Not all data in a typical training set help with generalization; some samples can be overly ambiguous or outrightly mislabeled. This paper introduces a new method to identify such samples and mitigate their impact when training neural networks. At the heart of our algorithm is the Area Under the Margin (AUM) statistic, which exploits differences in the training dynamics of clean and mislabeled samples. A simple procedure - adding an extra class populated with purposefully mislabeled threshold samples - learns a AUM upper bound that isolates mislabeled data. This approach consistently improves upon prior work on synthetic and real-world datasets. On the WebVision50 classification task our method removes 17% of training data, yielding a 1.6% (absolute) improvement in test error. On CIFAR100 removing 13% of the data leads to a 1.2% drop in error.

Graph Convolutional Networks (GCNs) and their variants have experienced significant attention and have become the de facto methods for learning graph representations. GCNs derive inspiration primarily from recent deep learning approaches, and as a result, may inherit unnecessary complexity and redundant computation. In this paper, we reduce this excess complexity through successively removing nonlinearities and collapsing weight matrices between consecutive layers. We theoretically analyze the resulting linear model and show that it corresponds to a fixed low-pass filter followed by a linear classifier. Notably, our experimental evaluation demonstrates that these simplifications do not negatively impact accuracy in many downstream applications. Moreover, the resulting model scales to larger datasets, is naturally interpretable, and yields up to two orders of magnitude speedup over FastGCN.