The rectified linear unit (ReLU) is a highly successful activation function in neural networks as it allows networks to easily obtain sparse representations, which reduces overfitting in overparameterized networks. However, in network pruning, we find that the sparsity introduced by ReLU, which we quantify by a term called dynamic dead neuron rate (DNR), is not beneficial for the pruned network. Interestingly, the more the network is pruned, the smaller the dynamic DNR becomes during optimization. This motivates us to propose a method to explicitly reduce the dynamic DNR for the pruned network, i.e., de-sparsify the network. We refer to our method as Activating-while-Pruning (AP). We note that AP does not function as a stand-alone method, as it does not evaluate the importance of weights. Instead, it works in tandem with existing pruning methods and aims to improve their performance by selective activation of nodes to reduce the dynamic DNR. We conduct extensive experiments using popular networks (e.g., ResNet, VGG) via two classical and three state-of-the-art pruning methods. The experimental results on public datasets (e.g., CIFAR-10/100) suggest that AP works well with existing pruning methods and improves the performance by 3% - 4%. For larger scale datasets (e.g., ImageNet) and state-of-the-art networks (e.g., vision transformer), we observe an improvement of 2% - 3% with AP as opposed to without. Lastly, we conduct an ablation study to examine the effectiveness of the components comprising AP.

The importance of learning rate (LR) schedules on network pruning has been observed in a few recent works. As an example, Frankle and Carbin (2019) highlighted that winning tickets (i.e., accuracy preserving subnetworks) can not be found without applying a LR warmup schedule and Renda, Frankle and Carbin (2020) demonstrated that rewinding the LR to its initial state at the end of each pruning cycle improves performance. In this paper, we go one step further by first providing a theoretical justification for the surprising effect of LR schedules. Next, we propose a LR schedule for network pruning called SILO, which stands for S-shaped Improved Learning rate Optimization. The advantages of SILO over existing state-of-the-art (SOTA) LR schedules are two-fold: (i) SILO has a strong theoretical motivation and dynamically adjusts the LR during pruning to improve generalization. Specifically, SILO increases the LR upper bound (max_lr) in an S-shape. This leads to an improvement of 2% - 4% in extensive experiments with various types of networks (e.g., Vision Transformers, ResNet) on popular datasets such as ImageNet, CIFAR-10/100. (ii) In addition to the strong theoretical motivation, SILO is empirically optimal in the sense of matching an Oracle, which exhaustively searches for the optimal value of max_lr via grid search. We find that SILO is able to precisely adjust the value of max_lr to be within the Oracle optimized interval, resulting in performance competitive with the Oracle with significantly lower complexity.

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。

现代深度神经网络需要大量的计算时间和训练和部署的功率，这限制了它们在边缘设备上的使用。受彩票票证假设中的迭代重量修剪的启发，我们提出了Dropnet，这是一种迭代修剪方法，可修剪节点/过滤器以降低网络复杂性。Dropnet迭代删除所有训练样本中平均激活值最低的节点/过滤器。从经验上讲，我们表明Dropnet在各种情况下都具有强大的功能，包括使用MNIST，CIFAR-10和Tiny Imagenet数据集，包括MLP和CNN。我们表明，可以去除多达90％的节点/过滤器，而不会出现任何明显的准确性损失。最终修剪的网络即使在重新定位权重和偏见的情况下也表现良好。Dropnet也具有与Oracle相似的精度，该甲骨文一次贪婪地去除节点/过滤器，以最大程度地减少训练损失，从而突出其有效性。

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 * .

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.

