Linearization of attention using various kernel approximation and kernel learning techniques has shown promise. Past methods used a subset of combinations of component functions and weight matrices within the random feature paradigm. We identify the need for a systematic comparison of different combinations of weight matrices and component functions for attention learning in Transformer. Hence, we introduce Spectraformer , a unified framework for approximating and learning the kernel function in the attention mechanism of the Transformer. Our empirical results demonstrate, for the first time, that a random feature-based approach can achieve performance comparable to top-performing sparse and low-rank methods on the challenging Long-Range Arena benchmark. Thus, we establish a new state-of-the-art for random feature-based efficient Transformers. The framework also produces many variants that offer different advantages in accuracy, training time, and memory consumption. Our code is available at: https://github.com/cruiseresearchgroup/spectraformer .

Spatial-temporal causal time series (STC-TS) involve region-specific temporal observations driven by causally relevant covariates and interconnected across geographic or network-based spaces. Existing methods often model spatial and temporal dynamics independently and overlook causality-driven probabilistic forecasting, limiting their predictive power. To address this, we propose STOAT (Spatial-Temporal Probabilistic Causal Inference Network), a novel framework for probabilistic forecasting in STC-TS. The proposed method extends a causal inference approach by incorporating a spatial relation matrix that encodes interregional dependencies, enabling spatially informed causal effect estimation. The resulting latent series are processed by deep probabilistic models to estimate the parameters of the distributions, enabling calibrated uncertainty modeling. Experiments on COVID-19 data across six countries demonstrate that STOAT outperforms state-of-the-art probabilistic forecasting models in key metrics, particularly in regions with strong spatial dependencies. By bridging causal inference and geospatial probabilistic forecasting, STOAT offers a generalizable framework for complex spatial-temporal tasks, such as epidemic management.

Traffic forecasting is crucial for smart cities and intelligent transportation initiatives, where deep learning has made significant progress in modeling complex spatio-temporal patterns in recent years. However, current public datasets have limitations in reflecting the distribution shift nature of real-world scenarios, characterized by continuously evolving infrastructures, varying temporal distributions, and long temporal gaps due to sensor downtimes or changes in traffic patterns. These limitations inevitably restrict the practical applicability of existing traffic forecasting datasets. To bridge this gap, we present XXLTraffic, the largest available public traffic dataset with the longest timespan collected from Los Angeles, USA, and New South Wales, Australia, curated to support research in extremely long forecasting beyond test adaptation. Our benchmark includes both typical time-series forecasting settings with hourly and daily aggregated data and novel configurations that introduce gaps and down-sample the training size to better simulate practical constraints. We anticipate the new XXL-Traffic will provide a fresh perspective for the time-series and traffic forecasting communities. It would also offer a robust platform for developing and evaluating models designed to tackle the extremely long forecasting problems beyond test adaptation. Our dataset supplements existing spatio-temporal data resources and leads to new research directions in this domain.

Training models on spatio-temporal (ST) data poses an open problem due to the complicated and diverse nature of the data itself, and it is challenging to ensure the model's performance directly trained on the original ST data. While limiting the variety of training data can make training easier, it can also lead to a lack of knowledge and information for the model, resulting in a decrease in performance. To address this challenge, we presented an innovative paradigm that incorporates three separate forms of curriculum learning specifically targeting from spatial, temporal, and quantile perspectives. Furthermore, our framework incorporates a stacking fusion module to combine diverse information from three types of curriculum learning, resulting in a strong and thorough learning process. We demonstrated the effectiveness of this framework with extensive empirical evaluations, highlighting its better performance in addressing complex ST challenges. We provided thorough ablation studies to investigate the effectiveness of our curriculum and to explain how it contributes to the improvement of learning efficiency on ST data.

Long-term time series forecasting (LTSF) represents a critical frontier in time series analysis, characterized by extensive input sequences, as opposed to the shorter spans typical of traditional approaches. While longer sequences inherently offer richer information for enhanced predictive precision, prevailing studies often respond by escalating model complexity. These intricate models can inflate into millions of parameters, resulting in prohibitive parameter scales. Our study demonstrates, through both theoretical and empirical evidence, that decomposition is key to containing excessive model inflation while achieving uniformly superior and robust results across various datasets. Remarkably, by tailoring decomposition to the intrinsic dynamics of time series data, our proposed model outperforms existing benchmarks, using over 99\% fewer parameters than the majority of competing methods. Through this work, we aim to unleash the power of a restricted set of parameters by capitalizing on domain characteristics—a timely reminder that in the realm of LTSF, bigger is not invariably better. The code is available at \url{https://anonymous.4open.science/r/SSCNN-321D/}.

