通道修剪用于减少卷积神经网络（CNN）中的权重次数。通道修剪去除重量张量的切片，从而使卷积层保持密集。从单层中去除这些重量切片会导致网络层之间的特征图数不匹配。一个简单的解决方案是迫使图层之间的特征映射数量通过从后续层中去除重量切片来匹配。在带有分支的DNN中，这种附加约束变得更加明显，其中需要将多个通道整理在一起以保持网络密度。流行的修剪显着性指标并不能考虑具有分支的DNN中产生的结构依赖性。我们建议多米诺骨牌指标（基于现有的渠道显着性指标）来反映这些结构性约束。我们测试了具有分支的多个网络上基线通道显着性指标的测试。 Domino显着性指标提高了大多数经过测试的网络的修剪率，在CIFAR-10上，Alexnet中最多可提高25％。

The success of CNNs in various applications is accompanied by a significant increase in the computation and parameter storage costs. Recent efforts toward reducing these overheads involve pruning and compressing the weights of various layers without hurting original accuracy. However, magnitude-based pruning of weights reduces a significant number of parameters from the fully connected layers and may not adequately reduce the computation costs in the convolutional layers due to irregular sparsity in the pruned networks. We present an acceleration method for CNNs, where we prune filters from CNNs that are identified as having a small effect on the output accuracy. By removing whole filters in the network together with their connecting feature maps, the computation costs are reduced significantly. In contrast to pruning weights, this approach does not result in sparse connectivity patterns. Hence, it does not need the support of sparse convolution libraries and can work with existing efficient BLAS libraries for dense matrix multiplications. We show that even simple filter pruning techniques can reduce inference costs for VGG-16 by up to 34% and ResNet-110 by up to 38% on CIFAR10 while regaining close to the original accuracy by retraining the networks.

We propose a new formulation for pruning convolutional kernels in neural networks to enable efficient inference. We interleave greedy criteria-based pruning with finetuning by backpropagation-a computationally efficient procedure that maintains good generalization in the pruned network. We propose a new criterion based on Taylor expansion that approximates the change in the cost function induced by pruning network parameters. We focus on transfer learning, where large pretrained networks are adapted to specialized tasks. The proposed criterion demonstrates superior performance compared to other criteria, e.g. the norm of kernel weights or feature map activation, for pruning large CNNs after adaptation to fine-grained classification tasks (Birds-200 and Flowers-102) relaying only on the first order gradient information. We also show that pruning can lead to more than 10× theoretical reduction in adapted 3D-convolutional filters with a small drop in accuracy in a recurrent gesture classifier. Finally, we show results for the largescale ImageNet dataset to emphasize the flexibility of our approach.

网络压缩对于使深网的效率更高，更快且可推广到低端硬件至关重要。当前的网络压缩方法有两个开放问题：首先，缺乏理论框架来估计最大压缩率；其次，有些层可能会过多地进行，从而导致网络性能大幅下降。为了解决这两个问题，这项研究提出了一种基于梯度矩阵分析方法，以估计最大网络冗余。在最大速率的指导下，开发了一种新颖而有效的层次网络修剪算法，以最大程度地凝结神经元网络结构而无需牺牲网络性能。进行实质性实验以证明新方法修剪几个高级卷积神经网络（CNN）体系结构的功效。与现有的修剪方法相比，拟议的修剪算法实现了最先进的性能。与其他方法相比，在相同或相似的压缩比下，新方法提供了最高的网络预测准确性。

Structural pruning of neural network parameters reduces computation, energy, and memory transfer costs during inference. We propose a novel method that estimates the contribution of a neuron (filter) to the final loss and iteratively removes those with smaller scores. We describe two variations of our method using the first and secondorder Taylor expansions to approximate a filter's contribution. Both methods scale consistently across any network layer without requiring per-layer sensitivity analysis and can be applied to any kind of layer, including skip connections. For modern networks trained on ImageNet, we measured experimentally a high (>93%) correlation between the contribution computed by our methods and a reliable estimate of the true importance. Pruning with the proposed methods leads to an improvement over state-ofthe-art in terms of accuracy, FLOPs, and parameter reduction. On ResNet-101, we achieve a 40% FLOPS reduction by removing 30% of the parameters, with a loss of 0.02% in the top-1 accuracy on ImageNet. Code is available at https://github.com/NVlabs/Taylor_pruning.

