Multivariate time series forecasting focuses on predicting future values based on historical context. State-of-the-art sequence-to-sequence models rely on neural attention between timesteps, which allows for temporal learning but fails to consider distinct spatial relationships between variables. In contrast, methods based on graph neural networks explicitly model variable relationships. However, these methods often rely on predefined graphs that cannot change over time and perform separate spatial and temporal updates without establishing direct connections between each variable at every timestep. Our work addresses these problems by translating multivariate forecasting into a "spatiotemporal sequence" formulation where each Transformer input token represents the value of a single variable at a given time. Long-Range Transformers can then learn interactions between space, time, and value information jointly along this extended sequence. Our method, which we call Spacetimeformer, achieves competitive results on benchmarks from traffic forecasting to electricity demand and weather prediction while learning spatiotemporal relationships purely from data.
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Spectral-temporal graph neural network is a promising abstraction underlying most time series forecasting models that are based on graph neural networks (GNNs). However, more is needed to know about the underpinnings of this branch of methods. In this paper, we establish a theoretical framework that unravels the expressive power of spectral-temporal GNNs. Our results show that linear spectral-temporal GNNs are universal under mild assumptions, and their expressive power is bounded by our extended first-order Weisfeiler-Leman algorithm on discrete-time dynamic graphs. To make our findings useful in practice on valid instantiations, we discuss related constraints in detail and outline a theoretical blueprint for designing spatial and temporal modules in spectral domains. Building on these insights and to demonstrate how powerful spectral-temporal GNNs are based on our framework, we propose a simple instantiation named Temporal Graph GegenConv (TGC), which significantly outperforms most existing models with only linear components and shows better model efficiency.
Graph neural networks aim to learn representations for graph-structured data and show impressive performance, particularly in node classification. Recently, many methods have studied the representations of GNNs from the perspective of optimization goals and spectral graph theory. However, the feature space that dominates representation learning has not been systematically studied in graph neural networks. In this paper, we propose to fill this gap by analyzing the feature space of both spatial and spectral models. We decompose graph neural networks into determined feature spaces and trainable weights, providing the convenience of studying the feature space explicitly using matrix space analysis. In particular, we theoretically find that the feature space tends to be linearly correlated due to repeated aggregations. Motivated by these findings, we propose 1) feature subspaces flattening and 2) structural principal components to expand the feature space. Extensive experiments verify the effectiveness of our proposed more comprehensive feature space, with comparable inference time to the baseline, and demonstrate its efficient convergence capability.
Learning from limited data is challenging because data scarcity leads to a poor generalization of the trained model. A classical global pooled representation will probably lose useful local information. Many few-shot learning methods have recently addressed this challenge using deep descriptors and learning a pixel-level metric. However, using deep descriptors as feature representations may lose image contextual information. Moreover, most of these methods independently address each class in the support set, which cannot sufficiently use discriminative information and task-specific embeddings. In this paper, we propose a novel transformer-based neural network architecture called sparse spatial transformers (SSFormers), which finds task-relevant features and suppresses task-irrelevant features. Particularly, we first divide each input image into several image patches of different sizes to obtain dense local features. These features retain contextual information while expressing local information. Then, a sparse spatial transformer layer is proposed to find spatial correspondence between the query image and the full support set to select task-relevant image patches and suppress task-irrelevant image patches. Finally, we propose using an image patch-matching module to calculate the distance between dense local representations, thus determining which category the query image belongs to in the support set. Extensive experiments on popular few-shot learning benchmarks demonstrate the superiority of our method over state-of-the-art methods. Our source code is available at \url{//github.com/chenhaoxing/ssformers}.
Multi-stage strategies are frequently employed in image restoration tasks. While transformer-based methods have exhibited high efficiency in single-image super-resolution tasks, they have not yet shown significant advantages over CNN-based methods in stereo super-resolution tasks. This can be attributed to two key factors: first, current single-image super-resolution transformers are unable to leverage the complementary stereo information during the process; second, the performance of transformers is typically reliant on sufficient data, which is absent in common stereo-image super-resolution algorithms. To address these issues, we propose a Hybrid Transformer and CNN Attention Network (HTCAN), which utilizes a transformer-based network for single-image enhancement and a CNN-based network for stereo information fusion. Furthermore, we employ a multi-patch training strategy and larger window sizes to activate more input pixels for super-resolution. We also revisit other advanced techniques, such as data augmentation, data ensemble, and model ensemble to reduce overfitting and data bias. Finally, our approach achieved a score of 23.90dB and emerged as the winner in Track 1 of the NTIRE 2023 Stereo Image Super-Resolution Challenge.
Although Transformer-based methods have significantly improved state-of-the-art results for long-term series forecasting, they are not only computationally expensive but more importantly, are unable to capture the global view of time series (e.g. overall trend). To address these problems, we propose to combine Transformer with the seasonal-trend decomposition method, in which the decomposition method captures the global profile of time series while Transformers capture more detailed structures. To further enhance the performance of Transformer for long-term prediction, we exploit the fact that most time series tend to have a sparse representation in well-known basis such as Fourier transform, and develop a frequency enhanced Transformer. Besides being more effective, the proposed method, termed as Frequency Enhanced Decomposed Transformer ({\bf FEDformer}), is more efficient than standard Transformer with a linear complexity to the sequence length. Our empirical studies with six benchmark datasets show that compared with state-of-the-art methods, FEDformer can reduce prediction error by $14.8\%$ and $22.6\%$ for multivariate and univariate time series, respectively. the code will be released soon.
