Title: Revisiting Layer-wise Sampling in Fast Training for Graph Convolutional Networks. Abstract: To accelerate the training of graph convolutional networks (GCN), many sampling-based methods have been developed for approximating the embedding aggregation. Among them, a layer-wise approach recursively performs importance sampling to select neighbors jointly for existing nodes in each layer. This paper revisits the approach from a matrix approximation perspective. We identify two issues in the existing layer-wise sampling methods: sub-optimal sampling probabilities and the approximation bias induced by sampling without replacement. We thus propose remedies to address these issues. The improvements are demonstrated by extensive analyses and experiments on common benchmarks.