Properties of the After Kernel

Understand

The Neural Tangent Kernel (NTK) is the wide-network limit of a kernel defined using neural networks at initialization, whose embedding is the gradient of the output of the network with respect to its parameters.

• We study the "after kernel", which is defined using the same embedding, except after training, for neural networks with standard architectures, on binary classification problems extracted from MNIST and CIFAR-10, trained using SGD in a standard way.
• For some dataset-architecture pairs, after a few epochs of neural network training, a hard-margin SVM using the network's after kernel is much more accurate than when the network's initial kernel is used.
• For networks with an architecture similar to VGG, the after kernel is more "global", in the sense that it is less invariant to transformations of input images that disrupt the global structure of the image while leaving the local statistics largely intact.