Net-Trim: Convex Pruning of Deep Neural Networks with Performance Guarantee

We introduce and analyze a new technique for model reduction for deep neural networks. While large networks are theoretically capable of learning arbitrarily complex models, overfitting and model redundancy negatively affects the prediction accuracy and model variance. Our Net-Trim algorithm prunes (sparsifies) a trained network layer-wise, removing connections at each layer by solving a convex optimization program. This program seeks a sparse set of weights at each layer that keeps the layer inputs and outputs consistent with the originally trained model. The algorithms and associated analysis are applicable to neural networks operating with the rectified linear unit (ReLU) as the nonlinear activation.