  This work investigates the usage of batch normalization in neural
architecture search (NAS). Specifically, Frankle et al. find that training
BatchNorm only can achieve nontrivial performance. Furthermore, Chen et al.
claim that training BatchNorm only can speed up the training of the one-shot
NAS supernet over ten times. Critically, there is no effort to understand 1)
why training BatchNorm only can find the perform-well architectures with the
reduced supernet-training time, and 2) what is the difference between the
train-BN-only supernet and the standard-train supernet. We begin by showing
that the train-BN-only networks converge to the neural tangent kernel regime,
obtain the same training dynamics as train all parameters theoretically. Our
proof supports the claim to train BatchNorm only on supernet with less training
time. Then, we empirically disclose that train-BN-only supernet provides an
advantage on convolutions over other operators, cause unfair competition
between architectures. This is due to only the convolution operator being
attached with BatchNorm. Through experiments, we show that such unfairness
makes the search algorithm prone to select models with convolutions. To solve
this issue, we introduce fairness in the search space by placing a BatchNorm
layer on every operator. However, we observe that the performance predictor in
Chen et al. is inapplicable on the new search space. To this end, we propose a
novel composite performance indicator to evaluate networks from three
perspectives: expressivity, trainability, and uncertainty, derived from the
theoretical property of BatchNorm. We demonstrate the effectiveness of our
approach on multiple NAS-benchmarks (NAS-Bench101, NAS-Bench-201) and search
spaces (DARTS search space and MobileNet search space).

Machine Learning;Computer Vision and Pattern Recognition