Turning the weights to zero when training a neural network helps in reducing the computational complexity at inference. To progressively increase the sparsity ratio in the network without causing sharp weight discontinuities during training, our work combines soft-thresholding and straight-through gradient estimation to update the raw, i.e. non-thresholded, version of zeroed weights. Our method, named ST-3 for straight-through/soft-thresholding/sparse-training, obtains SoA results, both in terms of accuracy/sparsity and accuracy/FLOPS trade-offs, when progressively increasing the sparsity ratio in a single training cycle. In particular, despite its simplicity, ST-3 favorably compares to the most recent methods, adopting differentiable formulations or bio-inspired neuroregeneration principles. This suggests that the key ingredients for effective sparsification primarily lie in the ability to give the weights the freedom to evolve smoothly across the zero state while progressively increasing the sparsity ratio. Source code and weights available at https://github.com/vanderschuea/stthree

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。

Many applications require sparse neural networks due to space or inference time restrictions. There is a large body of work on training dense networks to yield sparse networks for inference, but this limits the size of the largest trainable sparse model to that of the largest trainable dense model. In this paper we introduce a method to train sparse neural networks with a fixed parameter count and a fixed computational cost throughout training, without sacrificing accuracy relative to existing dense-tosparse training methods. Our method updates the topology of the sparse network during training by using parameter magnitudes and infrequent gradient calculations. We show that this approach requires fewer floating-point operations (FLOPs) to achieve a given level of accuracy compared to prior techniques. We demonstrate state-of-the-art sparse training results on a variety of networks and datasets, including ResNet-50, MobileNets on Imagenet-2012, and RNNs on WikiText-103. Finally, we provide some insights into why allowing the topology to change during the optimization can overcome local minima encountered when the topology remains static * .

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.

深度神经网络（DNN）的计算要求增加导致获得稀疏，且准确的DNN模型的兴趣。最近的工作已经调查了稀疏训练的更加困难的情况，其中DNN重量尽可能稀少，以减少训练期间的计算成本。现有的稀疏训练方法通常是经验的，并且可以具有相对于致密基线的准确性较低。在本文中，我们介绍了一种称为交替压缩/解压缩（AC / DC）训练DNN的一般方法，证明了算法变体的收敛，并表明AC / DC在类似的计算预算中准确地表现出现有的稀疏训练方法;在高稀疏水平下，AC / DC甚至优于现有的现有方法，依赖于准确的预训练密集模型。 AC / DC的一个重要属性是它允许联合培训密集和稀疏的型号，在训练过程结束时产生精确的稀疏密集模型对。这在实践中是有用的，其中压缩变体可能是为了在资源受限的设置中进行部署而不重新执行整个训练流，并且还为我们提供了深入和压缩模型之间的精度差距的见解。代码可在：https://github.com/ist-daslab/acdc。

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。

稀疏培训是一种自然的想法，可以加速深度神经网络的训练速度，并节省内存使用，特别是因为大型现代神经网络被显着过度参数化。然而，大多数现有方法在实践中无法实现这一目标，因为先前方法采用的基于链规则的梯度（W.R.T.结构参数）估计。至少在向后传播步骤中至少需要密集的计算。本文通过提出具有完全稀疏的前后通行证的有效稀疏训练方法来解决这个问题。我们首先在全球稀疏限制下将培训过程制定为连续最小化问题。然后，我们将优化过程分为两个步骤，对应于权重更新和结构参数更新。对于前一步，我们使用传统的链规则，这可以通过利用稀疏结构来稀疏。对于后一步，而不是使用基于链规则的梯度估计器，如现有方法中，我们提出了一个方差减少的策略梯度估计器，这只需要两个向前通过而不向后传播，从而实现完全稀疏的训练。我们证明了我们渐变估计器的差异是界定的。对现实世界数据集的广泛实验结果表明，与以前的方法相比，我们的算法在加速训练过程中更有效，速度快到速度更快。

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.

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.

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.

最近，稀疏培训已成为有希望的范式，可在边缘设备上有效地深入学习。当前的研究主要致力于通过进一步增加模型稀疏性来降低培训成本。但是，增加的稀疏性并不总是理想的，因为它不可避免地会在极高的稀疏度下引入严重的准确性降解。本文打算探索其他可能的方向，以有效，有效地降低稀疏培训成本，同时保持准确性。为此，我们研究了两种技术，即层冻结和数据筛分。首先，层冻结方法在密集的模型训练和微调方面取得了成功，但在稀疏训练域中从未采用过。然而，稀疏训练的独特特征可能会阻碍层冻结技术的结合。因此，我们分析了在稀疏培训中使用层冻结技术的可行性和潜力，并发现它有可能节省大量培训成本。其次，我们提出了一种用于数据集有效培训的数据筛分方法，该方法通过确保在整个培训过程中仅使用部分数据集来进一步降低培训成本。我们表明，这两种技术都可以很好地整合到稀疏训练算法中，以形成一个通用框架，我们将其配置为SPFDE。我们的广泛实验表明，SPFDE可以显着降低培训成本，同时从三个维度中保留准确性：重量稀疏性，层冻结和数据集筛分。

