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We introduce a mixed integer program (MIP) for assigning importance scores toeach neuron in deep neural network architectures which is guided by the impactof their simultaneous pruning on the main learning task of the network. Bycarefully devising the objective function of the MIP, we drive the solver tominimize the number of critical neurons (i.e., with high importance score) thatneed to be kept for maintaining the overall accuracy of the trained neuralnetwork. Further, the proposed formulation generalizes the recently consideredlottery ticket optimization by identifying multiple "lucky" sub-networksresulting in optimized architecture that not only performs well on a singledataset, but also generalizes across multiple ones upon retraining of networkweights. Finally, we present a scalable implementation of our method bydecoupling the importance scores across layers using auxiliary networks. Wedemonstrate the ability of our formulation to prune neural networks withmarginal loss in accuracy and generalizability on popular datasets andarchitectures.

Identifying Critical Neurons in ANN Architectures using Mixed Integer Programming