Real-world temporal graphs are largely driven by sequential dynamics, and edge repetitions are rare. This characteristic has spotlighted a key limitation of existing temporal graph neural networks (T-GNNs): on such graphs, state-of-the-art T-GNNs often achieve less than 70% MRR on link prediction. Two factors drive this shortfall: (1) Memory modules and neighbor co-occurrence encodings in existing T-GNNs often fail since they rely on memorizing exact neighbor identities and on the co-occurrence assumption. (2) Existing T-GNNs are sensitive to abrupt events, which are common in sequential settings that can exceed ten million updates, thereby compromising generalization. To tackle the challenges of sequential dynamics, we propose SeqFilter, a simple yet robust neural network that functions as a composite filter for link prediction on temporal graphs. SeqFilter comprises two modules: a node rhythm memory and a frequency-selective structure encoder. The node rhythm memory shifts the focus from who interacts to when, modeling absolute timestamps with recency awareness to capture each node's interaction rhythm. To model temporal structures in complex sequential dynamics, we propose a frequency-selective structure encoder that amplifies or suppresses specific frequencies in the neighbor spectrum, enabling the effective modeling of local structure correlations. Theoretically, this encoder functions as a cascade of three learnable filters that approximate the optimal linear denoiser, helping capture the underlying structural patterns. Last, SeqFilter fuses the outputs of two modules to generate high-quality node embeddings. Extensive experiments across eight sequential dynamic datasets show that SeqFilter outperforms 11 baselines by an average improvement of 15.82% in MRR while achieving an order of magnitude speedup compared to the frequency-enhanced baseline.

Temporal hypergraph representation learning is a concept that integrates high-order structure learning with temporal dynamics, enabling more accurate analysis of temporal and high-order interactions. To enhance model expressiveness, the latest work samples multi-hop hyperedge-centric neighbors directly from temporal hypergraphs and encodes them for high-order structure learning, achieving promising performance. Such modeling, however, incurs prohibitive computational complexity, which increases exponentially with model depth and quadratically with average hyperedge cardinality, thereby limiting model scalability. In this paper, we propose FastHeP, a fast and accurate approach for temporal hyperedge prediction, which can handle large temporal hypergraphs. The key idea is to minimize computational complexity while maintaining model expressiveness. Concretely, we design an online hyperedge-centric neighbor store, which can store time-aware and redundancy-aware neighbors for nodes with rational theoretical guarantees. Upon the neighbor store, we propose a novel hybrid message passing to model temporal high-order structures, theoretically preserving strong expressive power. This explicitly learns local high-order structures for nodes of each hyperedge via graph attention, generating the node-wise structure features. These structure features are then fused into global correlations modeling among hyperedges, with a theoretical guarantee of permutation invariance. Last, FastHeP leverages local and global high-order semantics to generate temporal hyperedge embeddings, which is efficient in a linear complexity w.r.t. model depth and average hyperedge cardinality. Extensive experiments show that FastHeP achieves up to two orders of magnitude speed-up against baselines, with an average accuracy improvement of 5.1%.

Ranking is an essential and practical task on dynamic graphs, which aims to prioritize future interaction candidates for given queries. While existing solutions achieve promising ranking performance, they leverage a single listwise loss to jointly optimize candidate sets, which leads to the gradient vanishing issue; and they employ neural networks to model complex temporal structures within a shared latent space, which fails to accurately capture multi-scale temporal patterns due to the frequency aliasing issue. To address these issues, we propose BandRank, a novel and robust band-pass disentangled ranking approach for dynamic graphs in the frequency domain. Concretely, we propose a band-pass disentangled representation (BPDR) approach, which disentangles complex temporal structures into multiple frequency bands and employs non-shared frequency-enhanced multilayer perceptrons (MLPs) to model each band independently. We prove that our BPDR approach ensures effective multi-scale learning for temporal structures by demonstrating its multi-scale global convolution property. Besides, we design a robust Harmonic Ranking (HR) loss to jointly optimize candidate sets and continuously track comparisons between real and virtual candidates, where we theoretically guarantee its ability to alleviate the gradient vanishing issue. Extensive experimental results show that our BandRank achieves an average improvement of 21.31% against eight baselines while demonstrating superior robustness across different learning scenarios.

