The Low-Rank Simplicity Bias in Deep Networks
This addresses the generalization puzzle in deep learning for researchers, though it is incremental as it builds on existing hypotheses about simplicity biases.
The paper investigates why deep neural networks generalize well despite over-parameterization, finding that deeper networks have an inductive bias toward solutions with low effective rank embeddings, which correlates with better generalization on datasets like CIFAR and ImageNet.
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.