Before revision:  Most per-parameter adaptive learning methods invented for machine learning cannot learn reasonable parameters for sparse-interaction systems. A modified Adam (ModAdam) method is invented to make step-size proportional to the partial derivative for sparse couplings and to use a soft thresholding function for group L_1.
After revision:  The Adam method is modified to make stepsize proportional to the partial derivative for sparse couplings and to use a soft thresholding function for group L_1.