Generalization Properties of NAS under Activation and Skip Connection Search

TL;DR

This paper provides a theoretical analysis of Neural Architecture Search (NAS), deriving bounds on the Neural Tangent Kernel's eigenvalues to guide architecture selection and enable train-free NAS methods.

Contribution

It introduces a unifying theoretical framework for NAS that includes skip connections and activation functions, deriving eigenvalue bounds to predict generalization performance.

Findings

Eigenvalue bounds of NTK inform NAS generalization

Theoretical results guide architecture selection without training

Experimental validation supports the train-free NAS approach

Abstract

Neural Architecture Search (NAS) has fostered the automatic discovery of state-of-the-art neural architectures. Despite the progress achieved with NAS, so far there is little attention to theoretical guarantees on NAS. In this work, we study the generalization properties of NAS under a unifying framework enabling (deep) layer skip connection search and activation function search. To this end, we derive the lower (and upper) bounds of the minimum eigenvalue of the Neural Tangent Kernel (NTK) under the (in)finite-width regime using a certain search space including mixed activation functions, fully connected, and residual neural networks. We use the minimum eigenvalue to establish generalization error bounds of NAS in the stochastic gradient descent training. Importantly, we theoretically and experimentally show how the derived results can guide NAS to select the top-performing architectures, even in the case without training, leading to a train-free algorithm based on our theory. Accordingly, our numerical validation shed light on the design of computationally efficient methods for NAS. Our analysis is non-trivial due to the coupling of various architectures and activation functions under the unifying framework and has its own interest in providing the lower bound of the minimum eigenvalue of NTK in deep learning theory.