Title: SpSC: A Fast and Provable Algorithm for Sampling-Based GNN Training. Abstract: Neighbor sampling is a commonly used technique for training Graph Neural Networks (GNNs) on large graphs. Previous work has shown that sampling-based GNN training can be considered as Stochastic Compositional Optimization (SCO) problems and can be better solved by SCO algorithms. However, we find that SCO algorithms are impractical for training GNNs on large graphs because they need to store the moving averages of the aggregated features of all nodes in the graph. The moving averages can easily exceed the GPU memory limit and even the CPU memory limit. In this work, we propose a variant of SCO algorithms with sparse moving averages for GNN training. By storing the moving averages in the most recent iterations, our algorithm only requires a fixed size buffer, regardless of the graph size. We show that our algorithm can achieve $O(\sqrt{1/K})$ convergence rate when the buffer size satisfies certain conditions. Our experiments validate our theoretical results and show that our algorithm outperforms the traditional Adam SGD for GNN training with a small memory overhead.