Dynamic graphs, which capture time-evolving edges between nodes, are formulated in continuous-time or discrete-time dynamic graphs. They differ in temporal granularity: Continuous-Time Dynamic Graphs (CTDGs) exhibit rapid, localized changes, while Discrete-Time Dynamic Graphs (DTDGs) show gradual, global updates. This difference leads to isolated developments in representation learning for each type. To advance dynamic graph representation learning, recent research attempts to design a unified model capable of handling both CTDGs and DTDGs, achieving promising results. However, it typically focuses on local dynamic propagation for temporal structure learning in the time domain, failing to accurately capture the underlying structural evolution associated with each temporal granularity and thus compromising model effectiveness. In addition, existing works-whether specific or unified-often overlook the issue of temporal noise, compromising the model's robustness. To better model both types of dynamic graphs, we propose UniDyG, a unified and effective representation learning approach, which can scale to large dynamic graphs. Specifically, we first propose a novel Fourier Graph Attention (FGAT) mechanism that can model local and global structural correlations based on recent neighbors and complex-number selective aggregation, while theoretically ensuring consistent representations of dynamic graphs over time. Based on approximation theory, we demonstrate that FGAT is well-suited to capture the underlying structures in both CTDGs and DTDGs. We further enhance FGAT to resist temporal noise by designing an energy-gated unit, which adaptively filters out high-frequency noise according to the energy. Last, we leverage our proposed FGAT mechanisms for temporal structure learning and employ the frequency-enhanced linear function for node-level dynamic updates, facilitating the generation of high-quality temporal embeddings. Extensive experiments show that our UniDyG achieves an average improvement of 14.4% over sixteen baselines across nine dynamic graphs while exhibiting superior robustness in noisy scenarios.

Temporal graph neural networks (T-GNNs) have emerged as leading approaches for representation learning over dynamic graphs. However, existing solutions typically suffer from exponential time complexity with model depth and excessive GPU memory usage due to acceleration techniques, and cannot handle large dynamic graphs. Furthermore, the core component of T-G NNs, temporal message passing, still predominantly derives from static GNNs. This neglects the distinct characteristics of two types of features, timestamps and edge features, and results in sub-optimal embedding quality. Consequently, existing T-GNNs fail to scale to large dynamic graphs and generalize well in unseen or complex scenarios, limiting their applicability. To bridge the gap, this paper first proposes a simple yet effective temporal message passing paradigm for T-GNNs, called the divided temporal message passing (DT-MP) paradigm, which enables effective feature learning for each feature type. We theoretically demonstrate that the DT-MP paradigm can reduce GPU memory usage compared to existing T-GNNs. Building on this foundation, we propose TimeSGN, a scalable and effective temporal graph neural network, which can handle billion-scale dynamic graphs. Specifically, we design a linear state updater to effectively capture node dynamic evolution and instantiate the DT-MP paradigm using two 1-layer self-attention mechanisms for temporal message passing to generate temporal embeddings. As a result, TimeSGN fundamentally avoids exponential time complexity and significantly reduces GPU memory usage. Extensive experiments demonstrate that TimeSGN achieves an average 10.56% improvement in accuracy, up to 42.48% reduction in training GPU memory, and up to 5 x speedup in per-epoch training time compared to the state-of-the-art baselines, while being one order of magnitude faster than vanilla T-GNNs.

Logical query answering over Knowledge Graphs (KGs) is a fundamental yet complex task. A promising approach to achieve this is to embed queries and entities jointly into the same embedding space. Research along this line suggests that using multi-modal distribution to represent answer entities is more suitable than uni-modal distribution, as a single query may contain multiple disjoint answer subsets due to the compositional nature of multi-hop queries and the varying latent semantics of relations. However, existing methods based on multi-modal distribution roughly represent each subset without capturing its accurate cardinality, or even degenerate into uni-modal distribution learning during the reasoning process due to the lack of an effective similarity measure. To better model queries with diversified answers, we propose Query2GMM for answering logical queries over knowledge graphs. In Query2GMM, we present the GMM embedding to represent each query using a univariate Gaussian Mixture Model (GMM). Each subset of a query is encoded by its cardinality, semantic center and dispersion degree, allowing for precise representation of multiple subsets. Then we design specific neural networks for each operator to handle the inherent complexity that comes with multi-modal distribution while alleviating the cascading errors. Last, we design a new similarity measure to assess the relationships between an entity and a query's multi-answer subsets, enabling effective multi-modal distribution learning for reasoning. Comprehensive experimental results show that Query2GMM outperforms the best competitor by an absolute average of 6.35%.

