One-Step Early Stopping Strategy using Neural Tangent Kernel Theory and Rademacher Complexity

TL;DR

This paper proposes an analytical early stopping strategy for neural networks based on Neural Tangent Kernel theory and Rademacher complexity, improving generalization in underparameterized settings.

Contribution

It introduces a novel analytical method to determine optimal early stopping time using NTK eigenvalues and initial errors, applicable to underparameterized neural networks.

Findings

Provides an upper bound on population loss for early stopping.

Demonstrates effectiveness on a neural network controlling a Van der Pol oscillator.

Offers a practical estimation method for optimal stopping time.

Abstract

The early stopping strategy consists in stopping the training process of a neural network (NN) on a set $S$ of input data before training error is minimal. The advantage is that the NN then retains good generalization properties, i.e. it gives good predictions on data outside $S$, and a good estimate of the statistical error (``population loss'') is obtained. We give here an analytical estimation of the optimal stopping time involving basically the initial training error vector and the eigenvalues of the ``neural tangent kernel''. This yields an upper bound on the population loss which is well-suited to the underparameterized context (where the number of parameters is moderate compared with the number of data). Our method is illustrated on the example of an NN simulating the MPC control of a Van der Pol oscillator.