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It has been observed \citep{zhang2016understanding} that deep neural networkscan memorize: they achieve 100\% accuracy on training data. Recent theoreticalresults explained such behavior in highly overparametrized regimes, where thenumber of neurons in each layer is larger than the number of training samples.In this paper, we show that neural networks can be trained to memorize trainingdata perfectly in a mildly overparametrized regime, where the number ofparameters is just a constant factor more than the number of training samples,and the number of neurons is much smaller.

Mildly Overparametrized Neural Nets can Memorize Training Data Efficiently