  Recent work suggests that convolutional neural networks of different
architectures learn to classify images in the same order. To understand this
phenomenon, we revisit the over-parametrized deep linear network model. Our
analysis reveals that, when the hidden layers are wide enough, the convergence
rate of this model's parameters is exponentially faster along the directions of
the larger principal components of the data, at a rate governed by the
corresponding singular values. We term this convergence pattern the Principal
Components bias (PC-bias). Empirically, we show how the PC-bias streamlines the
order of learning of both linear and non-linear networks, more prominently at
earlier stages of learning. We then compare our results to the simplicity bias,
showing that both biases can be seen independently, and affect the order of
learning in different ways. Finally, we discuss how the PC-bias may explain
some benefits of early stopping and its connection to PCA, and why deep
networks converge more slowly with random labels.
