# Self-Consistent Dynamical Field Theory of Kernel Evolution in Wide Neural Networks

@article{Bordelon2022SelfConsistentDF, title={Self-Consistent Dynamical Field Theory of Kernel Evolution in Wide Neural Networks}, author={Blake Bordelon and Cengiz Pehlevan}, journal={ArXiv}, year={2022}, volume={abs/2205.09653} }

We analyze feature learning in inﬁnite width neural networks trained with gradient ﬂow through a self-consistent dynamical ﬁeld theory. We construct a collection of deterministic dynamical order parameters which are inner-product kernels for hidden unit activations and gradients in each layer at pairs of time points, providing a reduced description of network activity through training. These kernel order parameters collectively deﬁne the hidden layer activation distribution, the evolution of…

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