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.

Federated Recommendation (FedRec) is popularly investigated in personalized recommenders for preserving user privacy. However, due to the distributed training paradigm, FedRec is vulnerable to model poisoning attacks. In this paper, we focus on the targeted model poisoning attack against FedRec, which aims at effectively attacking the FedRec via uploading poisoned gradients to raise the exposure ratio of a multi-target item set. Previous attack methods excel with fewer target items but suffer performance decline as the amount of target items increases, which reveals two perennially neglected issues: (i) The simple promotion of prediction scores without considering intrinsic collaborations between users and items is ineffective in multi-target cases. (ii) Target items are heterogeneous, which requires discriminative attacking users and strategies for different targets. To address the issues, we propose a novel Heterogeneous Multi-target Transfer Attack framework named HMTA which consists of two stages, i.e., (1) diverse user agent generation and (2) optimal multi-target transport attack. The former stage leverages collaboration-aware manifold learning to extract latent associations among users and items, and develops a differentiable contrastive sorting to generate user agents from both difficulty and diversity scale. The latter stage conducts poisoning in a fine-grained and distinguishing way, which first completes distribution mapping from target items to generated user agents and then achieves a hybrid multi-target attack. Extensive experiments on benchmark datasets demonstrate the effectiveness of HMTA.

Recommendation system has been a widely studied task both in academia and industry. Previous works mainly focus on homogeneous recommendation and little progress has been made for heterogeneous recommender systems. However, heterogeneous recommendations, e.g., recommending different types of items including products, videos, celebrity shopping notes, among many others, are dominant nowadays. State-of-the-art methods are incapable of leveraging attributes from different types of items and thus suffer from data sparsity problems. And it is indeed quite challenging to represent items with different feature spaces jointly. To tackle this problem, we propose a kernel-based neural network, namely deep unified representation (or DURation) for heterogeneous recommendation, to jointly model unified representations of heterogeneous items while preserving their original feature space topology structures. Theoretically, we prove the representation ability of the proposed model. Besides, we conduct extensive experiments on the real-world datasets. Experimental results demonstrate that with the unified representation, our model achieves remarkable improvement (e.g., 4.1% ~34.9% lift by AUC score and 3.7% lift by online CTR) over existing state-of-the-art models.