由于其实现的实际加速，过滤器修剪已广泛用于神经网络压缩。迄今为止，大多数现有滤波器修剪工作探索过滤器通过使用通道内信息的重要性。在本文中，从频道间透视开始，我们建议使用信道独立性进行有效的滤波器修剪，该指标测量不同特征映射之间的相关性。较少独立的特征映射被解释为包含较少有用的信息$ / $知识，因此可以修剪其相应的滤波器而不会影响模型容量。我们在过滤器修剪的背景下系统地调查了渠道独立性的量化度量，测量方案和敏感性$ / $可靠性。我们对各种数据集不同模型的评估结果显示了我们方法的卓越性能。值得注意的是，在CIFAR-10数据集上，我们的解决方案可以分别为基线Resnet-56和Resnet-110型号的0.75 \％$ 0.94 \％$ 0.94 \％。模型大小和拖鞋减少了42.8 \％$和$ 47.4 \％$（for Resnet-56）和48.3 \％$ 48.3 \％$ 52.1 \％$（for resnet-110）。在ImageNet DataSet上，我们的方法可以分别达到40.8 \％$ 44.8 \％$ 74.8 \％$ 0.15 \％$ 0.15 \％$ 0.15美元的准确性。该代码可在https://github.com/eclipsess/chip_neurivs2021上获得。

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.

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。

神经网络修剪具有显着性能，可以降低深网络模型的复杂性。最近的网络修剪方法通常集中在网络中删除不重要或冗余过滤器。在本文中，通过探索特征图之间的相似性，我们提出了一种新颖的滤波器修剪方法，中央滤波器（CF），这表明在适当的调整之后滤波器大致等于一组其他滤波器。我们的方法基于发现特征贴图之间的平均相似性的发现，而不管输入图像的数量如何，都会很少变化。基于此发现，我们在特征映射上建立相似性图，并计算每个节点的近密中心以选择中央滤波器。此外，我们设计一种方法，可以在与中央滤波器对应的下一层中直接调整权重，有效地最小化由修剪引起的误差。通过对各种基准网络和数据集的实验，CF产生最先进的性能。例如，对于Reset-56，CF通过去除47.1％的参数来减少约39.7％的絮凝物，甚至在CiFar-10上的精度改善0.33％。通过Googlenet，CF通过去除55.6％的参数来减少大约63.2％的拖鞋，仅在CIFAR-10上的前1个精度下降0.35％的损失。通过resnet-50，CF通过去除36.9％的参数减少约47.9％的拖鞋，仅在Imagenet上的前1个精度下降1.07％。该代码可以在https://github.com/8ubpshlr23/centrter上获得。

The mainstream approach for filter pruning is usually either to force a hard-coded importance estimation upon a computation-heavy pretrained model to select "important" filters, or to impose a hyperparameter-sensitive sparse constraint on the loss objective to regularize the network training. In this paper, we present a novel filter pruning method, dubbed dynamic-coded filter fusion (DCFF), to derive compact CNNs in a computation-economical and regularization-free manner for efficient image classification. Each filter in our DCFF is firstly given an inter-similarity distribution with a temperature parameter as a filter proxy, on top of which, a fresh Kullback-Leibler divergence based dynamic-coded criterion is proposed to evaluate the filter importance. In contrast to simply keeping high-score filters in other methods, we propose the concept of filter fusion, i.e., the weighted averages using the assigned proxies, as our preserved filters. We obtain a one-hot inter-similarity distribution as the temperature parameter approaches infinity. Thus, the relative importance of each filter can vary along with the training of the compact CNN, leading to dynamically changeable fused filters without both the dependency on the pretrained model and the introduction of sparse constraints. Extensive experiments on classification benchmarks demonstrate the superiority of our DCFF over the compared counterparts. For example, our DCFF derives a compact VGGNet-16 with only 72.77M FLOPs and 1.06M parameters while reaching top-1 accuracy of 93.47% on CIFAR-10. A compact ResNet-50 is obtained with 63.8% FLOPs and 58.6% parameter reductions, retaining 75.60% top-1 accuracy on ILSVRC-2012. Our code, narrower models and training logs are available at https://github.com/lmbxmu/DCFF.

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。

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.

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。

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

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。

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.

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。

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％。

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.

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.

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。

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.

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.

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.

彩票票证假设（LTH）表明，密集的模型包含高度稀疏的子网（即获奖门票），可以隔离培训以完全准确。尽管做出了许多激动人心的努力，但仍有一个“常识”很少受到挑战：通过迭代级修剪（IMP）发现了一张获胜的票，因此由此产生的修剪子网仅具有非结构化的稀疏性。这一差距限制了在实践中赢得门票的吸引力，因为高度不规则的稀疏模式在硬件上加速的挑战是挑战性的。同时，直接将结构化修剪替换为非结构化的修剪，以更严重地损害绩效，并且通常无法找到获胜的票。在本文中，我们证明了第一个积极的结果是，总体上可以有效地找到结构上稀疏的获胜票。核心思想是在每一轮（非结构化）IMP之后附加“后处理技术”，以实施结构稀疏的形成。具体而言，我们首先在某些被认为很重要的通道中“重新填充”修剪元素，然后“重新组”非零元素以创建灵活的群体结构模式。我们确定的渠道和团体结构子网都赢得了彩票，并以现有硬件很容易支持的大量推理加速。广泛的实验，在多个网络骨架的不同数据集上进行，一致验证了我们的建议，表明LTH的硬件加速障碍现在已被删除。具体而言，结构上的获胜票最多可获得{64.93％，64.84％，60.23％}的运行时间节省，以{36％〜80％，74％，58％}的稀疏性在{Cifar，cifar，tiny-imageNet，imageNet}上保持可比较的精度。代码在https://github.com/vita-group/structure-lth上。