Neural Kernels Without Tangents

Vaishaal Shankar, Alex Fang, Wenshuo Guo, Sara Fridovich-Keil, Ludwig Schmidt, Jonathan Ragan-Kelley, Benjamin Recht

Abstract:

We investigate the connections between neural networks and simple building blocks in kernel
space. In particular, using well established feature space tools such as direct sum, averaging, and
moment lifting, we present an algebra for creating “compositional" kernels from bags of features.
We show that these operations correspond to many of the building blocks of “neural tangent
kernels" (NTK). Experimentally, we show a correlation in test error between neural network
architectures and the associated kernels. We construct a simple neural network architecture
using only 3 × 3 convolutions, 2 × 2 average pooling, ReLU, and optimized with SGD and MSE
loss that achieves 96% accuracy on CIFAR10, and whose corresponding compositional kernel
achieves 90% accuracy. We also use our constructions to investigate the relative performance of
neural networks, NTKs, and compositional kernels in the small dataset regime. In particular, we
find that compositional kernels outperform NTKs and neural networks outperform both kernel
methods.