TITLE: Whitening and second order optimization both make information in the dataset unusable during training, and can reduce or prevent generalization 

ABSTRACT: 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.
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.
Whitening and second order optimization both make information in the dataset unusable during training, and can reduce or prevent generalization
http://arxiv.org/abs/2008.07545v4