Earlier methods for Neural Architecture Search were computationally expensive. Recently proposed Differentiable Neural Architecture Search algorithms such as DARTS can effectively speed up the computation. However, the current formulation relies on a relaxation of the original problem that leads to unstable and suboptimal solutions. We argue that these problems are caused by three fundamental reasons: (1) The difficulty of bi-level optimization; (2) Multicollinearity of correlated operations such as max pooling and average pooling; (3) The discrepancy between the optimization complexity of the search stage and the final training. In this paper, we propose a grouped variable pruning algorithm based on one-level optimization, which leads to a more stable and consistent optimization solution for differentiable NAS. Extensive experiments verify the superiority of the proposed method regarding both accuracy and stability. Our new approach obtains state-of-the-art accuracy on CIFAR-10, CIFAR-100 and ImageNet.

The goal of this paper is to study why stochastic gradient descent (SGD) is efficient for neural networks, and how neural net design affects SGD. In particular, we investigate how overparameterization -- an increase in the number of parameters beyond the number of training data -- affects the dynamics of SGD. We introduce a simple concept called gradient confusion. When confusion is high, stochastic gradients produced by different data samples may be negatively correlated, slowing down convergence. But when gradient confusion is low, we show that SGD has better convergence properties than predicted by classical theory. Using theoretical and experimental results, we study how overparameterization affects gradient confusion, and thus the convergence of SGD, on linear models and neural networks. We show that increasing the number of parameters of linear models or increasing the width of neural networks leads to lower gradient confusion, and thus faster and easier model training. We also show how overparameterization by increasing the depth of neural networks results in higher gradient confusion, making deeper models harder to train. Finally, we observe empirically that techniques like batch normalization and skip connections reduce gradient confusion, which helps reduce the training burden of deep networks.