Feature Learning in Infinite-Width Neural Networks

As its width tends to infinity, a deep neural network's behavior under gradient descent can become simplified and predictable (e.g.\ given by the Neural Tangent Kernel (NTK)), if it is parametrized appropriately (e.g.\ the NTK parametrization). However, we show that the standard and NTK parametrizations of a neural network do not admit infinite-width limits that can \emph{learn} features, which is crucial for pretraining and transfer learning such as with BERT. We propose simple modifications to the standard parametrization to allow for feature learning in the limit. Using the \emph{Tensor Programs} technique, we derive explicit formulas for such limits. On Word2Vec and few-shot learning on Omniglot via MAML, two canonical tasks that rely crucially on feature learning, we compute these limits exactly. We find that they outperform both NTK baselines and finite-width networks, with the latter approaching the infinite-width feature learning performance as width increases.