In many real-world systems, the evolution of one time series often leads or lags that of its related peers rather than moving in perfect synchrony. Graph Neural Networks (GNNs) are widely used to model such inter-Series Lead-Lag relationships, representing entities as graph nodes with time-series attributes. However, existing methods typically collapse temporal information into discrete points and adopt uniform messaging mechanisms assuming synchronized upward/downward effects and identical time lags among related peers, which are often inconsistent with real-world dynamics. Furthermore, stacking GNN layers to capture multi-hop influences reduces interpretability, hindering understanding of underlying dynamics. To address these issues, we propose the Lead-LagNet, a framework designed to capture diverse cross-series propagation patterns with lead-lag phenomenon in time series. The Lead-LagNet identifies meaningful subsequences in time series and employs a gating mechanism to establish lead-lag connections, enabling the model to uncover complex influencing patterns without relying on predefined relationships. By decoupling the linear messaging process from non-linear feature extraction, the proposed Lead-LagNet enhances both modeling flexibility and interoperability. Experimental evaluation of both synthetic tasks and real-world datasets demonstrates the superiority of Lead-LagNet over state-of-the-art algorithms, including BiGRU, SFM, TGC, FinGAT and ADGAT. Our code and data are available at https://github.com/FICLAB/LeadLagNet.

Recent advancements in time-series forecasting have highlighted the importance of frequency-domain modeling. However, deep learning models primarily operate in the time domain, limiting their ability to capture frequency-based patterns. Existing approaches normally introduce novel neural network architectures tailored to task-specific frequency properties, yet they often lack generalization and require extensive domain-specific adaptations. In this paper, we propose FAT, a novel pretraining framework that learns generalizable Frequency-Aware Time-series representations through self-supervised learning. The key idea of FAT is to pretrain any backbone model to directly extract generalizable frequency patterns from time-domain signals and encode them into robust representations-eliminating the need for architectural modifications or additional modules during inference. This is achieved via a frequency reformer that amplifies critical frequency components learned through self-supervision and enforces similarity between the original and frequency-reformed time-series representations produced by the encoder. In addition, recognizing that semantically equivalent time-series can exhibit different frequency expressions-analogous to how the same phrase is pronounced differently by different speakers-FAT introduces a Knowledge-Guided Frequency Reformer that unifies the expression of frequency patterns with the same underlying semantics and extends similarity constraints to frequency-invariant augmented samples to enhance robustness of learned representation. Experiments on 14 benchmark datasets across regression and classification tasks show that FAT consistently achieves state-of-the-art performance while maintaining robustness across diverse backbone models, significantly outperforming existing pretraining methods. Our code is available at https://github.com/JiaXiangfei/FAT.

In the realm of deep graph learning, our study uniquely addresses the under-explored area of vague graph learning. While the effectiveness of deep graph learning is recognized across various disciplines, the nuances of vague graph learning — whether its inherent vagueness should be incorporated or disregarded and its influence on deep graph learning efficiency — remain largely unexamined. We fill this gap by introducing a novel decoupled graph learning framework. This is achieved by proposing a matrix-based or a tensor-based fusion module to estimate unobservable node attributes, a hybrid attention mechanism to bridge nodes with both explicit and implicit relationships, and a message-passing mechanism for feature-sensitive transporting. The design principle of decoupling allows it to accommodate ambiguities in any or all of these aspects of node representation, linking, and message passing. Furthermore, we leverage an extensive stock dataset spanning 64 years across the entire U.S. market to assess our framework. This real-world data not only adds a practical dimension to our study but also highlights the effectiveness of vague graph learning. Remarkably, our framework demonstrates superiority over state-of-the-art algorithms, marking performance enhancements of at least 6.73%, 7.25%, and 11.39% in terms of Rank IC,$R^{2}$, and Rank ICIR, respectively.

In finance, the risk of an entity depends not only on its historical information but also on the risk propagated by its related peers. Pilot studies rely on Graph Neural Networks (GNNs) to model this risk propagation, where each entity is treated as a node and represented by its time-series information. However, conventional GNNs are constrained by their unified messaging mechanism with an assumption that the risk of a given entity only propagates to its related peers with the same time lag and has the same effect, which is against the ground truth. In this study, we propose the subsequence-based graph routing network (S-GRN) for capturing the variant risk propagation processes among different time-series represented entities. In S-GRN, the messaging mechanism between each node pair is dynamically and independently selected from multiple messaging mechanisms based on the dependencies of variant subsequence patterns. The S-GRN is extensively evaluated on two synthetic tasks and three real-world datasets and demonstrates state-of-the-art performance.

In finance, the momentum spillovers of listed firms is well acknowledged. Only few studies predicted the trend of one firm in terms of its relevant firms. A common strategy of the pilot work is to adopt graph convolution networks (GCNs) with some predefined firm relations. However, momentum spillovers are propagated via a variety of firm relations, of which the bridging importance varies with time. Restricting to several predefined relations inevitably makes noise and thus misleads stock predictions. In addition, traditional GCNs transfer and aggregate the peer influences without considering the states of both connected firms once a connection is built. Such non-attribute sensibility makes traditional GCNs inappropriate to deal with the attribute-sensitive momentum spillovers of listed firms wherein the abnormal price drop of one firm may not spill over if the trade volume of this decreasing price is small or the prices of the linked firms are undervalued. In this study, we propose an attribute-driven graph attention network (AD-GAT) to address both problems in modeling momentum spillovers. This is achieved by element-wisely multiplying the nonlinear transformation of the attributes of the connected firms with the attributes of the source firm to consider its attribute-sensitive momentum spillovers, and applying the unmasked attention mechanism to infer the general dynamic firm relation from observed market signals fused by a novel tensor-based feature extractor. Experiments on the three-year data of the S&P 500 demonstrate the superiority of the proposed framework over stateof-the-art algorithms, including GCN, eLSTM, and TGC.