Despite the recent progress of molecular representation learning, its effectiveness is assumed on the close-world assumptions that training and testing graphs are from identical distribution. The open-world test dataset is often mixed with out-of-distribution (OOD) samples, where the deployed models will struggle to make accurate predictions. The misleading estimations of molecules' properties in drug screening or design can result in the tremendous waste of wet-lab resources and delay the discovery of novel therapies. Traditional detection methods need to trade off OOD detection and in-distribution (ID) classification performance since they share the same representation learning model. In this work, we propose to detect OOD molecules by adopting an auxiliary diffusion model-based framework, which compares similarities between input molecules and reconstructed graphs. Due to the generative bias towards reconstructing ID training samples, the similarity scores of OOD molecules will be much lower to facilitate detection. Although it is conceptually simple, extending this vanilla framework to practical detection applications is still limited by two significant challenges. First, the popular similarity metrics based on Euclidian distance fail to consider the complex graph structure. Second, the generative model involving iterative denoising steps is notoriously time-consuming especially when it runs on the enormous pool of drugs. To address these challenges, our research pioneers an approach of Prototypical Graph Reconstruction for Molecular OOd Detection, dubbed as PGR-MOOD. Specifically, PGR-MOOD hinges on three innovations: i) An effective metric to comprehensively quantify the matching degree of input and reconstructed molecules according to their discrete edges and continuous node features; ii) A creative graph generator to construct a list of prototypical graphs that are in line with ID distribution but away from OOD one; iii) An efficient and scalable OOD detector to compare the similarity between test samples and pre-constructed prototypical graphs and omit the generative process on every new molecule. Extensive experiments on ten benchmark datasets and six baselines are conducted to demonstrate our superiority: PGR-MOOD achieves more than 8% of average improvement in terms of detection AUC and AUPR accompanied by the reduced cost of testing time and memory consumption. The anonymous code is in: https://github.com/se7esx/PGR-MOOD.

Graph neural networks (GNNs) are powerful models for processing graph data and have demonstrated state-of-the-art performance on many downstream tasks. However, existing GNNs can generally suffer from two limitations: over-smoothing and over-squashing, which can significantly undermine their learning ability for large graphs. To overcome these issues simultaneously, by utilizing the concept of effective resistances, we focus on minimizing total constrained resistance while identifying problematic edges using topological redundancy and bottleneck sparsity coefficients. We introduce a novel graph rewiring and preprocessing method guided by effective resistance (GPER), capable of edge addition or removal. Theoretical analysis validates our method's efficacy in mitigating over-smoothing and over-squashing. In the experiments, we conduct node and graph classifications on the benchmark datasets and can achieve an average improvement of 7.8% and 2.0%, respectively. We also conduct scalability analysis on large graphs with GCN and demonstrate that the proposed preprocess approach can reduce graph size by over 50% while improve the performance.

Link prediction is a classical problem in graph analysis with many practical applications. For directed graphs, recently developed deep learning approaches typically analyze node similarities through contrastive learning and aggregate neighborhood information through graph convolutions. In this work, we propose a novel graph neural network (GNN) framework to fuse feature embedding with community information. We theoretically demonstrate that such hybrid features can improve the performance of directed link prediction. To utilize such features efficiently, we also propose an approach to transform input graphs into directed line graphs so that nodes in the transformed graph can aggregate more information during graph convolutions. Experiments on benchmark datasets show that our approach outperforms the state-of-the-art in most cases when 30%, 40%, 50%, and 60% of the connected links are used as training data, respectively.

Graph neural networks (GNNs) with feature propagation have demonstrated their power in handling unstructured data. However, feature propagation is also a smooth process that tends to make all node representations similar as the number of propagation increases. To address this problem, we propose a novel Block-Based Adaptive Decoupling (BBAD) Framework to produce effective deep GNNs by utilizing backbone networks. In this framework, each block contains a shallow GNN with feature propagation and transformation decoupled. We also introduce layer regularizations and flexible receptive fields to automatically adjust the propagation depth and to provide different aggregation hops for each node, respectively. We prove that the traditional coupled GNNs are more likely to suffer from over-smoothing when they become deep. We also demonstrate the diversity of outputs from different blocks of our framework. In the experiments, we conduct semi-supervised and fully supervised node classifications on benchmark datasets, and the results verify that our method can not only improve the performance of various backbone networks, but also is superior to existing deep graph neural networks with less parameters.

Out-of-distribution (OOD) generalization has emerged as a critical challenge in graph learning, as real-world graph data often exhibit diverse and shifting environments that traditional models fail to generalize across. A promising solution to address this issue is graph invariant learning (GIL), which aims to learn invariant representations by disentangling label-correlated invariant subgraphs from environment-specific subgraphs. However, existing GIL methods face two major challenges: (1) the difficulty of capturing and modeling diverse environments in graph data, and (2) the semantic cliff, where in variant subgraphs from different classes are difficult to distinguish, leading to poor class separability and increased misclassifications. To tackle these challenges, we propose a novel method termed Multi-Prototype Hyperspherical Invariant Learning (MPHIL), which introduces two key innovations: (1) hyperspherical in variant representation extraction, enabling robust and highly discriminative hyperspherical invariant feature extraction, and (2) multi-prototype hyperspherical classification, which employs class prototypes as intermediate variables to eliminate the need for explicit environment modeling in GIL and mitigate the semantic cliff issue. Derived from the theoretical framework of GIL, we introduce two novel objective functions: the invariant prototype matching loss to ensure samples are matched to the correct class prototypes, and the prototype separation loss to increase the distinction between prototypes of different classes in the hyperspherical space. Extensive experiments on 13 OOD generalization benchmark datasets demonstrate that MPHIL achieves state-of-the-art performance, significantly outperforming existing methods across graph data from various domains and with different distribution shifts. The source code of MPHIL is available at https://github.com/se7esx/MPHIL.