在机器学习中，人工神经网络（ANN）是一种非常强大的工具，广泛用于许多应用程序。通常，所选的（深）架构包括许多层，因此包括大量参数，这使培训，存储和推理变得昂贵。这激发了有关将原始网络压缩为较小网络的一系列研究，而不会过分牺牲性能。在许多提出的压缩方法中，最受欢迎的方法之一是\ emph {Pruning}，该方法的整个元素（链接，节点，通道，\ ldots）和相应的权重删除。由于该问题的性质本质上是组合的（要修剪的要素，什么不是），因此我们提出了一种基于操作研究工具的新修剪方法。我们从为该问题的天然混合组编程模型开始，然后使用透视化重新制作技术来增强其持续放松。从该重新制定中投射指标变量产生了一个新的正则化术语，我们称之为结构化的正则化，从而导致初始体系结构的结构化修剪。我们测试了应用于CIFAR-10，CIFAR-100和Imagenet数据集的一些重新NET架构，获得了竞争性能W.R.T.

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.

修剪深度神经网络的现有方法专注于去除训练有素的网络的不必要参数，然后微调模型，找到恢复训练模型的初始性能的良好解决方案。与其他作品不同，我们的方法特别注意通过修剪神经元的压缩模型和推理计算时间的解决方案的质量。通过探索Hessian的光谱半径，所提出的算法通过探索Hessian的光谱半径来指示压缩模型的参数，这导致了更好地推广了未经看涨的数据。此外，该方法不适用于预先训练的网络，并同时执行训练和修剪。我们的结果表明，它改善了神经元压缩的最先进的结果。该方法能够在不同神经网络模型上实现具有小精度下降的非常小的网络。

由于稀疏神经网络通常包含许多零权重，因此可以在不降低网络性能的情况下潜在地消除这些不必要的网络连接。因此，设计良好的稀疏神经网络具有显着降低拖鞋和计算资源的潜力。在这项工作中，我们提出了一种新的自动修剪方法 - 稀疏连接学习（SCL）。具体地，重量被重新参数化为可培训权重变量和二进制掩模的元素方向乘法。因此，由二进制掩模完全描述网络连接，其由单位步进函数调制。理论上，从理论上证明了使用直通估计器（STE）进行网络修剪的基本原理。这一原则是STE的代理梯度应该是积极的，确保掩模变量在其最小值处收敛。在找到泄漏的Relu后，SoftPlus和Identity Stes可以满足这个原理，我们建议采用SCL的身份STE以进行离散面膜松弛。我们发现不同特征的面具梯度非常不平衡，因此，我们建议将每个特征的掩模梯度标准化以优化掩码变量训练。为了自动训练稀疏掩码，我们将网络连接总数作为我们的客观函数中的正则化术语。由于SCL不需要由网络层设计人员定义的修剪标准或超级参数，因此在更大的假设空间中探讨了网络，以实现最佳性能的优化稀疏连接。 SCL克服了现有自动修剪方法的局限性。实验结果表明，SCL可以自动学习并选择各种基线网络结构的重要网络连接。 SCL培训的深度学习模型以稀疏性，精度和减少脚波特的SOTA人类设计和自动修剪方法训练。

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.

网络修剪是一种广泛使用的技术，用于有效地压缩深神经网络，几乎没有在推理期间在性能下降低。迭代幅度修剪（IMP）是由几种迭代训练和修剪步骤组成的网络修剪的最熟悉的方法之一，其中在修剪后丢失了大量网络的性能，然后在随后的再培训阶段中恢复。虽然常用为基准参考，但经常认为a）通过不将稀疏纳入训练阶段来达到次优状态，b）其全球选择标准未能正确地确定最佳层面修剪速率和c）其迭代性质使它变得缓慢和不竞争。根据最近提出的再培训技术，我们通过严格和一致的实验来调查这些索赔，我们将Impr到培训期间的训练算法进行比较，评估其选择标准的建议修改，并研究实际需要的迭代次数和总培训时间。我们发现IMP与SLR进行再培训，可以优于最先进的修剪期间，没有或仅具有很少的计算开销，即全局幅度选择标准在很大程度上具有更复杂的方法，并且只有几个刷新时期在实践中需要达到大部分稀疏性与IMP的诽谤 - 与性能权衡。我们的目标既可以证明基本的进攻已经可以提供最先进的修剪结果，甚至优于更加复杂或大量参数化方法，也可以为未来的研究建立更加现实但易于可实现的基线。

