  Modern deep neural networks are highly over-parameterized compared to the
data on which they are trained, yet they often generalize remarkably well. A
flurry of recent work has asked: why do deep networks not overfit to their
training data? In this work, we make a series of empirical observations that
investigate and extend the hypothesis that deeper networks are inductively
biased to find solutions with lower effective rank embeddings. We conjecture
that this bias exists because the volume of functions that maps to low
effective rank embedding increases with depth. We show empirically that our
claim holds true on finite width linear and non-linear models on practical
learning paradigms and show that on natural data, these are often the solutions
that generalize well. We then show that the simplicity bias exists at both
initialization and after training and is resilient to hyper-parameters and
learning methods. We further demonstrate how linear over-parameterization of
deep non-linear models can be used to induce low-rank bias, improving
generalization performance on CIFAR and ImageNet without changing the modeling
capacity.
