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Deep learning has achieved state-of-the-art accuracies on several computer vision tasks. However, the computational and energy requirements associated with training such deep neural networks can be quite high. In this paper, we propose a cumulative training strategy with Net2Net transformation that achieves training computational efficiency without incurring large accuracy loss, in comparison to a model trained from scratch. We achieve this by first training a small network (with lesser parameters) on a small subset of the original dataset, and then gradually expanding the network using Net2Net transformation to train incrementally on larger subsets of the dataset. This incremental training strategy with Net2Net utilizes function-preserving transformations that transfers knowledge from each previous small network to the next larger network, thereby, reducing the overall training complexity. Our experiments demonstrate that compared with training from scratch, cumulative training yields ~2x reduction in computational complexity for training TinyImageNet using VGG19 at iso-accuracy. Besides training efficiency, a key advantage of our cumulative training strategy is that we can perform pruning during Net2Net expansion to obtain a final network with optimal configuration (~0.4x lower inference compute complexity) compared to conventional training from scratch. We also demonstrate that the final network obtained from cumulative training yields better generalization performance and noise robustness. Further, we show that mutual inference from all the networks created with cumulative Net2Net expansion enables improved adversarial input detection.