Layerwise Sparsifying Training and Sequential Learning Strategy for Neural Architecture Adaptation

This work presents a two-stage framework for progressively developing neural architectures to adapt/ generalize well on a given training data set. In the first stage, a manifold-regularized layerwise sparsifying training approach is adopted where a new layer is added each time and trained independently by freezing parameters in the previous layers. In order to constrain the functions that should be learned by each layer, we employ a sparsity regularization term, manifold regularization term and a physics-informed term. We derive the necessary conditions for trainability of a newly added layer and analyze the role of manifold regularization. In the second stage of the Algorithm, a sequential learning process is adopted where a sequence of small networks is employed to extract information from the residual produced in stage I and thereby making robust and more accurate predictions. Numerical investigations with fully connected network on prototype regression problem, and classification problem demonstrate that the proposed approach can outperform adhoc baseline networks. Further, application to physics-informed neural network problems suggests that the method could be employed for creating interpretable hidden layers in a deep network while outperforming equivalent baseline networks.