# Training Deep Neural Networks with Joint Quantization and Pruning of Weights and Activations

arXiv: https://arxiv.org/abs/2110.08271 · HTML: https://mlsanity.com/paper/2110.08271/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 65 references that are in the map.
- First posted on arXiv 15 Oct 2021.

## Builds on (most cited first, 30 of 41)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (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)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks](https://mlsanity.com/paper/1703.10593/) (2017)
- [To prune, or not to prune: exploring the efficacy of pruning for model compression](https://mlsanity.com/paper/1710.01878/) (2017)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [The State of Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1902.09574/) (2019)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [Rethinking ImageNet Pre-training](https://mlsanity.com/paper/1811.08883/) (2018)
- [How Does Batch Normalization Help Optimization?](https://mlsanity.com/paper/1805.11604/) (2018)
- [Pruning and Quantization for Deep Neural Network Acceleration: A Survey](https://mlsanity.com/paper/2101.09671/) (2021)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [Network Trimming: A Data-Driven Neuron Pruning Approach towards Efficient Deep Architectures](https://mlsanity.com/paper/1607.03250/) (2016)
- [Sparse Networks from Scratch: Faster Training without Losing Performance](https://mlsanity.com/paper/1907.04840/) (2019)
- [LSQ+: Improving low-bit quantization through learnable offsets and better initialization](https://mlsanity.com/paper/2004.09576/) (2020)
- [Integer Quantization for Deep Learning Inference: Principles and Empirical Evaluation](https://mlsanity.com/paper/2004.09602/) (2020)

## Built on by (most cited first, 7 of 7)

- [Effective Interplay between Sparsity and Quantization: From Theory to Practice](https://mlsanity.com/paper/2405.20935/) (2024)
- [Efficient Neural Networks for Tiny Machine Learning: A Comprehensive Review](https://mlsanity.com/paper/2311.11883/) (2023)
- [Reducing Computational Complexity of Neural Networks in Optical Channel Equalization: From Concepts to Implementation](https://mlsanity.com/paper/2208.12866/) (2022)
- [Towards Optimal Compression: Joint Pruning and Quantization](https://mlsanity.com/paper/2302.07612/) (2023)
- [QFT: Post-training quantization via fast joint finetuning of all degrees of freedom](https://mlsanity.com/paper/2212.02634/) (2022)
- [FireFly-S: Exploiting Dual-Side Sparsity for Spiking Neural Networks Acceleration with Reconfigurable Spatial Architecture](https://mlsanity.com/paper/2408.15578/) (2024)
- [DASS: Differentiable Architecture Search for Sparse neural networks](https://mlsanity.com/paper/2207.06968/) (2022)

## Abstract (arXiv)

Quantization and pruning are core techniques used to reduce the inference costs of deep neural networks. State-of-the-art quantization techniques are currently applied to both the weights and activations; however, pruning is most often applied to only the weights of the network. In this work, we jointly apply novel uniform quantization and unstructured pruning methods to both the weights and activations of deep neural networks during training. Using our methods, we empirically evaluate the currently accepted prune-then-quantize paradigm across a wide range of computer vision tasks and observe a non-commutative nature when applied to both the weights and activations of deep neural networks. Informed by these observations, we articulate the non-commutativity hypothesis: for a given deep neural network being trained for a specific task, there exists an exact training schedule in which quantization and pruning can be introduced to optimize network performance. We identify that this optimal ordering not only exists, but also varies across discriminative and generative tasks. Using the optimal training schedule within our training framework, we demonstrate increased performance per memory footprint over existing solutions.