# Training Convolutional ReLU Neural Networks in Polynomial Time: Exact Convex Optimization Formulations

@article{Ergen2020TrainingCR, title={Training Convolutional ReLU Neural Networks in Polynomial Time: Exact Convex Optimization Formulations}, author={Tolga Ergen and Mert Pilanci}, journal={ArXiv}, year={2020}, volume={abs/2006.14798} }

We study training of Convolutional Neural Networks (CNNs) with ReLU activations and introduce exact convex optimization formulations with a polynomial complexity with respect to the number of data samples, the number of neurons and data dimension. Particularly, we develop a convex analytic framework utilizing semi-infinite duality to obtain equivalent convex optimization problems for several CNN architectures. We first prove that two-layer CNNs can be globally optimized via an l2 norm… CONTINUE READING

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