With the development of deep neural networks, the size of network models becomes larger and larger. Model compression has become an urgent need for deploying these network models to mobile or embedded devices. Model quantization is a representative model compression technique. Although a lot of quantization methods have been proposed, many of them suffer from a high quantization error caused by a long-tail distribution of network weights. In this paper, we propose a novel quantization method, called weight normalization based quantization (WNQ), for model compression. WNQ adopts weight normalization to avoid the long-tail distribution of network weights and subsequently reduces the quantization error. Experiments on CIFAR-100 and ImageNet show that WNQ can outperform other baselines to achieve state-of-the-art performance.
Besides model quantization methods, pruning @cite_31 @cite_15 @cite_28 @cite_30 @cite_38 , tensor decomposition @cite_36 @cite_22 @cite_35 and knowledge distillation @cite_29 @cite_11 are also widely used techniques for model compression. We do not discuss the details about other techniques except quantization, because the focus of this paper is on quantization.
@cite_30 @cite_38 @cite_35 @cite_22 @cite_15 @cite_28 @cite_36 @cite_29 @cite_31 @cite_11
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In recent years considerable research efforts have been devoted to compression techniques of convolutional neural networks (CNNs). Many works so far have focused on CNN connection pruning methods which produce sparse parameter tensors in convolutional or fully-connected layers. It has been demonstrated in several studies that even simple methods can effectively eliminate connections of a CNN. However, since these methods make parameter tensors just sparser but no smaller, the compression may not transfer directly to acceleration without support from specially designed hardware. In this paper, we propose an iterative approach named Auto-balanced Filter Pruning, where we pre-train the network in an innovative auto-balanced way to transfer the representational capacity of its convolutional layers to a fraction of the filters, prune the redundant ones, then re-train it to restore the accuracy. In this way, a smaller version of the original network is learned and the floating-point operations (FLOPs) are reduced. By applying this method on several common CNNs, we show that a large portion of the filters can be discarded without obvious accuracy drop, leading to significant reduction of computational burdens. Concretely, we reduce the inference cost of LeNet-5 on MNIST, VGG-16 and ResNet-56 on CIFAR-10 by 95.1 , 79.7 and 60.9 , respectively. Copyright © 2018, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. This paper presents incremental network quantization (INQ), a novel method, targeting to efficiently convert any pre-trained full-precision convolutional neural network (CNN) model into a low-precision version whose weights are constrained to be either powers of two or zero. Unlike existing methods which are struggled in noticeable accuracy loss, our INQ has the potential to resolve this issue, as benefiting from two innovations. On one hand, we introduce three interdependent operations, namely weight partition, group-wise quantization and re-training. A well-proven measure is employed to divide the weights in each layer of a pre-trained CNN model into two disjoint groups. The weights in the first group are responsible to form a low-precision base, thus they are quantized by a variable-length encoding method. The weights in the other group are responsible to compensate for the accuracy loss from the quantization, thus they are the ones to be re-trained. On the other hand, these three operations are repeated on the latest re-trained group in an iterative manner until all the weights are converted into low-precision ones, acting as an incremental network quantization and accuracy enhancement procedure. Extensive experiments on the ImageNet classification task using almost all known deep CNN architectures including AlexNet, VGG-16, GoogleNet and ResNets well testify the efficacy of the proposed method. Specifically, at 5-bit quantization (a variable-length encoding: 1 bit for representing zero value, and the remaining 4 bits represent at most 16 different values for the powers of two), our models have improved accuracy than the 32-bit floating-point references. Taking ResNet-18 as an example, we further show that our quantized models with 4-bit, 3-bit and 2-bit ternary weights have improved or very similar accuracy against its 32-bit floating-point baseline. Besides, impressive results with the combination of network pruning and INQ are also reported. We believe that our method sheds new insights on how to make deep CNNs to be applicable on mobile or embedded devices. The code will be made publicly available. We rigorously evaluate three state-of-the-art techniques for inducing sparsity in deep neural networks on two large-scale learning tasks: Transformer trained on WMT 2014 English-to-German, and ResNet-50 trained on ImageNet. Across thousands of experiments, we demonstrate that complex techniques (, 2017; , 2017b) shown to yield high compression rates on smaller datasets perform inconsistently, and that simple magnitude pruning approaches achieve comparable or better results. Additionally, we replicate the experiments performed by (Frankle & Carbin, 2018) and (, 2018) at scale and show that unstructured sparse architectures learned through pruning cannot be trained from scratch to the same test set performance as a model trained with joint sparsification and optimization. Together, these results highlight the need for large-scale benchmarks in the field of model compression. We open-source our code, top performing model checkpoints, and results of all hyperparameter configurations to establish rigorous baselines for future work on compression and sparsification. Despite the state-of-the-art accuracy of Deep Neural Networks (DNN) in various classification problems, their deployment onto resource constrained edge computing devices remains challenging, due to their large size and complexity. Several recent studies have reported remarkable results in reducing this complexity through quantization of DNN models. However, these studies usually do not consider the change in loss when performing quantization, nor do they take the disparate importance of DNN connections to the accuracy into account. We address these issues in this paper by proposing a new method, called adaptive quantization, which simplifies a trained DNN model by finding a unique, optimal precision for each connection weight such that the increase in loss is minimized. The optimization problem at the core of this method iteratively uses the loss function gradient to determine an error margin for each weight and assign it a precision accordingly. Since this problem uses linear functions, it is computationally cheap and, as we will show, has a closed-form approximate solution. Experiments on MNIST, CIFAR, and SVHN datasets showed that the proposed method can achieve near or better than state-of-the-art reduction in model size with similar error rate. Furthermore, it can achieve compressions close to floating-point model compression methods without loss of accuracy.