This has led to a large body of work analyzing the capabilities and limitations of these models, particularly pertaining to their representation and extrapolation capacity.

GNN models to be effective.

The spectrum of the Laplace-Beltrami (LB) operator is central in geometric deep learning tasks, capturing intrinsic properties of the shape of the object under consideration. The best established method for its estimation, from a triangulated mesh of the object, is based on the Finite Element Method (FEM), and computes the top k LB eigenvalues with a complexity of O(Nk), where N is the number of points. This can render the FEM method inefficient when repeatedly applied to databases of CAD mechanical parts, or in quality control applications where part metrology is acquired as large meshes and decisions about the quality of each part are needed quickly and frequently. As a solution to this problem, we present a geometric deep learning framework to predict the LB spectrum efficiently given the CAD mesh of a part, achieving significant computational savings without sacrificing accuracy, demonstrating that the LB spectrum is learnable. The proposed Graph Neural Network architecture uses a rich set of part mesh features - including Gaussian curvature, mean curvature, and principal curvatures. In addition to our trained network, we make available, for repeatability, a large curated dataset of real-world mechanical CAD models derived from the publicly available ABC dataset used for training and testing. Experimental results show that our method reduces computation time of the LB spectrum by approximately 5 times over linear FEM while delivering competitive accuracy.

Graph Convolutional Networks (GCNs) have shown excellent performance in graph-structured tasks such as node classification and graph classification. However, recent research has shown that GCNs are vulnerable to a new type of threat called the backdoor attack, where the adversary can inject a hidden backdoor into the GCNs so that the backdoored model performs well on benign samples, whereas its prediction will be maliciously changed to the attacker-specified target label if the hidden backdoor is activated by the attacker-defined trigger. Clean-label backdoor attack and semantic backdoor attack are two new backdoor attacks to Deep Neural Networks (DNNs), they are more imperceptible and have posed new and serious threats. The semantic and clean-label backdoor attack is not fully explored in GCNs. In this paper, we propose a semantic and clean-label backdoor attack against GCNs under the context of graph classification to reveal the existence of this security vulnerability in GCNs. Specifically, SCLBA conducts an importance analysis on graph samples to select one type of node as semantic trigger, which is then inserted into the graph samples to create poisoning samples without changing the labels of the poisoning samples to the attacker-specified target label. We evaluate SCLBA on multiple datasets and the results show that SCLBA can achieve attack success rates close to 99% with poisoning rates of less than 3%, and with almost no impact on the performance of model on benign samples.

The relationships of many real-world networks are complex and go beyond pairwise associations. Hypergraphs provide a flexible and natural modeling tool to model such complex relationships. The authors propose HyperGCN, a novel way of training a GCN for semi-supervised learning on hypergraphs using tools from spectral theory of hypergraphs and introduce FastHyperGCN. They conduct some experiments on co-authorship and co-citation hypergraphs to demonstrate the effectiveness of HyperGCN, and provide theoretical analyses for the results. The paper proposes 1-HyperGCN and HyperGCN using the hypergraph Laplacian and the generalized hypergraph Laplacian with mediators.

Graph Convolutional Networks (GCNs) are widely used in graph-based applications, such as social networks and recommendation systems. Nevertheless, large-scale graphs or deep aggregation layers in full-batch GCNs consume significant GPU memory, causing out of memory (OOM) errors on mainstream GPUs (e.g., 29GB memory consumption on the Ogbnproducts graph with 5 layers). The subgraph sampling methods reduce memory consumption to achieve lightweight GCNs by partitioning the graph into multiple subgraphs and sequentially training GCNs on each subgraph. However, these methods yield gaps among subgraphs, i.e., GCNs can only be trained based on subgraphs instead of global graph information, which reduces the accuracy of GCNs. In this paper, we propose PromptGCN, a novel prompt-based lightweight GCN model to bridge the gaps among subgraphs. First, the learnable prompt embeddings are designed to obtain global information. Then, the prompts are attached into each subgraph to transfer the global information among subgraphs. Extensive experimental results on seven largescale graphs demonstrate that PromptGCN exhibits superior performance compared to baselines. Notably, PromptGCN improves the accuracy of subgraph sampling methods by up to 5.48% on the Flickr dataset. Overall, PromptGCN can be easily combined with any subgraph sampling method to obtain a lightweight GCN model with higher accuracy.

Several pioneering works [3, 4] introduced the initial concept of graph neural networks (GNNs), incorporating recurrent mechanisms and necessitating neural network parameters to define contraction mappings. Concurrently, Micheli [5] introduced the neural network for graphs, commonly referred to as NN4G, over a comparable timeframe. It is worth noting that the NN4G diverges from recurrent mechanisms and instead employs a feed-forward architecture, exhibiting similarities to contemporary GNNs. In recent years, (contemporary) GNNs have gained significant attention as an effective methodology for modeling graph data [6-11]. To obtain a comprehensive understanding of GNNs and deep learning for graphs, we refer the readers to relevant survey papers for an extensive overview [12-15]. Among the various GNN variants, one of the most powerful and frequently used GNNs is graph convolutional networks (GCNs). A widely accepted perspective posits that GCNs can be regarded as an extension or generalization of traditional spatial filters, which are commonly employed in Euclidean data analysis, to the realm of non-Euclidean data. Due to its success on non-Euclidean data, GCN has attracted widespread attention on its theoretical exploration.

Per- and polyfluoroalkyl substances (PFAS) are persistent environmental pollutants with known toxicity and bioaccumulation issues. Their widespread industrial use and resistance to degradation have led to global environmental contamination and significant health concerns. While a minority of PFAS have been extensively studied, the toxicity of many PFAS remains poorly understood due to limited direct toxicological data. This study advances the predictive modeling of PFAS toxicity by combining semi-supervised graph convolutional networks (GCNs) with molecular descriptors and fingerprints. We propose a novel approach to enhance the prediction of PFAS binding affinities by isolating molecular fingerprints to construct graphs where then descriptors are set as the node features. This approach specifically captures the structural, physicochemical, and topological features of PFAS without overfitting due to an abundance of features. Unsupervised clustering then identifies representative compounds for detailed binding studies. Our results provide a more accurate ability to estimate PFAS hepatotoxicity to provide guidance in chemical discovery of new PFAS and the development of new safety regulations.