我们为神经网络提出了一种新颖，结构化修剪算法 - 迭代，稀疏结构修剪算法，称为I-Spasp。从稀疏信号恢复的思想启发，I-Spasp通过迭代地识别网络内的较大的重要参数组（例如，滤波器或神经元），这些参数组大多数对修剪和密集网络输出之间的残差贡献，然后基于这些组阈值以较小的预定定义修剪比率。对于具有Relu激活的双层和多层网络架构，我们展示了通过多项式修剪修剪诱导的错误，该衰减是基于密集网络隐藏表示的稀疏性任意大的。在我们的实验中，I-Spasp在各种数据集（即MNIST和ImageNet）和架构（即馈送前向网络，Resnet34和MobileNetv2）中进行评估，其中显示用于发现高性能的子网和改进经过几种数量级的可提供基线方法的修剪效率。简而言之，I-Spasp很容易通过自动分化实现，实现强大的经验结果，具有理论收敛保证，并且是高效的，因此将自己区分开作为少数几个计算有效，实用，实用，实用，实用，实用，实用，实用，实用和可提供的修剪算法之一。

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。

深度神经网络（DNN）在解决许多真实问题方面都有效。较大的DNN模型通常表现出更好的质量（例如，精度，精度），但它们的过度计算会导致长期推理时间。模型稀疏可以降低计算和内存成本，同时保持模型质量。大多数现有的稀疏算法是单向移除的重量，而其他人则随机或贪婪地探索每层进行修剪的小权重子集。这些算法的局限性降低了可实现的稀疏性水平。此外，许多算法仍然需要预先训练的密集模型，因此遭受大的内存占地面积。在本文中，我们提出了一种新颖的预定生长和修剪（间隙）方法，而无需预先培训密集模型。它通过反复生长一个层次的层来解决以前的作品的缺点，然后在一些训练后修剪回到稀疏。实验表明，使用所提出的方法修剪模型匹配或击败高度优化的密集模型的质量，在各种任务中以80％的稀疏度，例如图像分类，客观检测，3D对象分段和翻译。它们还优于模型稀疏的其他最先进的（SOTA）方法。作为一个例子，通过间隙获得的90％不均匀的稀疏resnet-50模型在想象中实现了77.9％的前1个精度，提高了先前的SOTA结果1.5％。所有代码将公开发布。

在本文中，我们研究了在深网（DNS）中修剪的重要性，以及（1）修剪高度参数的DNS之间的Yin＆Yang关系，这些DNS已从随机初始化训练，并且（2）培训“巧妙”的小型DNS，这些DNS已“巧妙”。初始化。在大多数情况下，从业者只能诉诸随机初始化，因此强烈需要对DN修剪建立扎实的理解。当前的文献在很大程度上仍然是经验的，缺乏对修剪如何影响DNS决策边界，如何解释修剪以及如何设计相应的原则修剪技术的理论理解。为了解决这些问题，我们建议在连续分段仿射（CPA）DNS的理论分析中采用最新进展。从这个角度来看，我们将能够检测到早期的鸟类（EB）票务现象，为当前的修剪技术提供可解释性，并制定有原则的修剪策略。在研究的每个步骤中，我们进行了广泛的实验，以支持我们的主张和结果；尽管我们的主要目标是增强对DN修剪的当前理解，而不是开发一种新的修剪方法，但我们的样条修剪标准在层和全球修剪方面与先进的修剪方法相当甚至超过了。

Neural network pruning techniques can reduce the parameter counts of trained networks by over 90%, decreasing storage requirements and improving computational performance of inference without compromising accuracy. However, contemporary experience is that the sparse architectures produced by pruning are difficult to train from the start, which would similarly improve training performance.We find that a standard pruning technique naturally uncovers subnetworks whose initializations made them capable of training effectively. Based on these results, we articulate the lottery ticket hypothesis: dense, randomly-initialized, feed-forward networks contain subnetworks (winning tickets) that-when trained in isolationreach test accuracy comparable to the original network in a similar number of iterations. The winning tickets we find have won the initialization lottery: their connections have initial weights that make training particularly effective.We present an algorithm to identify winning tickets and a series of experiments that support the lottery ticket hypothesis and the importance of these fortuitous initializations. We consistently find winning tickets that are less than 10-20% of the size of several fully-connected and convolutional feed-forward architectures for MNIST and CIFAR10. Above this size, the winning tickets that we find learn faster than the original network and reach higher test accuracy.

