Graph Neural Networks (GNNs) excel in various graph learning tasks but face computational challenges when applied to large-scale graphs. A promising solution is to remove non-essential edges to reduce the computational overheads in GNN. Previous literature generally falls into two categories: topology-guided and semantic-guided. The former maintains certain graph topological properties yet often underperforms on GNNs due to low integration with neural network training. The latter performs well at lower sparsity on GNNs but faces performance collapse at higher sparsity levels. With this in mind, we take the first step to propose a new research line and concept termed Graph Sparse Training (GST), which dynamically manipulates sparsity at the data level. Specifically, GST initially constructs a topology & semantic anchor at a low training cost, followed by performing dynamic sparse training to align the sparse graph with the anchor. We introduce the Equilibria Sparsification Principle to guide this process, effectively balancing the preservation of both topological and semantic information. Ultimately, GST produces a sparse graph with maximum topological integrity and no performance degradation. Extensive experiments on 6 datasets and 5 backbones showcase that GST (I) identifies subgraphs at higher graph sparsity levels (1.67%~15.85% $\uparrow$) than state-of-the-art sparsification methods, (II) preserves more key spectral properties, (III) achieves 1.27-3.42$\times$ speedup in GNN inference and (IV) successfully helps graph adversarial defense and graph lottery tickets.

Graph Lottery Tickets (GLTs), comprising a sparse adjacency matrix and a sparse graph neural network (GNN), can significantly reduce the inference latency and compute footprint compared to their dense counterparts. Despite these benefits, their performance against adversarial structure perturbations remains to be fully explored. In this work, we first investigate the resilience of GLTs against different structure perturbation attacks and observe that they are highly vulnerable and show a large drop in classification accuracy. Based on this observation, we then present an adversarially robust graph sparsification (ARGS) framework that prunes the adjacency matrix and the GNN weights by optimizing a novel loss function capturing the graph homophily property and information associated with both the true labels of the train nodes and the pseudo labels of the test nodes. By iteratively applying ARGS to prune both the perturbed graph adjacency matrix and the GNN model weights, we can find adversarially robust graph lottery tickets that are highly sparse yet achieve competitive performance under different untargeted training-time structure attacks. Evaluations conducted on various benchmarks, considering different poisoning structure attacks, namely, PGD, MetaAttack, Meta-PGD, and PR-BCD demonstrate that the GLTs generated by ARGS can significantly improve the robustness, even when subjected to high levels of sparsity.

Graph Lottery Ticket (GLT), a combination of core subgraph and sparse subnetwork, has been proposed to mitigate the computational cost of deep Graph Neural Networks (GNNs) on large input graphs while preserving original performance. However, the winning GLTs in exisiting studies are obtained by applying iterative magnitude-based pruning (IMP) without re-evaluating and re-considering the pruned information, which disregards the dynamic changes in the significance of edges/weights during graph/model structure pruning, and thus limits the appeal of the winning tickets. In this paper, we formulate a conjecture, i.e., existing overlooked valuable information in the pruned graph connections and model parameters which can be re-grouped into GLT to enhance the final performance. Specifically, we propose an adversarial complementary erasing (ACE) framework to explore the valuable information from the pruned components, thereby developing a more powerful GLT, referred to as the ACE-GLT. The main idea is to mine valuable information from pruned edges/weights after each round of IMP, and employ the ACE technique to refine the GLT processing. Finally, experimental results demonstrate that our ACE-GLT outperforms existing methods for searching GLT in diverse tasks. Our code will be made publicly available.

Lottery Ticket Hypothesis (LTH) claims the existence of a winning ticket (i.e., a properly pruned sub-network together with original weight initialization) that can achieve competitive performance to the original dense network. A recent work, called UGS, extended LTH to prune graph neural networks (GNNs) for effectively accelerating GNN inference. UGS simultaneously prunes the graph adjacency matrix and the model weights using the same masking mechanism, but since the roles of the graph adjacency matrix and the weight matrices are very different, we find that their sparsifications lead to different performance characteristics. Specifically, we find that the performance of a sparsified GNN degrades significantly when the graph sparsity goes beyond a certain extent. Therefore, we propose two techniques to improve GNN performance when the graph sparsity is high. First, UGS prunes the adjacency matrix using a loss formulation which, however, does not properly involve all elements of the adjacency matrix; in contrast, we add a new auxiliary loss head to better guide the edge pruning by involving the entire adjacency matrix. Second, by regarding unfavorable graph sparsification as adversarial data perturbations, we formulate the pruning process as a min-max optimization problem to gain the robustness of lottery tickets when the graph sparsity is high. We further investigate the question: Can the "retrainable" winning ticket of a GNN be also effective for graph transferring learning? We call it the transferable graph lottery ticket (GLT) hypothesis. Extensive experiments were conducted which demonstrate the superiority of our proposed sparsification method over UGS, and which empirically verified our transferable GLT hypothesis.

