Generating 3D graphs of symmetry-group equivariance is of intriguing potential in broad applications from machine vision to molecular discovery. Emerging approaches adopt diffusion generative models (DGMs) with proper re-engineering to capture 3D graph distributions. In this paper, we raise an orthogonal and fundamental question of in what (latent) space we should diffuse 3D graphs. ❶ We motivate the study with theoretical analysis showing that the performance bound of 3D graph diffusion can be improved in a latent space versus the original space, provided that the latent space is of (i) low dimensionality yet (ii) high quality (i.e., low reconstruction error) and DGMs have (iii) symmetry preservation as an inductive bias. ❷ Guided by the theoretical guidelines, we propose to perform 3D graph diffusion in a low-dimensional latent space, which is learned through cascaded 2D–3D graph autoencoders for low-error reconstruction and symmetry-group invariance. The overall pipeline is dubbed latent 3D graph diffusion. ❸ Motivated by applications in molecular discovery, we further extend latent 3D graph diffusion to conditional generation given SE(3)-invariant attributes or equivariant 3D objects. ❹ We also demonstrate empirically that out-of-distribution conditional generation can be further improved by regularizing the latent space via graph self-supervised learning. We validate through comprehensive experiments that our method generates 3D molecules of higher validity / drug-likeliness and comparable or better conformations / energetics, while being an order of magnitude faster in training. Codes are released at https://github.com/Shen-Lab/LDM-3DG.

Graph neural networks (GNNs) have found extensive applications in learning from graph data. However, real-world graphs often possess diverse structures and comprise nodes and edges of varying types. To bolster the generalization capacity of GNNs, it has become customary to augment training graph structures through techniques like graph augmentations and large-scale pre-training on a wider array of graphs. Balancing this diversity while avoiding increased computational costs and the notorious trainability issues of GNNs is crucial. This study introduces the concept of Mixture-of-Experts (MoE) to GNNs, with the aim of augmenting their capacity to adapt to a diverse range of training graph structures, without incurring explosive computational overhead. The proposed Graph Mixture of Experts (GMoE) model empowers individual nodes in the graph to dynamically and adaptively select more general information aggregation experts. These experts are trained to capture distinct subgroups of graph structures and to incorporate information with varying hop sizes, where those with larger hop sizes specialize in gathering information over longer distances. The effectiveness of GMoE is validated through a series of experiments on a diverse set of tasks, including graph, node, and link prediction, using the OGB benchmark. Notably, it enhances ROC-AUC by $1.81\%$ in ogbg-molhiv and by $1.40\%$ in ogbg-molbbbp, when compared to the non-MoE baselines. Our code is publicly available at https://github.com/VITA-Group/Graph-Mixture-of-Experts.

This paper targets at improving the generalizability of hypergraph neural networks in the low-label regime, through applying the contrastive learning approach from images/graphs (we refer to it as HyperGCL). We focus on the following question: How to construct contrastive views for hypergraphs via augmentations? We provide the solutions in two folds. First, guided by domain knowledge, we fabricate two schemes to augment hyperedges with higher-order relations encoded, and adopt three vertex augmentation strategies from graph-structured data. Second, in search of more effective views in a data-driven manner, we for the first time propose a hypergraph generative model to generate augmented views, and then an end-to-end differentiable pipeline to jointly learn hypergraph augmentations and model parameters. Our technical innovations are reflected in designing both fabricated and generative augmentations of hypergraphs. The experimental findings include: (i) Among fabricated augmentations in HyperGCL, augmenting hyperedges provides the most numerical gains, implying that higher-order information in structures is usually more downstream-relevant; (ii) Generative augmentations do better in preserving higher-order information to further benefit generalizability; (iii) HyperGCL also boosts robustness and fairness in hypergraph representation learning. Codes are released at https://github.com/weitianxin/HyperGCL.

Self-supervision is recently surging at its new frontier of graph learning. It facilitates graph representations beneficial to downstream tasks; but its success could hinge on domain knowledge for handcraft or the often expensive trials and errors. Even its state-of-the-art representative, graph contrastive learning (GraphCL), is not completely free of those needs as GraphCL uses a prefabricated prior reflected by the ad-hoc manual selection of graph data augmentations. Our work aims at advancing GraphCL by answering the following questions: How to represent the space of graph augmented views? What principle can be relied upon to learn a prior in that space? And what framework can be constructed to learn the prior in tandem with contrastive learning? Accordingly, we have extended the prefabricated discrete prior in the augmentation set, to a learnable continuous prior in the parameter space of graph generators, assuming that graph priors per se, similar to the concept of image manifolds, can be learned by data generation. Furthermore, to form contrastive views without collapsing to trivial solutions due to the prior learnability, we have leveraged both principles of information minimization (InfoMin) and information bottleneck (InfoBN) to regularize the learned priors. Eventually, contrastive learning, InfoMin, and InfoBN are incorporated organically into one framework of bi-level optimization. Our principled and automated approach has proven to be competitive against the state-of-the-art graph self-supervision methods, including GraphCL, on benchmarks of small graphs; and shown even better generalizability on large-scale graphs, without resorting to human expertise or downstream validation. Our code is publicly released at https://github.com/Shen-Lab/GraphCL_Automated.

