One-Step Early Stopping Strategy using Neural Tangent Kernel Theory and Rademacher Complexity
This provides a theoretically-grounded early stopping strategy for neural network practitioners in underparameterized regimes, though it appears incremental to existing early stopping literature.
The authors tackled the problem of determining optimal early stopping time for neural networks to maintain generalization, deriving an analytical estimate using neural tangent kernel eigenvalues and initial training error. They demonstrated their method on a Van der Pol oscillator control simulation, obtaining an upper bound on population loss suitable for underparameterized contexts.
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.