Jingyun Zhang, Hao Peng, Jianxin Li +2cs.LG cs.AI cs.SI
Unsupervised graph clustering is a fundamental technique for uncovering underlying semantic patterns in large-scale networks. Although Graph Contrastive Learning has demonstrated promising performance, existing methods often suffer from the "structural isolation" issue during mini-batch training, making it challenging to capture cohesive community structures that characterize the global topological distribution. To address these challenges, we propose SCISE, a Scalable unsupervised graph Clustering framework that preserves structural Integrity by synergizing community-aware sampling with constrained Structural Entropy. Specifically, we first introduce the Structural Entropy Community Constraint operator (SECC), which optimizes structural information within a constrained solution space to mitigate community fragmentation and enhance partition cohesion. Second, to prevent global information loss during batch training, we design a Community-Aware Sampling Expansion (CSampE) mechanism that incorporates the community context of target nodes into sampling batches, effectively breaking structural barriers and preserving topological integrity. Finally, we devise a Structural Contrastive Learning (StructCL) module that refines edge weights based on intra-batch structural similarity, guiding the encoder to learn representations in a higher-order structural space. Extensive experiments on six mainstream benchmark datasets demonstrate that SCISE significantly outperforms state-of-the-art algorithms, with ablation studies and robustness analyses further validating its effectiveness and reliability for real-world large-scale graphs.
Filippo Biondi, Mirco Tribastone, Max Tschaikowskics.DC cs.LG
The stable coloring of the Weisfeiler-Leman (1-WL) test is a cornerstone of Graph Neural Networks because it provides an upper bound to the expressive power of message-passing architectures. Unfortunately, computing it presents two fundamental bottlenecks. First, classic algorithms are inherently sequential and cannot exploit modern massively parallel hardware. Second, these are \emph{global} algorithms, i.e., they require availability in memory of the full graph, severely limiting applicability to real-world instances. We leverage a linear-algebraic interpretation of 1-WL stable coloring and introduce two key contributions: (i)~a randomized refinement algorithm with tight probabilistic guarantees and (ii)~a correctness-preserving batching scheme that decomposes the graph into independently processable subgraphs while provably returning a stable coloring of the original graph. This approach maps directly to GPU-efficient primitives. In numerical experiments, our CUDA implementation delivers speedups up to two orders of magnitude over classical CPU-based partition refinement and, for the first time, successfully computes stable colorings on web-scale graphs with over 30 billion edges, where CPU baselines time out or fail.
Generating realistic and diverse graphs is a key problem in machine learning, with applications in molecular discovery, circuit design, cybersecurity, and beyond. However, current graph generative models remain limited by scalability and novelty. Diffusion-based methods often require costly full-adjacency operations and long denoising chains, while many autoregressive and hybrid models have at least quadratic complexity. In addition, these models often imitate training graphs rather than generalize beyond them. We propose a lightweight autoregressive framework to address these issues. It uses a structure-guided topological ordering to serialize graphs into regular edge sequences, enabling near log-linear generation, and a two-phase training strategy that combines exploration-oriented augmentation with iterative refinement to reduce overfitting and promote controlled novelty. Experiments on molecular and non-molecular benchmarks show that our approach improves novelty while preserving high validity and uniqueness. The framework also supports both LSTM and Mamba-style causal sequence backbones, with large-memory accelerators enabling longer graph-sequence experiments beyond typical GPU limits.
Pre-propagation graph neural networks (PPGNNs) push all graph-dependent computation into a preprocessing step and train only on the resulting dense hop features, which makes them highly scalable. A puzzle in this regime is that more complex hop aggregators do not reliably outperform simpler ones: on many benchmarks, a plain MLP-based aggregator matches or beats hop-attention variants. We revisit this behavior from a graph-filter perspective. Over a precomputed diffusion basis, existing PPGNNs differ mainly in how filter coefficients are shared across nodes and feature channels, rather than simply in raw aggregator capacity. MLP-based architectures learn channel-dependent filters that are largely shared across nodes, while hop-attention-based architectures learn node-dependent mixtures that are largely shared across channels. This reveals a missing regime in standard PPGNN designs: joint node- and channel-adaptive filtering under the pre-propagation computational contract. We propose FilterMoE, a mixture-of-experts PPGNN in which a small bank of learnable Chebyshev filter experts is routed jointly over nodes and channels by a 3D gating tensor. Across eleven homophilic and heterophilic benchmarks, FilterMoE outperforms strong PPGNN baselines on nine datasets and ranks first on all three large-scale benchmarks, improving the average test score by 1.53 points. These results establish joint node-channel filter routing as a robust alternative to dataset-specific hop-aggregator selection.