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 .

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 an efficient and unified framework, namely ThiNet, to simultaneously accelerate and compress CNN models in both training and inference stages. We focus on the filter level pruning, i.e., the whole filter would be discarded if it is less important. Our method does not change the original network structure, thus it can be perfectly supported by any off-the-shelf deep learning libraries. We formally establish filter pruning as an optimization problem, and reveal that we need to prune filters based on statistics information computed from its next layer, not the current layer, which differentiates ThiNet from existing methods. Experimental results demonstrate the effectiveness of this strategy, which has advanced the state-of-the-art. We also show the performance of ThiNet on ILSVRC-12 benchmark. ThiNet achieves 3.31× FLOPs reduction and 16.63× compression on VGG-16, with only 0.52% top-5 accuracy drop. Similar experiments with ResNet-50 reveal that even for a compact network, ThiNet can also reduce more than half of the parameters and FLOPs, at the cost of roughly 1% top-5 accuracy drop. Moreover, the original VGG-16 model can be further pruned into a very small model with only 5.05MB model size, preserving AlexNet level accuracy but showing much stronger generalization ability.

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

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。

Previous works utilized "smaller-norm-less-important" criterion to prune filters with smaller norm values in a convolutional neural network. In this paper, we analyze this norm-based criterion and point out that its effectiveness depends on two requirements that are not always met: (1) the norm deviation of the filters should be large; (2) the minimum norm of the filters should be small. To solve this problem, we propose a novel filter pruning method, namely Filter Pruning via Geometric Median (FPGM), to compress the model regardless of those two requirements. Unlike previous methods, FPGM compresses CNN models by pruning filters with redundancy, rather than those with "relatively less" importance. When applied to two image classification benchmarks, our method validates its usefulness and strengths. Notably, on CIFAR-10, FPGM reduces more than 52% FLOPs on ResNet-110 with even 2.69% relative accuracy improvement. Moreover, on ILSVRC-2012, FPGM reduces more than 42% FLOPs on ResNet-101 without top-5 accuracy drop, which has advanced the state-of-the-art. Code is publicly available on GitHub: https://github.com/he-y/filter-pruning-geometric-median * Corresponding Author. Part of this work was done when Yi Yang was visiting Baidu Research during his Professional Experience Program.

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.

Deploying convolutional neural networks (CNNs) on embedded devices is difficult due to the limited memory and computation resources. The redundancy in feature maps is an important characteristic of those successful CNNs, but has rarely been investigated in neural architecture design. This paper proposes a novel Ghost module to generate more feature maps from cheap operations. Based on a set of intrinsic feature maps, we apply a series of linear transformations with cheap cost to generate many ghost feature maps that could fully reveal information underlying intrinsic features. The proposed Ghost module can be taken as a plug-and-play component to upgrade existing convolutional neural networks. Ghost bottlenecks are designed to stack Ghost modules, and then the lightweight Ghost-Net can be easily established. Experiments conducted on benchmarks demonstrate that the proposed Ghost module is an impressive alternative of convolution layers in baseline models, and our GhostNet can achieve higher recognition performance (e.g. 75.7% top-1 accuracy) than MobileNetV3 with similar computational cost on the ImageNet ILSVRC-2012 classification dataset. Code is available at https: //github.com/huawei-noah/ghostnet.

Network pruning is widely used for reducing the heavy inference cost of deep models in low-resource settings. A typical pruning algorithm is a three-stage pipeline, i.e., training (a large model), pruning and fine-tuning. During pruning, according to a certain criterion, redundant weights are pruned and important weights are kept to best preserve the accuracy. In this work, we make several surprising observations which contradict common beliefs. For all state-of-the-art structured pruning algorithms we examined, fine-tuning a pruned model only gives comparable or worse performance than training that model with randomly initialized weights. For pruning algorithms which assume a predefined target network architecture, one can get rid of the full pipeline and directly train the target network from scratch. Our observations are consistent for multiple network architectures, datasets, and tasks, which imply that: 1) training a large, over-parameterized model is often not necessary to obtain an efficient final model, 2) learned "important" weights of the large model are typically not useful for the small pruned model, 3) the pruned architecture itself, rather than a set of inherited "important" weights, is more crucial to the efficiency in the final model, which suggests that in some cases pruning can be useful as an architecture search paradigm. Our results suggest the need for more careful baseline evaluations in future research on structured pruning methods. We also compare with the "Lottery Ticket Hypothesis" (Frankle & Carbin, 2019), and find that with optimal learning rate, the "winning ticket" initialization as used in Frankle & Carbin (2019) does not bring improvement over random initialization. * Equal contribution. † Work done while visiting UC Berkeley.

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.

