Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View

Graph Neural Networks (GNNs) have achieved promising performance on a wide range of graph-based tasks. Despite their success, one severe limitation of GNNs is the over-smoothing issue (indistinguishable representations of nodes in different classes). In this work, we present a systematic and quantitative study on the over-smoothing issue of GNNs. First, we introduce two quantitative metrics, MAD and MADGap, to measure the smoothness and over-smoothness of the graph nodes representations, respectively. Then, we verify that smoothing is the nature of GNNs and the critical factor leading to over-smoothness is the low information-to-noise ratio of the message received by the nodes, which is partially determined by the graph topology. Finally, we propose two methods to alleviate the over-smoothing issue from the topological view: (1) MADReg which adds a MADGap-based regularizer to the training objective;(2) AdaGraph which optimizes the graph topology based on the model predictions. Extensive experiments on 7 widely-used graph datasets with 10 typical GNN models show that the two proposed methods are effective for relieving the over-smoothing issue, thus improving the performance of various GNN models.Comment: Accepted by AAAI 2020. This complete version contains the appendi

Directed Message Passing Based on Attention for Prediction of Molecular Properties

Molecular representation learning (MRL) has long been crucial in the fields of drug discovery and materials science, and it has made significant progress due to the development of natural language processing (NLP) and graph neural networks (GNNs). NLP treats the molecules as one dimensional sequential tokens while GNNs treat them as two dimensional topology graphs. Based on different message passing algorithms, GNNs have various performance on detecting chemical environments and predicting molecular properties. Herein, we propose Directed Graph Attention Networks (D-GATs): the expressive GNNs with directed bonds. The key to the success of our strategy is to treat the molecular graph as directed graph and update the bond states and atom states by scaled dot-product attention mechanism. This allows the model to better capture the sub-structure of molecular graph, i.e., functional groups. Compared to other GNNs or Message Passing Neural Networks (MPNNs), D-GATs outperform the state-of-the-art on 13 out of 15 important molecular property prediction benchmarks.Comment: Computational Materials Science, In pres

Multiparameter Persistent Homology for Molecular Property Prediction

In this study, we present a novel molecular fingerprint generation method based on multiparameter persistent homology. This approach reveals the latent structures and relationships within molecular geometry, and detects topological features that exhibit persistence across multiple scales along multiple parameters, such as atomic mass, partial charge, and bond type, and can be further enhanced by incorporating additional parameters like ionization energy, electron affinity, chirality and orbital hybridization. The proposed fingerprinting method provides fresh perspectives on molecular structure that are not easily discernible from single-parameter or single-scale analysis. Besides, in comparison with traditional graph neural networks, multiparameter persistent homology has the advantage of providing a more comprehensive and interpretable characterization of the topology of the molecular data. We have established theoretical stability guarantees for multiparameter persistent homology, and have conducted extensive experiments on the Lipophilicity, FreeSolv, and ESOL datasets to demonstrate its effectiveness in predicting molecular properties.Comment: ICLR 2023-Machine Learning for Drug Discovery. arXiv admin note: text overlap with arXiv:2211.0380

ifMixup: Interpolating Graph Pair to Regularize Graph Classification

We present a simple and yet effective interpolation-based regularization technique, aiming to improve the generalization of Graph Neural Networks (GNNs) on supervised graph classification. We leverage Mixup, an effective regularizer for vision, where random sample pairs and their labels are interpolated to create synthetic images for training. Unlike images with grid-like coordinates, graphs have arbitrary structure and topology, which can be very sensitive to any modification that alters the graph's semantic meanings. This posts two unanswered questions for Mixup-like regularization schemes: Can we directly mix up a pair of graph inputs? If so, how well does such mixing strategy regularize the learning of GNNs? To answer these two questions, we propose ifMixup, which first adds dummy nodes to make two graphs have the same input size and then simultaneously performs linear interpolation between the aligned node feature vectors and the aligned edge representations of the two graphs. We empirically show that such simple mixing schema can effectively regularize the classification learning, resulting in superior predictive accuracy to popular graph augmentation and GNN methods.Comment: To appear in AAAI202