization. The group-irrelevant and -relevant representations form highly informative representations, facilitating to share the knowledge from advantaged variables to disadvantaged variables and guarantee the fairness of forecasting. Extensive experiments on four public datasets demonstrate theFairForeffectiveness for fair forecasting and significant performance improvement.

Multivariate time series (MTS) forecasting is crucial in many real-world applications. To achieve accurate MTS forecasting, it is essential to simultaneously consider both intra- and inter-series relationships among time series data. However, previous work has typically modeled intra- and inter-series relationships separately and has disregarded multi-order interactions present within and between time series data, which can seriously degrade forecasting accuracy. In this article, we reexamine intra- and inter-series relationships from the perspective of mutual information and accordingly construct a comprehensive relationship learning mechanism tailored to simultaneously capture the intricate multi-order intra- and inter-series couplings. Based on the mechanism, we propose a novel deep coupling network for MTS forecasting, named DeepCN, which consists of a coupling mechanism dedicated to explicitly exploring the multi-order intra- and inter-series relationships among time series data concurrently, a coupled variable representation module aimed at encoding diverse variable patterns, and an inference module facilitating predictions through one forward step. Extensive experiments conducted on seven real-world datasets demonstrate that our proposed DeepCN achieves superior performance compared with the state-of-the-art baselines.

Urban prediction tasks that aim to model the complicated spatial and temporal patterns of urban indicators (such as weather, vehicle charging demand, etc.) for accurate prediction, have been increasingly important in constructing smart cities and accelerating the urbanization process in the modern era. However, most existing works of urban prediction have only concentrated on spatial and temporal correlations, but ignored the effect of distribution shift from spatial and temporal perspectives; this could largely hinder the performance of urban prediction tasks. In order to solve this problem, in this paper, we propose a Shift-Aware Urban Prediction (SAUP) framework to eliminate the inherent shift effect among spatial-temporal urban time series data. Specifically, SAUP starts with a Shift Elimination Module, built upon our proposed Spatial-Temporal Attention Flows (STAF) composed of invertible attentions and coupling layers of normalizing flows in order to transform the raw shifted data into a unified distribution to remove the spatiotemporal shift. After the shift effect is eliminated, the Correlation Processing Module of SAUP further captures the core correlations to learn spatiotemporal dependencies, in which topological correlations and geographic correlations are jointly learned by GCN and CNN based on pre-defined graphs and extracted POI information. In addition, SAUP includes a model-agnostic Forecasting Module, which can be employed as any forecasting architecture to accomplish the predictions. To recover the raw distribution information, the output of the Forecasting Module is further taken for the inverse transformation of the Shift Elimination Module to produce the final forecasts. We have conducted extensive experiments in the SAUP framework, coupled with six state-of-the-art spatiotemporal forecasting models on two real-world datasets. Experimental results have demonstrated the consistent improvements of SAUP over the baseline algorithms.

Multivariate time series (MTS) forecasting has shown great importance in numerous industries. Current state-of-the-art graph neural network (GNN)-based forecasting methods usually require both graph networks (e.g., GCN) and temporal networks (e.g., LSTM) to capture inter-series (spatial) dynamics and intra-series (temporal) dependencies, respectively. However, the uncertain compatibility of the two networks puts an extra burden on handcrafted model designs. Moreover, the separate spatial and temporal modeling naturally violates the unified spatiotemporal inter-dependencies in real world, which largely hinders the forecasting performance. To overcome these problems, we explore an interesting direction of directly applying graph networks and rethink MTS forecasting from a pure graph perspective. We first define a novel data structure, hypervariate graph, which regards each series value (regardless of variates or timestamps) as a graph node, and represents sliding windows as space-time fully-connected graphs. This perspective considers spatiotemporal dynamics unitedly and reformulates classic MTS forecasting into the predictions on hypervariate graphs. Then, we propose a novel architecture Fourier Graph Neural Network (FourierGNN) by stacking our proposed Fourier Graph Operator (FGO) to perform matrix multiplications in Fourier space. FourierGNN accommodates adequate expressiveness and achieves much lower complexity, which can effectively and efficiently accomplish {the forecasting}. Besides, our theoretical analysis reveals FGO's equivalence to graph convolutions in the time domain, which further verifies the validity of FourierGNN. Extensive experiments on seven datasets have demonstrated our superior performance with higher efficiency and fewer parameters compared with state-of-the-art methods. Code is available at this repository: https://github.com/aikunyi/FourierGNN.

Time series forecasting has played the key role in different industrial, including finance, traffic, energy, and healthcare domains. While existing literatures have designed many sophisticated architectures based on RNNs, GNNs, or Transformers, another kind of approaches based on multi-layer perceptrons (MLPs) are proposed with simple structure, low complexity, and superior performance. However, most MLP-based forecasting methods suffer from the point-wise mappings and information bottleneck, which largely hinders the forecasting performance. To overcome this problem, we explore a novel direction of applying MLPs in the frequency domain for time series forecasting. We investigate the learned patterns of frequency-domain MLPs and discover their two inherent characteristic benefiting forecasting, (i) global view: frequency spectrum makes MLPs own a complete view for signals and learn global dependencies more easily, and (ii) energy compaction: frequency-domain MLPs concentrate on smaller key part of frequency components with compact signal energy. Then, we propose FreTS, a simple yet effective architecture built upon Frequency-domain MLPs for Time Series forecasting. FreTS mainly involves two stages, (i) Domain Conversion, that transforms time-domain signals into complex numbers of frequency domain; (ii) Frequency Learning, that performs our redesigned MLPs for the learning of real and imaginary part of frequency components. The above stages operated on both inter-series and intra-series scales further contribute to channel-wise and time-wise dependency learning. Extensive experiments on 13 real-world benchmarks (including 7 benchmarks for short-term forecasting and 6 benchmarks for long-term forecasting) demonstrate our consistent superiority over state-of-the-art methods. Code is available at this repository: https://github.com/aikunyi/FreTS.

Modeling complex hierarchical and grouped feature interaction in the multivariate time series data is indispensable to comprehend the data dynamics and predicting the future condition. The implicit feature interaction and high-dimensional data make multivariate forecasting very challenging. Many existing works did not put more emphasis on exploring explicit correlation among multiple time series data, and complicated models are designed to capture long- and short-range pattern with the aid of attention mechanism. In this work, we think that pre-defined graph or general learning method is difficult due to their irregular structure. Hence, we present CATN, an end-to-end model of Cross Attentive Tree-aware Network to jointly capture the inter-series correlation and intra-series temporal pattern. We first construct a tree structure to learn hierarchical and grouped correlation and design an embedding approach that can pass dynamic message to generalize implicit but interpretable cross features among multiple time series. Next in temporal aspect, we propose a multi-level dependency learning mechanism including global&local learning and cross attention mechanism, which can combine long-range dependencies, short-range dependencies as well as cross dependencies at different time steps. The extensive experiments on different datasets from real world show the effectiveness and robustness of the method we proposed when compared with existing state-of-the-art methods.