# Dynamical Isometry: The Missing Ingredient for Neural Network Pruning

arXiv: https://arxiv.org/abs/2105.05916 · HTML: https://mlsanity.com/paper/2105.05916/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 55 references that are in the map.
- First posted on arXiv 12 May 2021.

## Builds on (most cited first, 30 of 35)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [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)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Learning Efficient Convolutional Networks through Network Slimming](https://mlsanity.com/paper/1708.06519/) (2017)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [What is the State of Neural Network Pruning?](https://mlsanity.com/paper/2003.03033/) (2020)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [The State of Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1902.09574/) (2019)
- [Picking Winning Tickets Before Training by Preserving Gradient Flow](https://mlsanity.com/paper/2002.07376/) (2020)
- [ThiNet: A Filter Level Pruning Method for Deep Neural Network Compression](https://mlsanity.com/paper/1707.06342/) (2017)
- [Efficient Processing of Deep Neural Networks: A Tutorial and Survey](https://mlsanity.com/paper/1703.09039/) (2017)
- [Comparing Rewinding and Fine-tuning in Neural Network Pruning](https://mlsanity.com/paper/2003.02389/) (2020)
- [What's Hidden in a Randomly Weighted Neural Network?](https://mlsanity.com/paper/1911.13299/) (2019)
- [Pruning Neural Networks at Initialization: Why are We Missing the Mark?](https://mlsanity.com/paper/2009.08576/) (2020)
- [Data-Driven Sparse Structure Selection for Deep Neural Networks](https://mlsanity.com/paper/1707.01213/) (2017)
- [Dynamical Isometry and a Mean Field Theory of CNNs: How to Train 10,000-Layer Vanilla Convolutional Neural Networks](https://mlsanity.com/paper/1806.05393/) (2018)
- [All you need is a good init](https://mlsanity.com/paper/1511.06422/) (2015)
- [EigenDamage: Structured Pruning in the Kronecker-Factored Eigenbasis](https://mlsanity.com/paper/1905.05934/) (2019)
- [Neural Pruning via Growing Regularization](https://mlsanity.com/paper/2012.09243/) (2020)
- [A Signal Propagation Perspective for Pruning Neural Networks at Initialization](https://mlsanity.com/paper/1906.06307/) (2019)

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

- [Trainability Preserving Neural Pruning](https://mlsanity.com/paper/2207.12534/) (2022)
- [EPSD: Early Pruning with Self-Distillation for Efficient Model Compression](https://mlsanity.com/paper/2402.00084/) (2024)

## Abstract (arXiv)

Several recent works [40, 24] observed an interesting phenomenon in neural network pruning: A larger finetuning learning rate can improve the final performance significantly. Unfortunately, the reason behind it remains elusive up to date. This paper is meant to explain it through the lens of dynamical isometry [42]. Specifically, we examine neural network pruning from an unusual perspective: pruning as initialization for finetuning, and ask whether the inherited weights serve as a good initialization for the finetuning? The insights from dynamical isometry suggest a negative answer. Despite its critical role, this issue has not been well-recognized by the community so far. In this paper, we will show the understanding of this problem is very important -- on top of explaining the aforementioned mystery about the larger finetuning rate, it also unveils the mystery about the value of pruning [5, 30]. Besides a clearer theoretical understanding of pruning, resolving the problem can also bring us considerable performance benefits in practice.