Mildly Overparametrized Neural Nets can Memorize Training Data Efficiently
This addresses the theoretical understanding of memorization in neural networks for researchers, but it is incremental as it builds on prior work on overparametrization.
The paper tackles the problem of neural networks memorizing training data by showing they can achieve perfect memorization in a mildly overparametrized regime, where the number of parameters is only a constant factor more than the number of training samples and neurons are much fewer.
It has been observed \citep{zhang2016understanding} that deep neural networks can memorize: they achieve 100\% accuracy on training data. Recent theoretical results explained such behavior in highly overparametrized regimes, where the number 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 training data perfectly in a mildly overparametrized regime, where the number of parameters is just a constant factor more than the number of training samples, and the number of neurons is much smaller.