Title: Node-Level Differentially Private Graph Neural Networks. Abstract: Graph neural networks (GNNs) are a popular technique for modelling graph-structured data that compute node-level predictions via aggregation of information from the local neighborhood of each node. However, this aggregation implies increased risk of revealing sensitive information, as a node can participate in the inference for multiple nodes. This implies that standard privacy preserving machine learning techniques like differentially private stochastic gradient descent (DP-SGD) – which are designed for situations where each node/data point participate in inference of one point only – either do not apply or lead to inaccurate solutions. In this work, we formally define the problem of learning 1-layer GNNs with node-level privacy, and provide a method for the problem with a strong differential privacy guarantee. Even though each node can be involved in the inference for multiple nodes, by employing a careful sensitivity analysis and a non-trivial extension of the privacy-by-amplification technique, our method is able to provide accurate solutions with solid privacy parameters. Empirical evaluation on standard benchmarks demonstrates that our method is indeed able to learn accurate privacy preserving GNNs, while still outperforming standard non-private methods that completely ignore graph information.