The World Wide Web thrives on intelligent services that depend heavily on accurate time series forecasting to navigate dynamic and evolving environments. Due to the partially-observed nature of real world, exclusively focusing on the target of interest, so-called endogenous variables, is insufficient for accurate forecasting, especially in web systems that are susceptible to external influences. Thus, utilizing exogenous variables to harness external information, i.e., forecasting with exogenous variable (FEV), is imperative. Nevertheless, as the external environment is complex and ever-evolving, inadequately capturing external influences can even lead to learning spurious correlations and invalid prediction. Fortunately, recent studies have demonstrated that large language models (LLMs) exhibit exceptional recognition capabilities across open real-world systems, including a deep understanding of exogenous environments. However, it is difficult to directly apply LLMs for FEV due to challenges of task activation, exogenous knowledge extraction, and feature space alignment. In this work, we devise ExoLLM, an LLM-driven method to sufficiently utilize Exogenous variables for time series forecasting. We begin by Meta-task Instruction to activate the knowledge transfer of LLM from natural language processing to FEV. To comprehensively understand the intricate and hierarchical influences of exogenous variables, we propose Multi-grained Prompts, encompassing diverse external influences, including natural attributes, trend correlations, and period relationships between two types of variables. Additionally, a Dual TS-Text Attention is devised to bridge the feature gap between text and numeric data in LLM. Evaluation on real-world datasets demonstrates ExoLLM's superiority in exploiting exogenous information for forecasting with open-world language knowledge.

Subgraph learning has dominated most practices of improving the expressive power of Message Passing Neural Networks (MPNNs). Existing subgraph discovery policies can be classified into node-based and partition-based, which both achieve impressive performance in most scenarios. However, both mainstream solutions still face a subgraph degradation trap. Subgraph degradation is reflected in the phenomenon that the subgraph-level methods fail to offer any benefits over node-level MPNNs. In this work, we empirically investigate the existence of the subgraph degradation issue and introduce a unified perspective, perfect reconstruction, to provide insights for improving two lines of methods. We further propose a subgraph learning strategy guided by the principle of perfect reconstruction. To achieve this, two major issues should be well-addressed, i.e.,(i) how to ensure the subgraphs to possess with ‘perfect’ information? (ii) how to guarantee the ‘reconstruction’ power of obtained subgraphs?First, we propose a subgraph partition strategyRayleigh-resistanceto extract non-overlap subgraphs by leveraging the graph spectral theory. Second, we put forward aQuerymechanism to achieve subgraph-level equivariant learning, which guarantees subgraph reconstruction ability. These two parts,perfect subgraph partitionandequivariant subgraph learningare seamlessly unified as a novelRayleigh-resistanceEquivariantSubgraph learningarchitecture (RayE-Sub). Comprehensive experiments on both synthetic and real datasets demonstrate that our approach can consistently outperform previous subgraph learning architectures.

Subgraph learning has received considerable attention in its capacity of interpreting important structural information for predictions. Existing subgraph learning usually exploits statistics on predefined structures e.g., node degrees, occurrence frequency, to extract subgraphs, or refine the contents via only capturing label-relevant information with node-level sampling. Given diverse subgraph patterns, and mutual independence with local correlations on graphs, current solutions on subgraph learning still have two limitations in extraction and refinement stages. 1) The universality of extracting substructure patterns across domains is still lacking, 2) node-level sampling in refinement will distort the original local topology and none explicit guidance eliminating redundant information contribute to inefficiency issue. In this paper, we propose a unified subgraph learning scheme, Poly-Pivot Graph Neural Network (P2GNN) where we designate the centric node of each subgraph as the pivot. In the extraction stage, we present a general subgraph extraction principle, i.e., Local; Asymmetry between the centric and affiliated nodes. To this end, we asymmetrically model the similarity between each pair of nodes with random walk and quantify mutual affiliations in Affinity Propagation architecture, to extract subgraph structures. In the refinement, we devise a subgraph-level exclusion regularization to squash the target-independent information by considering mutual relations across subgraphs, cooperatively preserving a support set of subgraphs and facilitating the refinement process for graph representation. Empirical experiments on diverse web and biological graphs reveal 1.1%~7.3% improvements against best baselines, and visualized case studies prove the universality and interpretability of our P2GNN.

Spatiotemporal (ST) learning has become a crucial technique for urban digitalization. Due to expansions and dynamics of cities, current spatiotemporal models are inclined to suffer distribution shifts between training and testing sets, leading to the OOD delimma. However, few studies focus on such OOD problem in temporal regressions, let alone spatiotemporal learning. Spatiotemporal data usually reveals segment-level heterogeneity within periodicity and complex spatial dependencies, posing challenges to invariance extraction. In this paper, we find that ST relations make sense for generalization and devise a Causal ST learning framework, CauSTG, which enables invariant relation transferred to OOD scenarios. Specifically, we take temporal steps as environments, and transform spatial-temporal relations into learnable parameters. To tackle heterogeneity in periodicity, we partition temporal steps into sub-environments by identifying distinctive trend patterns, enabling re-organized samples trained separately. To extract invariance within ST observations, we propose a spatiotemporal consistency learner and a hierarchical invariance explorer to jointly filter out stable relations. Our spatiotemporal learner quantifies bi-directional spatial consistency and extracts disentangled seasonal-trend patterns via trainable parameters. Further, the hierarchical invariance explorer constructs variation-based filter to achieve both local and global invariances. Experiments reveal that CauSTG can increase at most 10.26% performance against best baselines, and visualized invariant relations can well interpret the physical rationales. The appendix and codes can be available in our Github repository.

Spatiotemporal forecasting is an imperative topic in data science due to its critical applications in smart cities. Existing works mostly perform consecutive predictions of following steps with observations continuously obtained, where nearest observations can be exploited as the key knowledge for status estimation. However, the practical issues of early activity planning and sensor failures elicit a new task, non-consecutive forecasting. In this paper, we define spatiotemporal learning systems with missing observations as Grey Spatiotemporal Systems (G2S) and propose a Factor-Decoupled learning framework for G2S to hierarchically decouple multi-level factors, and enable flexible aggregations with uncertainty estimations. We especially select representative sequences to capture periodicity and instantaneous variations, and infer the non-consecutive future statuses under expected exogenous factors, compensating the missing observations. Given the inherent incompleteness and critical applications of G2S, a DisEntangled Uncertainty Quantification is put forward, to identify two types of uncertainty for model interpretations and robustness promotions. Experiments demonstrate that our solution can promote the performance by at least 8.50% on early planning and 2.01%-18.00% on sensor failures. The appendix of this paper can be found at https://github.com/zzyy0929/SDM-G2S.