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。

Pruning refers to the elimination of trivial weights from neural networks. The sub-networks within an overparameterized model produced after pruning are often called Lottery tickets. This research aims to generate winning lottery tickets from a set of lottery tickets that can achieve similar accuracy to the original unpruned network. We introduce a novel winning ticket called Cyclic Overlapping Lottery Ticket (COLT) by data splitting and cyclic retraining of the pruned network from scratch. We apply a cyclic pruning algorithm that keeps only the overlapping weights of different pruned models trained on different data segments. Our results demonstrate that COLT can achieve similar accuracies (obtained by the unpruned model) while maintaining high sparsities. We show that the accuracy of COLT is on par with the winning tickets of Lottery Ticket Hypothesis (LTH) and, at times, is better. Moreover, COLTs can be generated using fewer iterations than tickets generated by the popular Iterative Magnitude Pruning (IMP) method. In addition, we also notice COLTs generated on large datasets can be transferred to small ones without compromising performance, demonstrating its generalizing capability. We conduct all our experiments on Cifar-10, Cifar-100 & TinyImageNet datasets and report superior performance than the state-of-the-art methods.

Neural network pruning-the task of reducing the size of a network by removing parameters-has been the subject of a great deal of work in recent years. We provide a meta-analysis of the literature, including an overview of approaches to pruning and consistent findings in the literature. After aggregating results across 81 papers and pruning hundreds of models in controlled conditions, our clearest finding is that the community suffers from a lack of standardized benchmarks and metrics. This deficiency is substantial enough that it is hard to compare pruning techniques to one another or determine how much progress the field has made over the past three decades. To address this situation, we identify issues with current practices, suggest concrete remedies, and introduce ShrinkBench, an open-source framework to facilitate standardized evaluations of pruning methods. We use ShrinkBench to compare various pruning techniques and show that its comprehensive evaluation can prevent common pitfalls when comparing pruning methods.

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.

深度神经网络已用于多种成功的应用中。但是，由于包含数百万个参数，它们的高度复杂性质导致在延迟需求低的管道中部署期间有问题。结果，更希望获得在推理期间具有相同性能的轻型神经网络。在这项工作中，我们提出了一种基于重量的修剪方法，其中权重根据以前的迭代势头逐渐修剪。神经网络的每个层都根据其相对稀疏性分配了一个重要性值，然后在先前迭代中的重量幅度分配。我们在Alexnet，VGG16和Resnet50等网络上评估了我们的方法，其中包括图像分类数据集，例如CIFAR-10和CIFAR-100。我们发现，在准确性和压缩比方面，结果优于先前的方法。我们的方法能够在两个数据集上获得同一降解的相同降解的15％压缩。

现代深度神经网络往往太大而无法在许多实际情况下使用。神经网络修剪是降低这种模型的大小的重要技术和加速推断。Gibbs修剪是一种表达和设计神经网络修剪方法的新框架。结合统计物理和随机正则化方法的方法，它可以同时培训和修剪网络，使得学习的权重和修剪面膜彼此很好地适应。它可用于结构化或非结构化修剪，我们为每个提出了许多特定方法。我们将拟议的方法与许多当代神经网络修剪方法进行比较，发现Gibbs修剪优于它们。特别是，我们通过CIFAR-10数据集来实现修剪Reset-56的新型最先进的结果。

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.

在神经网络中引入稀疏性是一种有效的方法，可以降低其复杂性，同时保持其性能几乎完好无损。在大多数情况下，使用三阶段管道引入稀疏性：1）训练模型以收敛，2）根据某些标准修剪模型，3）微调修剪模型以恢复性能。最后两个步骤通常是迭代执行的，从而导致合理的结果，但也取得了耗时且复杂的过程。在我们的工作中，我们建议摆脱管道的第一步，并在单个修剪训练周期中结合其他两个步骤，从而使模型在修剪时共同学习最佳权重。我们通过介绍一个名为One Cycle Pruning的小说修剪时间表来做到这一点，该时间表从培训开始就开始修剪，直到最后。采用这样的时间表不仅可以更好地执行修剪模型，而且还大大降低了修剪模型所需的培训预算。实验是在多种架构（VGG-16和RESNET-18）和数据集（CIFAR-10，CIFAR-100和CALTECH-101）上进行的，以及相对较高的稀疏值（80％，90％，95％的权重，删除）。我们的结果表明，按固定的培训预算，一环修剪始终优于通常使用的修剪时间表，例如单发修剪，迭代修剪和自动化逐渐修剪。

有效地近似损失函数的局部曲率信息是用于深神经网络的优化和压缩的关键工具。然而，大多数现有方法近似二阶信息具有高计算或存储成本，这可以限制其实用性。在这项工作中，我们调查矩阵，用于估计逆象征的矢量产品（IHVPS）的矩阵线性时间方法，因为当Hessian可以近似为乘语 - 一个矩阵的总和时，如Hessian的经典近似由经验丰富的Fisher矩阵。我们提出了两个新的算法作为称为M-FAC的框架的一部分：第一个算法朝着网络压缩量身定制，如果Hessian给出了M $等级的总和，则可以计算Dimension $ D $的IHVP。 ，使用$ O（DM ^ 2）$预压制，$ O（DM）$代价计算IHVP，并查询逆Hessian的任何单个元素的费用$ O（m）$。第二算法针对优化设置，我们希望在反向Hessian之间计算产品，估计在优化步骤的滑动窗口和给定梯度方向上，根据预先说明的SGD所需的梯度方向。我们为计算IHVP和OHVP和O（DM + M ^ 3）$ of $ o（dm + m ^ 2）$提供算法，以便从滑动窗口添加或删除任何渐变。这两种算法产生最先进的结果，用于网络修剪和相对于现有二阶方法的计算开销的优化。在[9]和[17]可用实现。

