We develop an algorithm for systematic design of a large artificial neural
network using a progression property. We find that some non-linear functions,
such as the rectifier linear unit and its derivatives, hold the property. The
systematic design addresses the choice of network size and regularization of
parameters. The number of nodes and layers in network increases in progression
with the objective of consistently reducing an appropriate cost. Each layer is
optimized at a time, where appropriate parameters are learned using convex
optimization. Regularization parameters for convex optimization do not need a
significant manual effort for tuning. We also use random instances for some
weight matrices, and that helps to reduce the number of parameters we learn.
The developed network is expected to show good generalization power due to
appropriate regularization and use of random weights in the layers. This
expectation is verified by extensive experiments for classification and
regression problems, using standard databases.