Neural network pruning offers a promising prospect to facilitate deploying deep neural networks on resourcelimited devices. However, existing methods are still challenged by the training inefficiency and labor cost in pruning designs, due to missing theoretical guidance of non-salient network components. In this paper, we propose a novel filter pruning method by exploring the High Rank of feature maps (HRank). Our HRank is inspired by the discovery that the average rank of multiple feature maps generated by a single filter is always the same, regardless of the number of image batches CNNs receive. Based on HRank, we develop a method that is mathematically formulated to prune filters with low-rank feature maps. The principle behind our pruning is that low-rank feature maps contain less information, and thus pruned results can be easily reproduced. Besides, we experimentally show that weights with high-rank feature maps contain more important information, such that even when a portion is not updated, very little damage would be done to the model performance. Without introducing any additional constraints, HRank leads to significant improvements over the state-of-the-arts in terms of FLOPs and parameters reduction, with similar accuracies. For example, with ResNet-110, we achieve a 58.2%-FLOPs reduction by removing 59.2% of the parameters, with only a small loss of 0.14% in top-1 accuracy on CIFAR-10. With Res-50, we achieve a 43.8%-FLOPs reduction by removing 36.7% of the parameters, with only a loss of 1.17% in the top-1 accuracy on ImageNet. The codes can be available at https://github.com/lmbxmu/HRank.

Model compression is a critical technique to efficiently deploy neural network models on mobile devices which have limited computation resources and tight power budgets. Conventional model compression techniques rely on hand-crafted heuristics and rule-based policies that require domain experts to explore the large design space trading off among model size, speed, and accuracy, which is usually sub-optimal and time-consuming. In this paper, we propose AutoML for Model Compression (AMC) which leverage reinforcement learning to provide the model compression policy. This learning-based compression policy outperforms conventional rule-based compression policy by having higher compression ratio, better preserving the accuracy and freeing human labor. Under 4× FLOPs reduction, we achieved 2.7% better accuracy than the handcrafted model compression policy for VGG-16 on ImageNet. We applied this automated, push-the-button compression pipeline to MobileNet and achieved 1.81× speedup of measured inference latency on an Android phone and 1.43× speedup on the Titan XP GPU, with only 0.1% loss of ImageNet Top-1 accuracy.

We introduce an extremely computation-efficient CNN architecture named ShuffleNet, which is designed specially for mobile devices with very limited computing power (e.g., 10-150 MFLOPs). The new architecture utilizes two new operations, pointwise group convolution and channel shuffle, to greatly reduce computation cost while maintaining accuracy. Experiments on ImageNet classification and MS COCO object detection demonstrate the superior performance of ShuffleNet over other structures, e.g. lower top-1 error (absolute 7.8%) than recent MobileNet [12] on Ima-geNet classification task, under the computation budget of 40 MFLOPs. On an ARM-based mobile device, ShuffleNet achieves ∼13× actual speedup over AlexNet while maintaining comparable accuracy.

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。

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％。

Low-rankness plays an important role in traditional machine learning, but is not so popular in deep learning. Most previous low-rank network compression methods compress the networks by approximating pre-trained models and re-training. However, the optimal solution in the Euclidean space may be quite different from the one in the low-rank manifold. A well-pre-trained model is not a good initialization for the model with low-rank constraints. Thus, the performance of a low-rank compressed network degrades significantly. Compared to other network compression methods such as pruning, low-rank methods attracts less attention in recent years. In this paper, we devise a new training method, low-rank projection with energy transfer (LRPET), that trains low-rank compressed networks from scratch and achieves competitive performance. First, we propose to alternately perform stochastic gradient descent training and projection onto the low-rank manifold. Compared to re-training on the compact model, this enables full utilization of model capacity since solution space is relaxed back to Euclidean space after projection. Second, the matrix energy (the sum of squares of singular values) reduction caused by projection is compensated by energy transfer. We uniformly transfer the energy of the pruned singular values to the remaining ones. We theoretically show that energy transfer eases the trend of gradient vanishing caused by projection. Third, we propose batch normalization (BN) rectification to cut off its effect on the optimal low-rank approximation of the weight matrix, which further improves the performance. Comprehensive experiments on CIFAR-10 and ImageNet have justified that our method is superior to other low-rank compression methods and also outperforms recent state-of-the-art pruning methods. Our code is available at https://github.com/BZQLin/LRPET.

