General V alue Functions (GVFs) (Sutton et al., 2011) represent predictive knowledge in reinforcement learning.

Recently,Sutton[23]proposed anewview on action selection.

However, the structure of their hidden layer representations is only theoretically well-understood incertain infinite-width limits, inwhichtheserepresentations cannot flexibly adapt tolearn data-dependent features [3-11,24]. Inthe Bayesian setting, these representations are described by fixed, deterministic kernels [3-11].

Despite its theoretical appeal, this viewpoint lacks a crucial ingredient of deep learning in finite DNNs, laying at the heart of their success --feature learning. Here we consider DNNs trained with noisy gradient descent on a large training set and derive a self-consistent Gaussian Process theory accounting forstrongfinite-DNN and feature learning effects.