Abstract We develop new theoretical results on matrix perturbation to shed light the impact of architecture performance a deep network. In particular, we explain analytically what learning practitioners have long observed empirically: parameters some architectures (e.g., residual networks, ResNets, and Dense DenseNets) are easier optimize than others convolutional ConvNets). Building our earlie...

n this paper, we apply picard’s iteration method followed by adomian decomposition method to solve a nonlinear singular cauchy problem of euler- poisson- darboux equation. the solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by carroll and showalter (1976)in the solution of singular cauchy problem.