### Abstract

Batch Normalization (BN) has become a cornerstone of deep learning across diverse architectures, appearing to help optimization as well as generalization. While the idea makes intuitive sense, theoretical analysis of its effectiveness has been lacking. Here theoretical support is provided for one of its conjectured properties, namely, the ability to allow gradient descent to succeed with less tuning of learning rates. It is shown that even if we fix the learning rate of scale-invariant parameters (e.g., weights of each layer with BN) to a constant (say, 0.3), gradient descent still approaches a stationary point (i.e., a solution where gradient is zero) in the rate of T^{−}^{1}/^{2} in T iterations, asymptotically matching the best bound for gradient descent with well-tuned learning rates. A similar result with convergence rate T^{−}^{1}/^{4} is also shown for stochastic gradient descent.

Original language | English (US) |
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State | Published - Jan 1 2019 |

Event | 7th International Conference on Learning Representations, ICLR 2019 - New Orleans, United States Duration: May 6 2019 → May 9 2019 |

### Conference

Conference | 7th International Conference on Learning Representations, ICLR 2019 |
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Country | United States |

City | New Orleans |

Period | 5/6/19 → 5/9/19 |

### All Science Journal Classification (ASJC) codes

- Education
- Computer Science Applications
- Linguistics and Language
- Language and Linguistics

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## Cite this

*Theoretical analysis of auto rate-tuning by batch normalization*. Paper presented at 7th International Conference on Learning Representations, ICLR 2019, New Orleans, United States.