MOTIVATION: Computational methods for compound-protein affinity and contact (CPAC) prediction aim at facilitating rational drug discovery by simultaneous prediction of the strength and the pattern of compound-protein interactions. Although the desired outputs are highly structure-dependent, the lack of protein structures often makes structure-free methods rely on protein sequence inputs alone. The scarcity of compound-protein pairs with affinity and contact labels further limits the accuracy and the generalizability of CPAC models. RESULTS: To overcome the aforementioned challenges of structure naivety and labeled-data scarcity, we introduce cross-modality and self-supervised learning, respectively, for structure-aware and task-relevant protein embedding. Specifically, protein data are available in both modalities of 1D amino-acid sequences and predicted 2D contact maps that are separately embedded with recurrent and graph neural networks, respectively, as well as jointly embedded with two cross-modality schemes. Furthermore, both protein modalities are pre-trained under various self-supervised learning strategies, by leveraging massive amount of unlabeled protein data. Our results indicate that individual protein modalities differ in their strengths of predicting affinities or contacts. Proper cross-modality protein embedding combined with self-supervised learning improves model generalizability when predicting both affinities and contacts for unseen proteins. AVAILABILITY AND IMPLEMENTATION: Data and source codes are available at https://github.com/Shen-Lab/CPAC. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Self-supervised learning on graph-structured data has drawn recent interest for learning generalizable, transferable and robust representations from unlabeled graphs. Among many, graph contrastive learning (GraphCL) has emerged with promising representation learning performance. Unfortunately, unlike its counterpart on image data, the effectiveness of GraphCL hinges on ad-hoc data augmentations, which have to be manually picked per dataset, by either rules of thumb or trial-and-errors, owing to the diverse nature of graph data. That significantly limits the more general applicability of GraphCL. Aiming to fill in this crucial gap, this paper proposes a unified bi-level optimization framework to automatically, adaptively and dynamically select data augmentations when performing GraphCL on specific graph data. The general framework, dubbed JOint Augmentation Optimization (JOAO), is instantiated as min-max optimization. The selections of augmentations made by JOAO are shown to be in general aligned with previous "best practices" observed from handcrafted tuning: yet now being automated, more flexible and versatile. Moreover, we propose a new augmentation-aware projection head mechanism, which will route output features through different projection heads corresponding to different augmentations chosen at each training step. Extensive experiments demonstrate that JOAO performs on par with or sometimes better than the state-of-the-art competitors including GraphCL, on multiple graph datasets of various scales and types, yet without resorting to any laborious dataset-specific tuning on augmentation selection. We release the code at https://github.com/Shen-Lab/GraphCL_Automated.

Graph convolution networks (GCN) are increasingly popular in many applications, yet remain notoriously hard to train over large graph datasets. They need to compute node representations recursively from their neighbors. Current GCN training algorithms suffer from either high computational costs that grow exponentially with the number of layers, or high memory usage for loading the entire graph and node embeddings. In this paper, we propose a novel efficient layer-wise training framework for GCN (L-GCN), that disentangles feature aggregation and feature transformation during training, hence greatly reducing time and memory complexities. We present theoretical analysis for L-GCN under the graph isomorphism framework, that L-GCN leads to as powerful GCNs as the more costly conventional training algorithm does, under mild conditions. We further propose L^2-GCN, which learns a controller for each layer that can automatically adjust the training epochs per layer in L-GCN. Experiments show that L-GCN is faster than state-of-the-arts by at least an order of magnitude, with a consistent of memory usage not dependent on dataset size, while maintaining comparable prediction performance. With the learned controller, L^2-GCN can further cut the training time in half. Our codes are available at https://github.com/Shen-Lab/L2-GCN.

Self-supervision as an emerging technique has been employed to train convolutional neural networks (CNNs) for more transferrable, generalizable, and robust representation learning of images. Its introduction to graph convolutional networks (GCNs) operating on graph data is however rarely explored. In this study, we report the first systematic exploration and assessment of incorporating self-supervision into GCNs. We first elaborate three mechanisms to incorporate self-supervision into GCNs, analyze the limitations of pretraining & finetuning and self-training, and proceed to focus on multi-task learning. Moreover, we propose to investigate three novel self-supervised learning tasks for GCNs with theoretical rationales and numerical comparisons. Lastly, we further integrate multi-task self-supervision into graph adversarial training. Our results show that, with properly designed task forms and incorporation mechanisms, self-supervision benefits GCNs in gaining more generalizability and robustness. Our codes are available at https://github.com/Shen-Lab/SS-GCNs.

Generalizable, transferrable, and robust representation learning on graph-structured data remains a challenge for current graph neural networks (GNNs). Unlike what has been developed for convolutional neural networks (CNNs) for image data, self-supervised learning and pre-training are less explored for GNNs. In this paper, we propose a graph contrastive learning (GraphCL) framework for learning unsupervised representations of graph data. We first design four types of graph augmentations to incorporate various priors. We then systematically study the impact of various combinations of graph augmentations on multiple datasets, in four different settings: semi-supervised, unsupervised, and transfer learning as well as adversarial attacks. The results show that, even without tuning augmentation extents nor using sophisticated GNN architectures, our GraphCL framework can produce graph representations of similar or better generalizability, transferrability, and robustness compared to state-of-the-art methods. We also investigate the impact of parameterized graph augmentation extents and patterns, and observe further performance gains in preliminary experiments. Our codes are available at https://github.com/Shen-Lab/GraphCL.