Logical queries on Knowledge Graphs (KGs) is a fundamental sub-task of knowledge graph reasoning. A promising paradigm for answering logical queries, recently, has been proposed based on versatile deep learning techniques. In this line, the query is first broken down into a series of first-order logical predicates, and then both the query and knowledge graph entities are jointly encoded in the same embedding space. Some approaches are able to support the full range of traditional First-Order Logic (FOL) operations for complex queries in real-world scenarios, while others have attempted to create a new combination of FOL operations by replacing the negation operation with the difference operation due to the poor performance of the negation operation. Our empirical observations show that the difference operator is more effective for multi-hop reasoning, while the negation operator is better suited for use as the final operation in the query, particularly in single-hop settings. In addition, other fundamental limitations such as linear transformation assumption for negation operator and the fixed-lossy problem for difference operator further degrade the performance of these methods. In light of these, we propose the HaLk, a holistic approach for answering logical queries that, to our knowledge, is the first to support a full set of logical operators in a unified end-to-end framework. In this approach, we propose specific neural models for each operator by considering their own intrinsic properties, based on which HaLk effectively mitigates the cascading error of projection and negation operators as well as delicately provides closed-formed solutions for difference operator. Extensive experimental results on three datasets demonstrate that HaLk outperforms all competitors and achieves up to 32% improvement in accuracy.

Bipartite graph embedding (BGE), as the fundamental task in bipartite network analysis, is to map each node to compact low-dimensional vectors that preserve intrinsic properties. The existing solutions towards BGE fall into two groups: metric-based methods and graph neural network-based (GNN-based) methods. The latter typically generates higher-quality embeddings than the former due to the strong representation ability of deep learning. Nevertheless, none of the existing GNN-based methods can handle billion-scale bipartite graphs due to the expensive message passing or complex modelling choices. Hence, existing solutions face a challenge in achieving both embedding quality and model scalability. Motivated by this, we propose a novel graph neural network named AnchorGNN based on global-local learning framework, which can generate high-quality BGE and scale to billion-scale bipartite graphs. Concretely, AnchorGNN leverages a novel anchor-based message passing schema for global learning, which enables global knowledge to be incorporated to generate node embeddings. Meanwhile, AnchorGNN offers an efficient one-hop local structure modelling using maximum likelihood estimation for bipartite graphs with rational analysis, avoiding large adjacency matrix construction. Both global information and local structure are integrated to generate distinguishable node embeddings. Extensive experiments demonstrate that AnchorGNN outperforms the best competitor by up to 36% in accuracy and achieves up to 28 times speed-up against the only metric-based baseline on billion-scale bipartite graphs.

Semi-supervised learning and multi-label learning pose different challenges for feature selection, which is one of the core techniques for dimension reduction, and the exploration of reducing feature space for multi-label learning with incomplete label information is far from satisfactory. Existing feature selection approaches devote attention to either of two issues, namely, alleviating negative effects of imperfectly predicted labels and quantitatively evaluating label correlations, exclusively for semi-supervised or multi-label scenarios. A unified framework to extract label correlation information with incomplete prior knowledge and embed this information in feature selection however, is rarely touched. In this paper, we propose a space consistency-based feature selection model to address this issue. Specifically, correlation information in feature space is learned based on the probabilistic neighborhood similarities, and correlation information in label space is optimized by preserving feature-label space consistency. This mechanism contributes to appropriately extracting label information in semi-supervised multi-label learning scenario and effectively employing this information to select discriminative features. An extensive experimental evaluation on real-world data shows the superiority of the proposed approach under various evaluation metrics.