# Learning Sparse Low-Precision Neural Networks With Learnable Regularization Source: [Learning Sparse Low-Precision Neural Networks With Learnable Regularization]() Collection index: [llms.txt]() Data updated: 2025-10-25T22:18:12.808Z Authors: Yoojin Choi, Mostafa El-Khamy, Jungwon Lee Published: 2018-09-01T01:28:21.000Z ## Abstract 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Image Classification on ImageNet (val) (Top-1/Top-5 Accuracy)](): Image Classification; ImageNet (val); Top-1 Accuracy: 65.8. - [Image Classification on ImageNet (val)](): Image Classification; ImageNet (val); Top-1 Acc: 68.1. - [Neural Architecture Search on ImageNet (train)](): Neural Architecture Search; ImageNet (train); GPU Days (GPUD): not recorded. ## Original sources and implementation [Original paper]() [PDF]()