# Learning Sparse Low-Precision Neural Networks With Learnable Regularization

arXiv: https://arxiv.org/abs/1809.00095 · HTML: https://mlsanity.com/paper/1809.00095/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Sep 2018.

## Built on by (most cited first, 4 of 4)

- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Towards Efficient Full 8-bit Integer DNN Online Training on Resource-limited Devices without Batch Normalization](https://mlsanity.com/paper/2105.13890/) (2021)
- [Efficient Visual Recognition with Deep Neural Networks: A Survey on Recent Advances and New Directions](https://mlsanity.com/paper/2108.13055/) (2021)
- [Arch-Net: Model Distillation for Architecture Agnostic Model Deployment](https://mlsanity.com/paper/2111.01135/) (2021)

## Abstract (arXiv)

We consider learning deep neural networks (DNNs) that consist of low-precision weights and activations for efficient inference of fixed-point operations. In training low-precision networks, gradient descent in the backward pass is performed with high-precision weights while quantized low-precision weights and activations are used in the forward pass to calculate the loss function for training. Thus, the gradient descent becomes suboptimal, and accuracy loss follows. In order to reduce the mismatch in the forward and backward passes, we utilize mean squared quantization error (MSQE) regularization. In particular, we propose using a learnable regularization coefficient with the MSQE regularizer to reinforce the convergence of high-precision weights to their quantized values. We also investigate how partial L2 regularization can be employed for weight pruning in a similar manner. Finally, combining weight pruning, quantization, and entropy coding, we establish a low-precision DNN compression pipeline. In our experiments, the proposed method yields low-precision MobileNet and ShuffleNet models on ImageNet classification with the state-of-the-art compression ratios of 7.13 and 6.79, respectively. Moreover, we examine our method for image super resolution networks to produce 8-bit low-precision models at negligible performance loss.