Dynamic Hypergraph Representation Learning for Multivariate Time Series without Prior Knowledge

The rich information underlying graphs has inspired further investigation of unsupervised graph representation. Existing studies mainly depend on node features and topological properties within static graphs to create self-supervised signals, neglecting the temporal components carried by real-world graph data, such as timestamps of edges. To overcome this limitation, this paper explores how to model temporal evolution on dynamic graphs elegantly. Specifically, we introduce a new inductive bias, namely temporal translation invariance, which illustrates the tendency of the identical node to keep similar labels across different timespans. Based on this assumption, we develop a dynamic graph representation framework CLDG that encourages the node to maintain locally consistent temporal translation invariance through contrastive learning on different timespans. Except for standard CLDG which only considers explicit topological links, our further proposed CLDG++ additionally employs graph diffusion to uncover global contextual correlations between nodes, and designs a multi-scale contrastive learning objective composed of local-local, local-global, and global-global contrasts to enhance representation capabilities. Interestingly, by measuring the consistency between different timespans to shape anomaly indicators, CLDG and CLDG++ are seamlessly integrated with the task of spotting anomalies on dynamic graphs, which has broad applications in many high-impact domains, such as finance, cybersecurity, and healthcare. Experiments demonstrate that CLDG and CLDG++ both exhibit desirable performance in downstream tasks including node classification and dynamic graph anomaly detection. Moreover, CLDG significantly reduces time and space complexity by implicitly exploiting temporal cues instead of complicated sequence models.

Representation learning on dynamic graphs requires capturing complex dependencies that evolve across both time and structure. Existing approaches typically adopt fixed temporal decay schemes or predetermined structural propagation depths, limiting their ability to generalize across graphs with diverse interaction frequencies and topological characteristics. We propose Dual-Scale Retentive Dynamics (DSRD), a unified framework that maintains a retentive representation state encoding both temporal memory and structural context. DSRD introduces two key components: (i) a retentive state with dual-scale adaptation that jointly models temporal dynamics and structural propagation within a single recurrent formulation, and (ii) adaptive decay kernels with learnable time-sensitivity parameters that automatically balance short-term responsiveness and long-term retention based on the underlying interaction patterns. We provide theoretical analysis establishing the equivalence between event-wise parallel aggregation and efficient recurrent state updates, as well as stability and boundedness guarantees for the learned dynamics. Extensive experiments on 14 real-world benchmarks demonstrate that DSRD consistently achieves state-of-the-art performance on both link prediction and node classification tasks, with strong generalization across transductive and inductive settings.

Dynamic topic modeling is widely used to analyze evolving trends in scientific literature, medical records, and social media. Traditional topic models represent each topic through a single probability vector on the multinomial simplex and implicitly couple word occurrence and repetition within one probabilistic mechanism. However, this formulation restricts the dependence structure among words and overlooks informative higher-order interactions, particularly in dynamic corpora with overlapping semantics. To address these limitations, we introduce a hypergraph representation of text where each document is modeled as a hyperedge connecting all co-occurring words, with repetition intensities encoded as node weights. This representation naturally separates word occurrence from repetition and induces a novel hypergraph-based multinomial distribution with a nonlinear normalization depending on the observed word set of each document. Building on this likelihood, we develop a dynamic topic modeling framework via structured low-rank factorizations with explicit temporal regularization on topic-word profiles. Moreover, we establish local convergence guarantees and derive non-asymptotic error bounds despite the intrinsic nonconvexity induced by bilinear factorization and document-specific nonlinear normalization. Numerical experiments on synthetic data and an application to the International Conference on Learning Representations (ICLR) corpus demonstrate consistent improvements over existing multinomial-based topic models.