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。

人们通常认为，修剪网络不仅会降低深网的计算成本，而且还可以通过降低模型容量来防止过度拟合。但是，我们的工作令人惊讶地发现，网络修剪有时甚至会加剧过度拟合。我们报告了出乎意料的稀疏双后裔现象，随着我们通过网络修剪增加模型稀疏性，首先测试性能变得更糟（由于过度拟合），然后变得更好（由于过度舒适），并且终于变得更糟（由于忘记了有用的有用信息）。尽管最近的研究集中在模型过度参数化方面，但他们未能意识到稀疏性也可能导致双重下降。在本文中，我们有三个主要贡献。首先，我们通过广泛的实验报告了新型的稀疏双重下降现象。其次，对于这种现象，我们提出了一种新颖的学习距离解释，即$ \ ell_ {2} $稀疏模型的学习距离（从初始化参数到最终参数）可能与稀疏的双重下降曲线良好相关，并更好地反映概括比最小平坦。第三，在稀疏的双重下降的背景下，彩票票假设中的获胜票令人惊讶地并不总是赢。

Pruning large neural networks to create highquality, independently trainable sparse masks, which can maintain similar performance to their dense counterparts, is very desirable due to the reduced space and time complexity. As research effort is focused on increasingly sophisticated pruning methods that leads to sparse subnetworks trainable from the scratch, we argue for an orthogonal, under-explored theme: improving training techniques for pruned sub-networks, i.e. sparse training. Apart from the popular belief that only the quality of sparse masks matters for sparse training, in this paper we demonstrate an alternative opportunity: one can carefully customize the sparse training techniques to deviate from the default dense network training protocols, consisting of introducing "ghost" neurons and skip connections at the early stage of training, and strategically modifying the initialization as well as labels. Our new sparse training recipe is generally applicable to improving training from scratch with various sparse masks. By adopting our newly curated techniques, we demonstrate significant performance gains across various popular datasets (CIFAR-10, CIFAR-100, TinyIma-geNet), architectures (ResNet-18/32/104, Vgg16, MobileNet), and sparse mask options (lottery ticket, SNIP/GRASP, SynFlow, or even randomly pruning), compared to the default training protocols, especially at high sparsity levels. Code is at https://github.com/VITA-Group/ToST.

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。

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。

模型压缩的目的是减小大型神经网络的大小，同时保持可比的性能。结果，通过减少冗余重量，神经元或层，可以大大降低资源有限应用中的计算和内存成本。提出了许多模型压缩算法，这些算法提供了令人印象深刻的经验成功。但是，对模型压缩的理论理解仍然受到限制。一个问题是了解网络是否比另一个相同结构更可压缩。另一个问题是量化有多少人可以通过理论上保证的准确性降解来修剪网络。在这项工作中，我们建议使用对稀疏敏感的$ \ ell_q $ -norm（$ 0 <q <1 $）来表征可压缩性，并提供网络中的软稀疏性与受控程度的压缩程度之间的关系准确性降解结合。我们还开发了自适应算法，用于修剪我们理论所告知的网络中的每个神经元。数值研究表明，与标准修剪算法相比，提出的方法的表现有希望。

基于变压器的大型模型在各种自然语言处理和计算机视觉任务中表现出卓越的性能。但是，这些模型包含大量参数，这些参数将其部署限制为现实世界应用程序。为了减少模型大小，研究人员根据权重的重要性得分修剪这些模型。但是，这种分数通常在训练过程中估计在小批次上，这会由于迷你批次采样和复杂的训练动力学而产生巨大的可变性/不确定性。结果，由于这种不确定性，可以通过常用的修剪方法来修剪一些关键权重，从而使训练不稳定并受到概括。为了解决这个问题，我们提出了Platon，该问题通过对重要性估计的上限（UCB）捕获了重要性得分的不确定性。特别是，对于较低的分数但不确定性较高的权重，柏拉图倾向于保留它们并探索其能力。我们对基于自然语言的理解，问答和图像分类的几种基于变压器的模型进行了广泛的实验，以验证柏拉图的有效性。结果表明，柏拉图在不同的稀疏度水平下显着改善。我们的代码可在https://github.com/qingruzhang/platon上公开获取。

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.

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.