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.

Tradition financial studies on asset pricing focused on the economic indicators and media information of a stock. Recent financial studies found that the momentum spillovers of relevant firms are salient as well for measuring asset risk. However, previous studies on asset pricing via machine learning only relied on partial of these market information types. In this study, a deep learning framework is proposed to combine these three market information types with different data structures, that is, numerical economic indicators represented as scalars, media represented as textual vectors, and the influences of related firms captured by graphs. More importantly, the unique data characteristics brought by such data fusion are well addressed in the proposed learning framework. Specifically, a matrix-based module is first proposed to fuse numerical economic data and textual media, which specifically considers the interactions of the fused features. Such fused information, along with the firm relevance represented in graphs, is further integrated by a novel self-adaptive graph neural network that can address the dynamic merging of multilinked listed firms. Experiments performed on real market data demonstrate the effectiveness of the proposed approach over state-of-the-art algorithms, including eLSTM, RGCN, and TGC.