Transformers have achieved superior performances in many tasks in natural language processing and computer vision, which also intrigues great interests in the time series community. Among multiple advantages of transformers, the ability to capture long-range dependencies and interactions is especially attractive for time series modeling, leading to exciting progress in various time series applications. In this paper, we systematically review transformer schemes for time series modeling by highlighting their strengths as well as limitations through a new taxonomy to summarize existing time series transformers in two perspectives. From the perspective of network modifications, we summarize the adaptations of module level and architecture level of the time series transformers. From the perspective of applications, we categorize time series transformers based on common tasks including forecasting, anomaly detection, and classification. Empirically, we perform robust analysis, model size analysis, and seasonal-trend decomposition analysis to study how Transformers perform in time series. Finally, we discuss and suggest future directions to provide useful research guidance. To the best of our knowledge, this paper is the first work to comprehensively and systematically summarize the recent advances of Transformers for modeling time series data. We hope this survey will ignite further research interests in time series Transformers.
There recently has been a surge of interest in developing a new class of deep learning (DL) architectures that integrate an explicit time dimension as a fundamental building block of learning and representation mechanisms. In turn, many recent results show that topological descriptors of the observed data, encoding information on the shape of the dataset in a topological space at different scales, that is, persistent homology of the data, may contain important complementary information, improving both performance and robustness of DL. As convergence of these two emerging ideas, we propose to enhance DL architectures with the most salient time-conditioned topological information of the data and introduce the concept of zigzag persistence into time-aware graph convolutional networks (GCNs). Zigzag persistence provides a systematic and mathematically rigorous framework to track the most important topological features of the observed data that tend to manifest themselves over time. To integrate the extracted time-conditioned topological descriptors into DL, we develop a new topological summary, zigzag persistence image, and derive its theoretical stability guarantees. We validate the new GCNs with a time-aware zigzag topological layer (Z-GCNETs), in application to traffic forecasting and Ethereum blockchain price prediction. Our results indicate that Z-GCNET outperforms 13 state-of-the-art methods on 4 time series datasets.
Many real-world applications require the prediction of long sequence time-series, such as electricity consumption planning. Long sequence time-series forecasting (LSTF) demands a high prediction capacity of the model, which is the ability to capture precise long-range dependency coupling between output and input efficiently. Recent studies have shown the potential of Transformer to increase the prediction capacity. However, there are several severe issues with Transformer that prevent it from being directly applicable to LSTF, such as quadratic time complexity, high memory usage, and inherent limitation of the encoder-decoder architecture. To address these issues, we design an efficient transformer-based model for LSTF, named Informer, with three distinctive characteristics: (i) a $ProbSparse$ Self-attention mechanism, which achieves $O(L \log L)$ in time complexity and memory usage, and has comparable performance on sequences' dependency alignment. (ii) the self-attention distilling highlights dominating attention by halving cascading layer input, and efficiently handles extreme long input sequences. (iii) the generative style decoder, while conceptually simple, predicts the long time-series sequences at one forward operation rather than a step-by-step way, which drastically improves the inference speed of long-sequence predictions. Extensive experiments on four large-scale datasets demonstrate that Informer significantly outperforms existing methods and provides a new solution to the LSTF problem.
Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables depend on one another but, upon looking closely, it is fair to say that existing methods fail to fully exploit latent spatial dependencies between pairs of variables. In recent years, meanwhile, graph neural networks (GNNs) have shown high capability in handling relational dependencies. GNNs require well-defined graph structures for information propagation which means they cannot be applied directly for multivariate time series where the dependencies are not known in advance. In this paper, we propose a general graph neural network framework designed specifically for multivariate time series data. Our approach automatically extracts the uni-directed relations among variables through a graph learning module, into which external knowledge like variable attributes can be easily integrated. A novel mix-hop propagation layer and a dilated inception layer are further proposed to capture the spatial and temporal dependencies within the time series. The graph learning, graph convolution, and temporal convolution modules are jointly learned in an end-to-end framework. Experimental results show that our proposed model outperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets and achieves on-par performance with other approaches on two traffic datasets which provide extra structural information.
Multivariate time series forecasting is extensively studied throughout the years with ubiquitous applications in areas such as finance, traffic, environment, etc. Still, concerns have been raised on traditional methods for incapable of modeling complex patterns or dependencies lying in real word data. To address such concerns, various deep learning models, mainly Recurrent Neural Network (RNN) based methods, are proposed. Nevertheless, capturing extremely long-term patterns while effectively incorporating information from other variables remains a challenge for time-series forecasting. Furthermore, lack-of-explainability remains one serious drawback for deep neural network models. Inspired by Memory Network proposed for solving the question-answering task, we propose a deep learning based model named Memory Time-series network (MTNet) for time series forecasting. MTNet consists of a large memory component, three separate encoders, and an autoregressive component to train jointly. Additionally, the attention mechanism designed enable MTNet to be highly interpretable. We can easily tell which part of the historic data is referenced the most.
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