An Exact Kernel Equivalence for Finite Classification Models

Brian Wesley Bell, Michael Geyer, David Glickenstein, Amanda S Fernandez, Juston Moore

Keywords: deep learning theory, kernel machines, neural tangent kernel, gaussian process, parametric model, generalizatiion

TL;DR: We derive the first exact kernel representation for parametric classification models trained with discrete gradient descent and show that this kernel is computable and explicative.

Abstract: We explore the equivalence between neural networks and kernel methods by deriving the first exact representation of any finite-size parametric classification model trained with gradient descent as a kernel machine. We compare our exact representation to the well-known Neural Tangent Kernel (NTK) and discuss approximation error relative to the NTK and other non-exact path kernel formulations. We experimentally demonstrate that the kernel can be computed for realistic networks up to machine precision. We use this exact kernel to show that our theoretical contribution can provide useful insights into the predictions made by neural networks, particularly the way in which they generalize.

Type Of Submission: Proceedings Track (8 pages)

Submission Number: 35