Whitening and second order optimization both make information in the dataset unusable during training, and can reduce or prevent generalization
This addresses a foundational problem in ML by identifying practices that can degrade model performance, though it is incremental in refining optimization and preprocessing techniques.
The paper demonstrates that data whitening and second-order optimization can harm or prevent generalization in machine learning by reducing access to information in the sample-sample second moment matrix, with experimental verification across architectures and a tradeoff noted for regularized methods.
Machine learning is predicated on the concept of generalization: a model achieving low error on a sufficiently large training set should also perform well on novel samples from the same distribution. We show that both data whitening and second order optimization can harm or entirely prevent generalization. In general, model training harnesses information contained in the sample-sample second moment matrix of a dataset. For a general class of models, namely models with a fully connected first layer, we prove that the information contained in this matrix is the only information which can be used to generalize. Models trained using whitened data, or with certain second order optimization schemes, have less access to this information, resulting in reduced or nonexistent generalization ability. We experimentally verify these predictions for several architectures, and further demonstrate that generalization continues to be harmed even when theoretical requirements are relaxed. However, we also show experimentally that regularized second order optimization can provide a practical tradeoff, where training is accelerated but less information is lost, and generalization can in some circumstances even improve.