We implement training of neural networks in secure multi-partycomputation (MPC) using quantization commonly used in said setting. Weare the first to present an MNIST classifier purely trained in MPCthat comes within 0.2 percent of the accuracy of the sameconvolutional neural network trained via plaintext computation. Moreconcretely, we have trained a network with two convolutional and twodense layers to 99.2% accuracy in 3.5 hours (under one hour for 99%accuracy). We have also implemented AlexNet for CIFAR-10, whichconverges in a few hours. We develop novel protocols forexponentiation and inverse square root. Finally, we presentexperiments in a range of MPC security models for up to ten parties,both with honest and dishonest majority as well as semi-honest andmalicious security.