  Convergence and generalization are two crucial aspects of performance in
neural networks. When analyzed separately, these properties may lead to
contradictory results. Optimizing a convergence rate yields fast training, but
does not guarantee the best generalization error. To avoid the conflict, recent
studies suggest adopting a moderately large step size for optimizers, but the
added value on the performance remains unclear. We propose the LIGHT function
with the four configurations which regulate explicitly an improvement in
convergence and generalization on testing. This contribution allows to: 1)
improve both convergence and generalization of neural networks with no need to
guarantee their stability; 2) build more reliable and explainable network
architectures with no need for overparameterization. We refer to it as
"painless" step size adaptation.