结构化修剪是一种降低卷积神经网络成本的流行方法，这是许多计算机视觉任务中最先进的方法。但是，根据体系结构，修剪会引入维数差异，以防止实际减少修剪的网络。为了解决这个问题，我们提出了一种能够采用任何结构化的修剪面膜并生成一个不会遇到这些问题的网络并可以有效利用的网络。我们提供了对解决方案的准确描述，并显示了嵌入式硬件，修剪卷积神经网络的能源消耗和推理时间的增长结果。

In this paper, we introduce a new channel pruning method to accelerate very deep convolutional neural networks. Given a trained CNN model, we propose an iterative two-step algorithm to effectively prune each layer, by a LASSO regression based channel selection and least square reconstruction. We further generalize this algorithm to multi-layer and multi-branch cases. Our method reduces the accumulated error and enhance the compatibility with various architectures. Our pruned VGG-16 achieves the state-of-the-art results by 5× speed-up along with only 0.3% increase of error. More importantly, our method is able to accelerate modern networks like ResNet, Xception and suffers only 1.4%, 1.0% accuracy loss under 2× speedup respectively, which is significant. Code has been made publicly available 1 .

虽然残留连接使训练非常深的神经网络，但由于其多分支拓扑而​​导致在线推断不友好。这鼓励许多研究人员在推动时没有残留连接的情况下设计DNN。例如，repvgg在部署时将多分支拓扑重新参数化为vgg型（单分支）模型，当网络相对较浅时显示出具有很大的性能。但是，RepVGG不能等效地将Reset转换为VGG，因为重新参数化方法只能应用于线性块，并且必须将非线性层（Relu）放在残余连接之外，这导致了有限的表示能力，特别是更深入网络。在本文中，我们的目标是通过在Resblock上的保留和合并（RM）操作等效地纠正此问题，并提出删除Vanilla Reset中的残留连接。具体地，RM操作允许输入特征映射通过块，同时保留其信息，并在每个块的末尾合并所有信息，这可以去除残差而不改变原始输出。作为一个插件方法，RM操作基本上有三个优点：1）其实现使其实现高比率网络修剪。 2）它有助于打破RepVGG的深度限制。 3）与Reset和RepVGG相比，它导致更好的精度速度折衷网络（RMNet）。我们相信RM操作的意识形态可以激发对未来社区的模型设计的许多见解。代码可用：https://github.com/fxmeng/rmnet。

过滤器修剪方法通过去除选定的过滤器来引入结构稀疏性，因此对于降低复杂性特别有效。先前的作品从验证较小规范的过滤器的角度从经验修剪网络中造成了较小的最终结果贡献。但是，此类标准已被证明对过滤器的分布敏感，并且由于修剪后的容量差距是固定的，因此准确性可能很难恢复。在本文中，我们提出了一种称为渐近软簇修剪（ASCP）的新型过滤器修剪方法，以根据过滤器的相似性来识别网络的冗余。首先通过聚类来区分来自参数过度的网络的每个过滤器，然后重建以手动将冗余引入其中。提出了一些聚类指南，以更好地保留特征提取能力。重建后，允许更新过滤器，以消除错误选择的效果。此外，还采用了各种修剪率的衰减策略来稳定修剪过程并改善最终性能。通过逐渐在每个群集中生成更相同的过滤器，ASCP可以通过通道添加操作将其删除，几乎没有准确性下降。 CIFAR-10和Imagenet数据集的广泛实验表明，与许多最新算法相比，我们的方法可以取得竞争性结果。

To reduce the significant redundancy in deep Convolutional Neural Networks (CNNs), most existing methods prune neurons by only considering statistics of an individual layer or two consecutive layers (e.g., prune one layer to minimize the reconstruction error of the next layer), ignoring the effect of error propagation in deep networks. In contrast, we argue that it is essential to prune neurons in the entire neuron network jointly based on a unified goal: minimizing the reconstruction error of important responses in the "final response layer" (FRL), which is the secondto-last layer before classification, for a pruned network to retrain its predictive power. Specifically, we apply feature ranking techniques to measure the importance of each neuron in the FRL, and formulate network pruning as a binary integer optimization problem and derive a closed-form solution to it for pruning neurons in earlier layers. Based on our theoretical analysis, we propose the Neuron Importance Score Propagation (NISP) algorithm to propagate the importance scores of final responses to every neuron in the network. The CNN is pruned by removing neurons with least importance, and then fine-tuned to retain its predictive power. NISP is evaluated on several datasets with multiple CNN models and demonstrated to achieve significant acceleration and compression with negligible accuracy loss.

The deployment of deep convolutional neural networks (CNNs) in many real world applications is largely hindered by their high computational cost. In this paper, we propose a novel learning scheme for CNNs to simultaneously 1) reduce the model size; 2) decrease the run-time memory footprint; and 3) lower the number of computing operations, without compromising accuracy. This is achieved by enforcing channel-level sparsity in the network in a simple but effective way. Different from many existing approaches, the proposed method directly applies to modern CNN architectures, introduces minimum overhead to the training process, and requires no special software/hardware accelerators for the resulting models. We call our approach network slimming, which takes wide and large networks as input models, but during training insignificant channels are automatically identified and pruned afterwards, yielding thin and compact models with comparable accuracy. We empirically demonstrate the effectiveness of our approach with several state-of-the-art CNN models, including VGGNet, ResNet and DenseNet, on various image classification datasets. For VGGNet, a multi-pass version of network slimming gives a 20× reduction in model size and a 5× reduction in computing operations.