Tensor time series (TTS) data, a generalization of one-dimensional time series on a high-dimensional space, is ubiquitous in real-world applications. Compared to modeling time series or multivariate time series, which has received much attention and achieved tremendous progress in recent years, tensor time series has been paid less effort. However, properly coping with the TTS is a much more challenging task, due to its high-dimensional and complex inner structure. In this article, we start by revealing the structure of TTS data from afn statistical view of point. Then, in line with this analysis, we perform T ensor T ime S eries forecasting via a proposed Multi-way Norm alization ( TTS-Norm ), which effectively disentangles multiple heterogeneous low-dimensional substructures from the original high-dimensional structure. Finally, we design a novel objective function for TTS forecasting, accounting for the numerical heterogeneity among different low-dimensional subspaces of TTS. Extensive experiments on two real-world datasets verify the superior performance of our proposed model. 1

Multivariate time-series (MTS) forecasting is a paramount and fundamental problem in many real-world applications. The core issue in MTS forecasting is how to effectively model complex spatial-temporal patterns. In this paper, we develop a adaptive, interpretable and scalable forecasting framework, which seeks to individually model each component of the spatial-temporal patterns. We name this framework SCNN, as an acronym ofStructuredComponent-basedNeuralNetwork. SCNN works with a pre-defined generative process of MTS, which arithmetically characterizes the latent structure of the spatial-temporal patterns. In line with its reverse process, SCNN decouples MTS data into structured and heterogeneous components and then respectively extrapolates the evolution of these components, the dynamics of which are more traceable and predictable than the original MTS. Extensive experiments are conducted to demonstrate that SCNN can achieve superior performance over state-of-the-art models on three real-world datasets. Additionally, we examine SCNN with different configurations and perform in-depth analyses of the properties of SCNN.

Friend recommendation from human mobility is a vital real-world application of location-based social networks (LBSN). It is necessary to recognize patterns from human mobility to assist friend recommendation because previous works have shown complex relations between them. However, most of previous works either modelled social networks and user trajectories separately, or only used classical simple graph-based methods with an edge linking two nodes that cannot fully model the complex data structure of LBSN. Inspired by the fact that hyperedges can connect multiple nodes of different types, we model user trajectories and check-in records as hyperedges in a novel heterogeneous LBSN hypergraph to represent complex spatio-temporal information. And then, we design a type-specific attention mechanism for an end-to-end trainable heterogeneous hypergraph neural network (HHGNN) with supervised contrastive learning, which can learn hypergraph node embedding for the next friend recommendation task. At last, our model HHGNN outperforms the state-of-the-art methods on four real-world city datasets, while ablation studies also confirm the effectiveness of each model part.

Nowadays, with the rapid development of IoT (Internet of Things) and CPS (Cyber-Physical Systems) technologies, big spatiotemporal data are being generated from mobile phones, car navigation systems, and traffic sensors. By leveraging state-of-the-art deep learning technologies on such data, urban traffic prediction has drawn a lot of attention in AI and Intelligent Transportation System community. The problem can be uniformly modeled with a 3D tensor (T, N, C), where T denotes the total time steps, N denotes the size of the spatial domain (i.e., mesh-grids or graph-nodes), and C denotes the channels of information. According to the specific modeling strategy, the state-of-the-art deep learning models can be divided into three categories: grid-based, graph-based, and multivariate time-series models. In this study, we first synthetically review the deep traffic models as well as the widely used datasets, then build a standard benchmark to comprehensively evaluate their performances with the same settings and metrics. Our study named DL-Traff is implemented with two most popular deep learning frameworks, i.e., TensorFlow and PyTorch, which is already publicly available as two GitHub repositories https://github.com/deepkashiwa20/DL-Traff-Grid and https://github.com/deepkashiwa20/DL-Traff-Graph. With DL-Traff, we hope to deliver a useful resource to researchers who are interested in spatiotemporal data analysis.