The Quadratic Assignment Problem (QAP) has attracted lasting attention for its wide applications and computational challenges. Despite the rich literature in machine learning for QAP, most works often address the problem in the setting of image matching, whereby deep networks could play a vital role in extracting useful features for the subsequent matching. While its power on pure numerical QAP instances is limited in node embedding, often with a vanilla graph neural network. This paper tries to tap the potential of deep nets for QAP, specifically by modifying the input instance, which is orthogonal to previous efforts. Specifically, we develop a bi-level unsupervised framework, where the inner optimization involves trying to solve the modified instance with entropic regularization that can be solved iteratively using the Sinkhorn algorithm without affecting backpropagation by truncating gradients during training. The outer minimization deals with the quadratic objective function of the original QAP. In particular, seeing the intractable scale of the most general form, i.e., Lawler's QAP and the practical utility of the more efficient Koopmans-Beckmann QAP (KBQAP) form for solving other graph and combinatorial problems like TSP and graph edit distance, we embody our network on the KBQAP, and show its strong performance on various benchmarks in our experiments.

Hypergraph neural networks (HyperGNNs) show promise in modeling online networks with high-order correlations. Despite notable progress, training these models on large-scale raw hypergraphs entails substantial computational and storage costs, thereby increasing the need of hypergraph size reduction. However, existing size reduction methods primarily capture pairwise association pattern within conventional graphs, making them challenging to adapt to hypergraphs with high-order correlations. To fill this gap, we introduce a novel hypergraph condensation framework, HG-Cond, designed to distill large-scale hypergraphs into compact, synthetic versions while maintaining comparable HyperGNN performance. Within this framework, we develop a Neural Hyperedge Linker to capture the high-order connectivity pattern through variational inference, achieving linear complexity with respect to the number of nodes. Moreover, We propose a multi-aspectual amelioration strategy including a Gradient-Parameter Synergistic Matching objective to holistically refine synthetic hypergraphs by coordinating improvements in node attributes, high-order connectivity, and label distributions. Extensive experiments demonstrate the efficacy of HG-Cond in hypergraph condensation, notably outperforming the original test accuracy on the 20News dataset while concurrently reducing the hypergraph size to a mere 5% of its initial scale. Furthermore, the condensed hypergraphs demonstrate robust cross-architectural generalizability and potential for expediting neural architecture search.

Graph clustering, a fundamental and challenging task in graph mining, aims to classify nodes in a graph into several disjoint clusters. In recent years, graph contrastive learning (GCL) has emerged as a dominant line of research in graph clustering and advances the new state-of-the-art. However, GCL-based methods heavily rely on graph augmentations and contrastive schemes, which may potentially introduce challenges such as semantic drift and scalability issues. Another promising line of research involves the adoption of modularity maximization, a popular and effective measure for community detection, as the guiding principle for clustering tasks. Despite the recent progress, the underlying mechanism of modularity maximization is still not well understood. In this work, we dig into the hidden success of modularity maximization for graph clustering. Our analysis reveals the strong connections between modularity maximization and graph contrastive learning, where positive and negative examples are naturally defined by modularity. In light of our results, we propose a community-aware graph clustering framework, coined øurs, which leverages modularity maximization as a contrastive pretext task to effectively uncover the underlying information of communities in graphs, while avoiding the problem of semantic drift. Extensive experiments on multiple graph datasets verify the effectiveness of øurs in terms of scalability and clustering performance compared to state-of-the-art graph clustering methods. Notably, øurs easily scales a sufficiently large graph with 100M nodes while outperforming strong baselines.

Graph convolutional networks (GCNs) have been shown to be vulnerable to small adversarial perturbations, which becomes a severe threat and largely limits their applications in security-critical scenarios. To mitigate such a threat, considerable research efforts have been devoted to increasing the robustness of GCNs against adversarial attacks. However, current defense approaches are typically designed to prevent GCNs from untargeted adversarial attacks and focus on overall performance, making it challenging to protect important local nodes from more powerful targeted adversarial attacks. Additionally, a trade-off between robustness and performance is often made in existing research. Such limitations highlight the need for developing an effective and efficient approach that can defend local nodes against targeted attacks, without compromising the overall performance of GCNs. In this work, we present a simple yet effective method, named Graph Universal AdveRsarial Defense (GUARD). Unlike previous works, GUARD protects each individual node from attacks with a universal defensive patch, which is generated once and can be applied to any node (node-agnostic) in a graph. GUARD is fast, straightforward to implement without any change to network architecture nor any additional parameters, and is broadly applicable to any GCNs. Extensive experiments on four benchmark datasets demonstrate that GUARD significantly improves robustness for several established GCNs against multiple adversarial attacks and outperforms state-of-the-art defense methods by large margins.

The last years have witnessed the emergence of a promising self-supervised learning strategy, referred to as masked autoencoding. However, there is a lack of theoretical understanding of how masking matters on graph autoencoders (GAEs). In this work, we present masked graph autoencoder (MaskGAE), a self-supervised learning framework for graph-structured data. Different from standard GAEs, MaskGAE adopts masked graph modeling (MGM) as a principled pretext task - masking a portion of edges and attempting to reconstruct the missing part with partially visible, unmasked graph structure. To understand whether MGM can help GAEs learn better representations, we provide both theoretical and empirical evidence to comprehensively justify the benefits of this pretext task. Theoretically, we establish close connections between GAEs and contrastive learning, showing that MGM significantly improves the self-supervised learning scheme of GAEs. Empirically, we conduct extensive experiments on a variety of graph benchmarks, demonstrating the superiority of MaskGAE over several state-of-the-arts on both link prediction and node classification tasks.