当前的深神经网络（DNN）被过度参数化，并在推断每个任务期间使用其大多数神经元连接。然而，人的大脑开发了针对不同任务的专门区域，并通过其神经元连接的一小部分进行推断。我们提出了一种迭代修剪策略，引入了一个简单的重要性评分度量度量，该指标可以停用不重要的连接，解决DNN中的过度参数化并调节射击模式。目的是找到仍然能够以可比精度解决给定任务的最小连接，即更简单的子网。我们在MNIST上实现了LENET体系结构的可比性能，并且与CIFAR-10/100和Tiny-ImageNet上的VGG和Resnet架构的最先进算法相比，参数压缩的性能明显更高。我们的方法对于考虑到ADAM和SGD的两个不同优化器也表现良好。该算法并非旨在在考虑当前的硬件和软件实现时最小化失败，尽管与最新技术相比，该算法的性能合理。

Structured channel pruning has been shown to significantly accelerate inference time for convolution neural networks (CNNs) on modern hardware, with a relatively minor loss of network accuracy. Recent works permanently zero these channels during training, which we observe to significantly hamper final accuracy, particularly as the fraction of the network being pruned increases. We propose Soft Masking for cost-constrained Channel Pruning (SMCP) to allow pruned channels to adaptively return to the network while simultaneously pruning towards a target cost constraint. By adding a soft mask re-parameterization of the weights and channel pruning from the perspective of removing input channels, we allow gradient updates to previously pruned channels and the opportunity for the channels to later return to the network. We then formulate input channel pruning as a global resource allocation problem. Our method outperforms prior works on both the ImageNet classification and PASCAL VOC detection datasets.

在过去几年中，神经网络的性能在越来越多的浮点操作（拖鞋）的成本上显着提高。但是，当计算资源有限时，更多的拖鞋可能是一个问题。作为解决这个问题的尝试，修剪过滤器是一种常见的解决方案，但大多数现有的修剪方法不有效地保持模型精度，因此需要大量的芬降时期。在本文中，我们提出了一种自动修剪方法，该方法学习保存的神经元以保持模型精度，同时将絮凝到预定目标。为了完成这项任务，我们介绍了一种可训练的瓶颈，只需要一个单一的单一时期，只需要一个数据集的25.6％（Cifar-10）或7.49％（ILSVRC2012）来了解哪些过滤器。在各种架构和数据集上的实验表明，该方法不仅可以在修剪后保持精度，而且在FineTuning之后也优越现有方法。我们在Reset-50上达到了52.00％的拖鞋，在ILSVRC2012上的灌溉后的前1个精度为47.51％，最先进的（SOTA）精度为76.63％。代码可用（链接匿名审核）。

While machine learning is traditionally a resource intensive task, embedded systems, autonomous navigation, and the vision of the Internet of Things fuel the interest in resource-efficient approaches. These approaches aim for a carefully chosen trade-off between performance and resource consumption in terms of computation and energy. The development of such approaches is among the major challenges in current machine learning research and key to ensure a smooth transition of machine learning technology from a scientific environment with virtually unlimited computing resources into everyday's applications. In this article, we provide an overview of the current state of the art of machine learning techniques facilitating these real-world requirements. In particular, we focus on deep neural networks (DNNs), the predominant machine learning models of the past decade. We give a comprehensive overview of the vast literature that can be mainly split into three non-mutually exclusive categories: (i) quantized neural networks, (ii) network pruning, and (iii) structural efficiency. These techniques can be applied during training or as post-processing, and they are widely used to reduce the computational demands in terms of memory footprint, inference speed, and energy efficiency. We also briefly discuss different concepts of embedded hardware for DNNs and their compatibility with machine learning techniques as well as potential for energy and latency reduction. We substantiate our discussion with experiments on well-known benchmark datasets using compression techniques (quantization, pruning) for a set of resource-constrained embedded systems, such as CPUs, GPUs and FPGAs. The obtained results highlight the difficulty of finding good trade-offs between resource efficiency and predictive performance.