With graphs rapidly growing in size and deeper graph neural networks (GNNs) emerging, the training and inference of GNNs become increasingly expensive. Existing network weight pruning algorithms cannot address the main space and computational bottleneck in GNNs, caused by the size and connectivity of the graph. To this end, this paper first presents a unified GNN sparsification (UGS) framework that simultaneously prunes the graph adjacency matrix and the model weights, for effectively accelerating GNN inference on large-scale graphs. Leveraging this new tool, we further generalize the recently popular lottery ticket hypothesis to GNNs for the first time, by defining a graph lottery ticket (GLT) as a pair of core sub-dataset and sparse sub-network, which can be jointly identified from the original GNN and the full dense graph by iteratively applying UGS. Like its counterpart in convolutional neural networks, GLT can be trained in isolation to match the performance of training with the full model and graph, and can be drawn from both randomly initialized and self-supervised pre-trained GNNs. Our proposal has been experimentally verified across various GNN architectures and diverse tasks, on both small-scale graph datasets (Cora, Citeseer and PubMed), and large-scale datasets from the challenging Open Graph Benchmark (OGB). Specifically, for node classification, our found GLTs achieve the same accuracies with 20%~98% MACs saving on small graphs and 25%~85% MACs saving on large ones. For link prediction, GLTs lead to 48%~97% and 70% MACs saving on small and large graph datasets, respectively, without compromising predictive performance. Codes available at https://github.com/VITA-Group/Unified-LTH-GNN.

Given an undirected measurement graph $G = ([n], E)$, the classical angular synchronization problem consists of recovering unknown angles $\theta_1,\dots,\theta_n$ from a collection of noisy pairwise measurements of the form $(\theta_i - \theta_j) \mod 2\pi$, for each $\{i,j\} \in E$. This problem arises in a variety of applications, including computer vision, time synchronization of distributed networks, and ranking from preference relationships. In this paper, we consider a generalization to the setting where there exist $k$ unknown groups of angles $\theta_{l,1}, \dots,\theta_{l,n}$, for $l=1,\dots,k$. For each $ \{i,j\} \in E$, we are given noisy pairwise measurements of the form $\theta_{\ell,i} - \theta_{\ell,j}$ for an unknown $\ell \in \{1,2,\ldots,k\}$. This can be thought of as a natural extension of the angular synchronization problem to the heterogeneous setting of multiple groups of angles, where the measurement graph has an unknown edge-disjoint decomposition $G = G_1 \cup G_2 \ldots \cup G_k$, where the $G_i$'s denote the subgraphs of edges corresponding to each group. We propose a probabilistic generative model for this problem, along with a spectral algorithm for which we provide a detailed theoretical analysis in terms of robustness against both sampling sparsity and noise. The theoretical findings are complemented by a comprehensive set of numerical experiments, showcasing the efficacy of our algorithm under various parameter regimes. Finally, we consider an application of bi-synchronization to the graph realization problem, and provide along the way an iterative graph disentangling procedure that uncovers the subgraphs $G_i$, $i=1,\ldots,k$ which is of independent interest, as it is shown to improve the final recovery accuracy across all the experiments considered.

We introduce a novel regularization approach for deep learning that incorporates and respects the underlying graphical structure of the neural network. Existing regularization methods often focus on dropping/penalizing weights in a global manner that ignores the connectivity structure of the neural network. We propose to use the Fiedler value of the neural network's underlying graph as a tool for regularization. We provide theoretical support for this approach via spectral graph theory. We demonstrate the convexity of this penalty and provide an approximate, variational approach for fast computation in practical training of neural networks. We provide bounds on such approximations. We provide an alternative but equivalent formulation of this framework in the form of a structurally weighted L1 penalty, thus linking our approach to sparsity induction. We performed experiments on datasets that compare Fiedler regularization with traditional regularization methods such as dropout and weight decay. Results demonstrate the efficacy of Fiedler regularization.

Various sparse regularizers have been applied to machine learning problems, among which structured sparsity has been proposed for a better adaption to structured data. In this paper, motivated by effectively classifying linked data (e.g. Web pages, tweets, articles with references, and biological network data) where a group structure exists over the whole dataset and links exist between specific samples, we propose a joint sparse representation model that combines group sparsity and graph sparsity, to select a small number of connected components from the graph of linked samples, meanwhile promoting the sparsity of edges that link samples from different groups in each connected component. Consequently, linked samples are selected from a few sparsely-connected groups. Both theoretical analysis and experimental results on four benchmark datasets show that the joint sparsity model outperforms traditional group sparsity model and graph sparsity model, as well as the latest group-graph sparsity model.

In many learning tasks with structural properties, structural sparsity methods help induce sparse models, usually leading to better interpretability and higher generalization performance. One popular approach is to use group sparsity regularization that enforces sparsity on the clustered groups of features, while another popular approach is to adopt graph sparsity regularization that considers sparsity on the link structure of graph embedded features. Both the group and graph structural properties co-exist in many applications. However, group sparsity and graph sparsity have not been considered simultaneously yet. In this paper, we propose a g 2 -regularization that takes group and graph sparsity into joint consideration, and present an effective approach for its optimization. Experiments on both synthetic and real data show that, enforcing group-graph sparsity lead to better performance than using group sparsity or graph sparsity only.