关于稀疏神经网络训练（稀疏训练）的最新研究表明，通过从头开始训练本质上稀疏的神经网络可以实现绩效和效率之间的令人信服的权衡。现有的稀疏训练方法通常努力在一次跑步中找到最佳的稀疏子网，而无需涉及任何昂贵的密集或预训练步骤。例如，作为最突出的方向之一，动态稀疏训练（DST）能够通过在训练过程中迭代发展稀疏拓扑来实现竞争性训练的竞争性能。在本文中，我们认为最好分配有限的资源来创建多个低损失的稀疏子网并将其超级置于更强的基因，而不是完全分配所有资源以找到单个子网络。为了实现这一目标，需要两个Desiderata：（1）在一个培训过程中有效生产许多低损失的子网，即所谓的廉价门票，仅限于用于密集培训的标准培训时间； （2）将这些廉价的门票有效地超级为一个更强的子网，而无需超越约束参数预算。为了证实我们的猜想，我们提出了一种新颖的稀疏训练方法，称为\ textbf {sup-tickets}，可以在单个稀疏到较小的训练过程中同时满足上述两个desiderata。在CIFAR-10/100和Imagenet上的各种现代体系结构中，我们表明，SUP-Tickets与现有的稀疏训练方法无缝集成，并显示出一致的性能提高。

网络的稀疏性主要是由于其降低网络复杂性的能力而受欢迎。广泛的研究挖掘了梯度驱动的稀疏性。通常，这些方法是在体重独立性前提下构建的，但是与重量受到相互影响的事实相反。因此，他们的性能仍有待改进。在本文中，我们建议通过解决这种独立悖论来进一步优化梯度驱动的稀疏性（OPTG）。我们的动机来自最近对超级策略训练的进步，该进步表明，稀疏子网可以通过简单地更新掩码值而无需修改任何权重的情况下将其位于随机初始化的网络中。我们证明，超级手机训练是积累重量梯度，并可以部分解决独立悖论。因此，OPTG将Supermask训练集成到梯度驱动的稀疏度中，并且设计了专门的掩模优化器来解决独立悖论。实验表明，OPTG可以很好地超越许多现有的最先进的竞争对手。我们的代码可在\ url {https://github.com/zyxxmu/optg}上找到。

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.

最先进的计算机视觉方法的性能飞跃归因于深度神经网络的发展。但是，它通常以计算价格可能会阻碍其部署。为了减轻这种限制，结构化修剪是一种众所周知的技术，它包括去除通道，神经元或过滤器，并且通常用于生产更紧凑的模型。在大多数情况下，根据相对重要性标准选择要删除的计算。同时，对可解释的预测模型的需求极大地增加了，并激发了强大归因方法的发展，该方法突出了输入图像或特征图的像素的相对重要性。在这项工作中，我们讨论了现有的修剪启发式方法的局限性，其中包括基于梯度和基于梯度的方法。我们从归因方法中汲取灵感来设计一种新型的集成梯度修剪标准，其中每个神经元的相关性被定义为梯度变化在通往这种神经元去除的路径上的积分。此外，我们提出了一个纠缠的DNN修剪和微调流程图，以更好地保留DNN准确性，同时删除参数。我们通过在几个数据集，架构以及修剪场景上进行广泛的验证，该方法称为Singe，大大优于现有的最新DNN修剪方法。

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.

最近的几项著作从经验上发现，鉴定学习率对于神经网络结构修剪的最终表现至关重要。进一步的研究发现，网络训练性通过修剪答案而破坏，因此呼吁迫切需要在填充之前恢复训练性。现有的尝试建议利用重量正交化以实现动态等轴测图，以提高训练性。但是，它们仅适用于线性MLP网络。如何开发一种维护或恢复可训练性并且可扩展到现代深网的过滤器修剪方法仍然难以捉摸。在本文中，我们提出了维护修剪（TPP）的训练性，这是一种基于正则化的结构化修剪方法，可以有效地维持稀疏期间的训练性。具体而言，TPP将卷积内核的革兰氏矩阵正规化，以从保存的过滤器中解除修剪过滤器。除了卷积层外，我们还建议将BN参数正规化，以更好地保留训练性。从经验上讲，TPP可以与线性MLP网络上的基地真相动力学恢复方法竞争。在非线性网络（RESNET56/VGG19，CIFAR数据集）上，它的表现优于其他对应解决方案。此外，与许多表现最好的滤镜修剪方法相比，TPP还可以在ImageNet上与现代深层网络（RESENET）有效地工作，从而提供了令人鼓舞的性能。据我们所知，这是第一种在大规模深度神经网络修剪过程中有效维持训练性的第一种方法。

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.

我们考虑在具有挑战性的训练后环境中，深度神经网络（DNN）的模型压缩问题，在该设置中，我们将获得精确的训练模型，并且必须仅基于少量校准输入数据而无需任何重新培训即可压缩它。鉴于新兴软件和硬件支持通过加速修剪和/或量化压缩的模型，并且已经针对两种压缩方法独立提出了良好的表现解决方案，因此该问题已变得流行。在本文中，我们引入了一个新的压缩框架，该框架涵盖了统一环境中的重量修剪和量化，时间和空间效率高，并且在现有的后训练方法的实际性能上大大改善。在技​​术层面上，我们的方法基于[Lecun，Denker和Solla，1990年]在现代DNN的规模上的经典最佳脑外科医生（OBS）框架的第一个精确实现，我们进一步扩展到覆盖范围。重量量化。这是通过一系列可能具有独立利益的算法开发来实现的。从实际的角度来看，我们的实验结果表明，它可以在现有后训练方法的压缩 - 准确性权衡方面显着改善，并且甚至可以在训练后进行修剪和量化的准确共同应用。

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。