This paper presents a novel strategy for pre-training Graph Neural Networks (GNNs) to improve their performance on downstream tasks. The key idea is to pre-train GNNs at both the node and graph levels, enabling them to learn both local and global representations. The authors systematically study pre-training on multiple graph classification datasets and find that naive strategies, which pre-train GNNs at either the node or graph level alone, can lead to negative transfer and limited improvement. In contrast, their strategy avoids negative transfer and significantly improves generalization across downstream tasks, achieving up to 9.4% absolute improvements in ROC-AUC over non-pre-trained models and state-of-the-art performance for molecular property prediction and protein function prediction. The authors propose two self-supervised methods for pre-training GNNs: Context Prediction and Attribute Masking. Context Prediction uses subgraphs to predict their surrounding graph structures, while Attribute Masking randomly masks node/edge attributes and asks the GNN to predict them. They also introduce a graph-level supervised pre-training strategy that jointly predicts a diverse set of supervised labels for individual graphs. The authors evaluate their pre-training strategy on two domains: molecular property prediction in chemistry and protein function prediction in biology. They find that their strategy outperforms naive pre-training strategies and non-pre-trained models, achieving state-of-the-art performance. Additionally, their pre-training strategy leads to significantly faster training and convergence in the fine-tuning stage. The authors conclude that pre-training GNNs at both the node and graph levels is essential for achieving good performance on downstream tasks. They also highlight the importance of using expressive GNN architectures and effective pre-training strategies to improve generalization and avoid negative transfer. The paper provides a comprehensive overview of the pre-training strategies for GNNs and their effectiveness on various graph classification tasks.This paper presents a novel strategy for pre-training Graph Neural Networks (GNNs) to improve their performance on downstream tasks. The key idea is to pre-train GNNs at both the node and graph levels, enabling them to learn both local and global representations. The authors systematically study pre-training on multiple graph classification datasets and find that naive strategies, which pre-train GNNs at either the node or graph level alone, can lead to negative transfer and limited improvement. In contrast, their strategy avoids negative transfer and significantly improves generalization across downstream tasks, achieving up to 9.4% absolute improvements in ROC-AUC over non-pre-trained models and state-of-the-art performance for molecular property prediction and protein function prediction. The authors propose two self-supervised methods for pre-training GNNs: Context Prediction and Attribute Masking. Context Prediction uses subgraphs to predict their surrounding graph structures, while Attribute Masking randomly masks node/edge attributes and asks the GNN to predict them. They also introduce a graph-level supervised pre-training strategy that jointly predicts a diverse set of supervised labels for individual graphs. The authors evaluate their pre-training strategy on two domains: molecular property prediction in chemistry and protein function prediction in biology. They find that their strategy outperforms naive pre-training strategies and non-pre-trained models, achieving state-of-the-art performance. Additionally, their pre-training strategy leads to significantly faster training and convergence in the fine-tuning stage. The authors conclude that pre-training GNNs at both the node and graph levels is essential for achieving good performance on downstream tasks. They also highlight the importance of using expressive GNN architectures and effective pre-training strategies to improve generalization and avoid negative transfer. The paper provides a comprehensive overview of the pre-training strategies for GNNs and their effectiveness on various graph classification tasks.