由于存储器和计算资源有限，部署在移动设备上的卷积神经网络（CNNS）是困难的。我们的目标是通过利用特征图中的冗余来设计包括CPU和GPU的异构设备的高效神经网络，这很少在神经结构设计中进行了研究。对于类似CPU的设备，我们提出了一种新颖的CPU高效的Ghost（C-Ghost）模块，以生成从廉价操作的更多特征映射。基于一组内在的特征映射，我们使用廉价的成本应用一系列线性变换，以生成许多幽灵特征图，可以完全揭示内在特征的信息。所提出的C-Ghost模块可以作为即插即用组件，以升级现有的卷积神经网络。 C-Ghost瓶颈旨在堆叠C-Ghost模块，然后可以轻松建立轻量级的C-Ghostnet。我们进一步考虑GPU设备的有效网络。在建筑阶段的情况下，不涉及太多的GPU效率（例如，深度明智的卷积），我们建议利用阶段明智的特征冗余来制定GPU高效的幽灵（G-GHOST）阶段结构。舞台中的特征被分成两个部分，其中使用具有较少输出通道的原始块处理第一部分，用于生成内在特征，另一个通过利用阶段明智的冗余来生成廉价的操作。在基准测试上进行的实验证明了所提出的C-Ghost模块和G-Ghost阶段的有效性。 C-Ghostnet和G-Ghostnet分别可以分别实现CPU和GPU的准确性和延迟的最佳权衡。代码可在https://github.com/huawei-noah/cv-backbones获得。

在物联网（IoT）支持的网络边缘（IOT）上的人工智能（AI）的最新进展已通过启用低延期性和计算效率来实现多种应用程序（例如智能农业，智能医院和智能工厂）的优势情报。但是，部署最先进的卷积神经网络（CNN），例如VGG-16和在资源约束的边缘设备上的重新连接，由于其大量参数和浮点操作（Flops），因此实际上是不可行的。因此，将网络修剪作为一种模型压缩的概念正在引起注意在低功率设备上加速CNN。结构化或非结构化的最先进的修剪方法都不认为卷积层表现出的复杂性的不同基本性质，并遵循训练放回训练的管道，从而导致其他计算开销。在这项工作中，我们通过利用CNN的固有层层级复杂性来提出一种新颖和计算高效的修剪管道。与典型的方法不同，我们提出的复杂性驱动算法根据其对整体网络复杂性的贡献选择了特定层用于滤波器。我们遵循一个直接训练修剪模型并避免计算复杂排名和微调步骤的过程。此外，我们定义了修剪的三种模式，即参数感知（PA），拖网（FA）和内存感知（MA），以引入CNN的多功能压缩。我们的结果表明，我们的方法在准确性和加速方面的竞争性能。最后，我们提出了不同资源和准确性之间的权衡取舍，这对于开发人员在资源受限的物联网环境中做出正确的决策可能会有所帮助。

重量修剪是一种有效的模型压缩技术，可以解决在移动设备上实现实时深神经网络（DNN）推断的挑战。然而，由于精度劣化，难以利用硬件加速度，以及某些类型的DNN层的限制，难以降低的应用方案具有有限的应用方案。在本文中，我们提出了一般的细粒度的结构化修剪方案和相应的编译器优化，适用于任何类型的DNN层，同时实现高精度和硬件推理性能。随着使用我们的编译器优化所支持的不同层的灵活性，我们进一步探讨了确定最佳修剪方案的新问题，了解各种修剪方案的不同加速度和精度性能。两个修剪方案映射方法，一个是基于搜索，另一个是基于规则的，建议自动推导出任何给定DNN的每层的最佳修剪规则和块大小。实验结果表明，我们的修剪方案映射方法，以及一般细粒化结构修剪方案，优于最先进的DNN优化框架，最高可达2.48 $ \ times $和1.73 $ \ times $ DNN推理加速在CiFar-10和Imagenet DataSet上没有准确性损失。

High demand for computation resources severely hinders deployment of large-scale Deep Neural Networks (DNN) in resource constrained devices. In this work, we propose a Structured Sparsity Learning (SSL) method to regularize the structures (i.e., filters, channels, filter shapes, and layer depth) of DNNs. SSL can: (1) learn a compact structure from a bigger DNN to reduce computation cost; (2) obtain a hardware-friendly structured sparsity of DNN to efficiently accelerate the DNN's evaluation. Experimental results show that SSL achieves on average 5.1× and 3.1× speedups of convolutional layer computation of AlexNet against CPU and GPU, respectively, with off-the-shelf libraries. These speedups are about twice speedups of non-structured sparsity; (3) regularize the DNN structure to improve classification accuracy. The results show that for CIFAR-10, regularization on layer depth can reduce 20 layers of a Deep Residual Network (ResNet) to 18 layers while improve the accuracy from 91.25% to 92.60%, which is still slightly higher than that of original ResNet with 32 layers. For AlexNet, structure regularization by SSL also reduces the error by ∼ 1%. Our source code can be found at https://github.com/wenwei202/caffe/tree/scnn