# Training BatchNorm Only in Neural Architecture Search and Beyond

arXiv: https://arxiv.org/abs/2112.00265 · HTML: https://mlsanity.com/paper/2112.00265/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 68 of its 81 references that are in the map.
- First posted on arXiv 1 Dec 2021.

## Builds on (most cited first, 30 of 68)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Learning Transferable Architectures for Scalable Image Recognition](https://mlsanity.com/paper/1707.07012/) (2017)
- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [Efficient Neural Architecture Search via Parameter Sharing](https://mlsanity.com/paper/1802.03268/) (2018)
- [ProxylessNAS: Direct Neural Architecture Search on Target Task and Hardware](https://mlsanity.com/paper/1812.00332/) (2018)
- [FBNet: Hardware-Aware Efficient ConvNet Design via Differentiable Neural Architecture Search](https://mlsanity.com/paper/1812.03443/) (2018)
- [BOHB: Robust and Efficient Hyperparameter Optimization at Scale](https://mlsanity.com/paper/1807.01774/) (2018)
- [NAS-Bench-201: Extending the Scope of Reproducible Neural Architecture Search](https://mlsanity.com/paper/2001.00326/) (2020)
- [Single Path One-Shot Neural Architecture Search with Uniform Sampling](https://mlsanity.com/paper/1904.00420/) (2019)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [How Does Batch Normalization Help Optimization?](https://mlsanity.com/paper/1805.11604/) (2018)
- [NAS-Bench-101: Towards Reproducible Neural Architecture Search](https://mlsanity.com/paper/1902.09635/) (2019)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [Model compression via distillation and quantization](https://mlsanity.com/paper/1802.05668/) (2018)

## Built on by (most cited first, 2 of 2)

- [Make A Long Image Short: Adaptive Token Length for Vision Transformers](https://mlsanity.com/paper/2307.02092/) (2023)
- [Make A Long Image Short: Adaptive Token Length for Vision Transformers](https://mlsanity.com/paper/2112.01686/) (2021)

## Abstract (arXiv)

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).