This paper proposed a Soft Filter Pruning (SFP) method to accelerate the inference procedure of deep Convolutional Neural Networks (CNNs). Specifically, the proposed SFP enables the pruned filters to be updated when training the model after pruning. SFP has two advantages over previous works: (1) Larger model capacity. Updating previously pruned filters provides our approach with larger optimization space than fixing the filters to zero. Therefore, the network trained by our method has a larger model capacity to learn from the training data. (2) Less dependence on the pretrained model. Large capacity enables SFP to train from scratch and prune the model simultaneously. In contrast, previous filter pruning methods should be conducted on the basis of the pre-trained model to guarantee their performance. Empirically, SFP from scratch outperforms the previous filter pruning methods. Moreover, our approach has been demonstrated effective for many advanced CNN architectures. Notably, on ILSCRC-2012, SFP reduces more than 42% FLOPs on ResNet-101 with even 0.2% top-5 accuracy improvement, which has advanced the state-of-the-art. Code is publicly available on GitHub: https://github.com/he-y/softfilter-pruning

卷积神经网络（CNN）具有一定量的参数冗余，滤波器修剪旨在去除冗余滤波器，并提供在终端设备上应用CNN的可能性。但是，以前的作品更加注重设计了滤波器重要性的评估标准，然后缩短了具有固定修剪率的重要滤波器或固定数量，以减少卷积神经网络的冗余。它不考虑为每层预留有多少筛选器是最合理的选择。从这个角度来看，我们通过搜索适当的过滤器（SNF）来提出新的过滤器修剪方法。 SNF专用于搜索每层的最合理的保留过滤器，然后是具有特定标准的修剪过滤器。它可以根据不同的拖鞋定制最合适的网络结构。通过我们的方法进行过滤器修剪导致CIFAR-10的最先进（SOTA）精度，并在Imagenet ILSVRC-2012上实现了竞争性能。基于Reset-56网络，在Top-中增加了0.14％的增加0.14％ 1对CIFAR-10拖出的52.94％的精度为52.94％。在减少68.68％拖鞋时，CiFar-10上的修剪Resnet-110还提高了0.03％的1 0.03％的精度。对于Imagenet，我们将修剪速率设置为52.10％的拖鞋，前1个精度只有0.74％。该代码可以在https://github.com/pk-l/snf上获得。

近年来，深度神经网络在各种应用领域中都有广泛的成功。但是，它们需要重要的计算和内存资源，严重阻碍其部署，特别是在移动设备上或实时应用程序。神经网络通常涉及大量参数，该参数对应于网络的权重。在培训过程中获得的这种参数是用于网络性能的决定因素。但是，它们也非常冗余。修剪方法尤其试图通过识别和移除不相关的重量来减小参数集的大小。在本文中，我们研究了培训策略对修剪效率的影响。考虑和比较了两种培训方式：（1）微调和（2）从头开始。在四个数据集（CIFAR10，CiFAR100，SVHN和CALTECH101）上获得的实验结果和两个不同的CNNS（VGG16和MOBILENET）证明已经在大语料库（例如想象成）上预先培训的网络，然后进行微调特定数据集可以更有效地修剪（高达80％的参数减少），而不是从头开始培训的相同网络。

过滤器修剪的目标是搜索不重要的过滤器以删除以便使卷积神经网络（CNNS）有效而不牺牲过程中的性能。挑战在于找到可以帮助确定每个过滤器关于神经网络的最终输出的重要或相关的信息的信息。在这项工作中，我们分享了我们的观察说，预先训练的CNN的批量标准化（BN）参数可用于估计激活输出的特征分布，而无需处理训练数据。在观察时，我们通过基于预先训练的CNN的BN参数评估每个滤波器的重要性来提出简单而有效的滤波修剪方法。 CiFar-10和Imagenet的实验结果表明，该方法可以在准确性下降和计算复杂性的计算复杂性和降低的折衷方面具有和不进行微调的卓越性能。

卷积神经网络（CNN）已在许多物联网（IoT）设备中应用于多种下游任务。但是，随着边缘设备上的数据量的增加，CNN几乎无法及时完成某些任务，而计算和存储资源有限。最近，过滤器修剪被认为是压缩和加速CNN的有效技术，但是从压缩高维张量的角度来看，现有的方法很少是修剪CNN。在本文中，我们提出了一种新颖的理论，可以在三维张量中找到冗余信息，即量化特征图（QSFM）之间的相似性，并利用该理论来指导滤波器修剪过程。我们在数据集（CIFAR-10，CIFAR-100和ILSVRC-12）上执行QSFM和Edge设备，证明所提出的方法可以在神经网络中找到冗余信息，具有可比的压缩和可耐受的准确性下降。没有任何微调操作，QSFM可以显着压缩CIFAR-56（48.7％的Flops和57.9％的参数），而TOP-1的准确性仅损失0.54％。对于边缘设备的实际应用，QSFM可以将Mobilenet-V2推理速度加速1.53倍，而ILSVRC-12 TOP-1的精度仅损失1.23％。