最近对深神经网络（DNN）效率的重点已导致了模型压缩方法的重要工作，其中重量修剪是最受欢迎的方法之一。同时，有快速增长的计算支持，以有效地执行通过修剪获得的非结构化模型。但是，大多数现有的修剪方法最小化仅剩余权重的数量，即模型的大小，而不是针对推理时间进行优化。我们通过引入SPDY来解决这一差距，SPDY是一种新的压缩方法，该方法会自动确定层次的稀疏性目标，可以在给定系统上实现所需的推理速度，同时最大程度地减少准确性损失。 SPDY由两种新技术组成：第一个是一种有效的动态编程算法，用于求解一组给定的层敏感性得分，以解决加速约束的层压缩问题；第二个是一个局部搜索程序，用于确定准确的层敏感性得分。跨流行视觉和语言模型的实验表明，SPDY可以保证相对于现有策略的恢复较高的准确性，无论是一次性和逐步修剪方案，并且与大多数现有的修剪方法兼容。我们还将方法扩展到了最近实施的修剪任务，几乎没有数据，在该数据中，我们在修剪GPU支持的2：4稀疏模式时实现了最著名的准确性恢复。

We propose a simultaneous learning and pruning algorithm capable of identifying and eliminating irrelevant structures in a neural network during the early stages of training. Thus, the computational cost of subsequent training iterations, besides that of inference, is considerably reduced. Our method, based on variational inference principles using Gaussian scale mixture priors on neural network weights, learns the variational posterior distribution of Bernoulli random variables multiplying the units/filters similarly to adaptive dropout. Our algorithm, ensures that the Bernoulli parameters practically converge to either 0 or 1, establishing a deterministic final network. We analytically derive a novel hyper-prior distribution over the prior parameters that is crucial for their optimal selection and leads to consistent pruning levels and prediction accuracy regardless of weight initialization or the size of the starting network. We prove the convergence properties of our algorithm establishing theoretical and practical pruning conditions. We evaluate the proposed algorithm on the MNIST and CIFAR-10 data sets and the commonly used fully connected and convolutional LeNet and VGG16 architectures. The simulations show that our method achieves pruning levels on par with state-of the-art methods for structured pruning, while maintaining better test-accuracy and more importantly in a manner robust with respect to network initialization and initial size.

Pruning large neural networks while maintaining their performance is often desirable due to the reduced space and time complexity. In existing methods, pruning is done within an iterative optimization procedure with either heuristically designed pruning schedules or additional hyperparameters, undermining their utility. In this work, we present a new approach that prunes a given network once at initialization prior to training. To achieve this, we introduce a saliency criterion based on connection sensitivity that identifies structurally important connections in the network for the given task. This eliminates the need for both pretraining and the complex pruning schedule while making it robust to architecture variations. After pruning, the sparse network is trained in the standard way. Our method obtains extremely sparse networks with virtually the same accuracy as the reference network on the MNIST, CIFAR-10, and Tiny-ImageNet classification tasks and is broadly applicable to various architectures including convolutional, residual and recurrent networks. Unlike existing methods, our approach enables us to demonstrate that the retained connections are indeed relevant to the given task.

现有的可区分通道修剪方法通常将缩放因子或掩模在通道后面的掩盖范围内，以减少重要性的修剪过滤器，并假设输入样品统一贡献以过滤重要性。具体而言，实例复杂性对修剪性能的影响尚未得到充分研究。在本文中，我们提出了一个基于实例复杂性滤波器的重要性得分的简单而有效的可区分网络修剪方法上限。我们通过给硬样品给出更高的权重来定义每个样品的实例复杂性与重量相关的重量，并测量样品特异性软膜的加权总和，以模拟不同输入的非均匀贡献，这鼓励硬样品主导修剪过程和模型性能保存完好。此外，我们还引入了一个新的正规器，以鼓励面具两极分化，以便很容易找到甜蜜的位置以识别要修剪的过滤器。各种网络体系结构和数据集的性能评估表明，CAP在修剪大型网络方面具有优势。例如，CAP在删除65.64％的拖鞋后，CAP在CIFAR-10数据集上的RESNET56的准确性提高了0.33％，而Prunes在ImagEnet数据集上的RESNET50的PRUNES 87.75％，只有0.89％的TOP-1精度损失。

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.