彩票（LTS）能够发现准确而稀疏的子网，可以隔离训练以匹配密集网络的性能。合奏并行，是机器学习中最古老的预期技巧之一，可以通过结合多个独立模型的输出来提高性能。但是，在LTS背景下，合奏的好处将被稀释，因为合奏并没有直接导致更稀疏的子网，而是利用其预测来做出更好的决定。在这项工作中，我们首先观察到，直接平均相邻学习的子网的权重显着提高了LT的性能。在这一观察结果的鼓励下，我们进一步提出了另一种方法，通过简单的插值策略通过迭代幅度修剪来识别的子网执行“合奏”。我们称我们的方法彩票池。与幼稚的合奏相比，每一个子网都不会带来性能，彩票池比原始LTS产生的稀疏子网稀疏得多，而无需任何额外的培训或推理成本。在CIFAR-10/100和Imagenet上的各种现代体系结构中，我们表明我们的方法在分布和分发场景方面都取得了显着的性能。令人印象深刻的是，用VGG-16和RESNET-18进行评估，生产的子网稀疏的子网在CIFAR-100上优于原始LTS，在CIFAR-100-C上高达1.88％，而CIFAR-100-C则高于2.36％。最终的致密网络超过了CIFAR-100的预训练密集模型，在CIFAR-100-C上超过2.22％。

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。

最近对稀疏神经网络的作品已经证明了独立从头开始训练稀疏子网，以匹配其相应密集网络的性能。然而，识别这种稀疏的子网（获奖票）涉及昂贵的迭代火车 - 培训 - 培训过程（例如，彩票票证假设）或过度扩展的训练时间（例如，动态稀疏训练）。在这项工作中，我们在稀疏神经网络训练和深度合并技术之间汲取了独特的联系，产生了一个名为FreeTickets的新型集合学习框架。 FreeTickets而不是从密集的网络开始，随机初始化稀疏的子网，然后在动态调整其稀疏掩码的同时列举子网，从而在整个训练过程中产生许多不同的稀疏子网。 FreeTickets被定义为这些稀疏子网的集合，在这种单次通过，稀疏稀疏训练中自由获得，其仅使用Vanilla密集培训所需的计算资源的一小部分。此外，尽管是模型的集合，但与单一密集模型相比，FreeTickets的参数和训练拖鞋更少：这种看似反向直观的结果是由于每个子网的高稀疏性。与标准致密基线相比，观察到惯性基因术，以预测准确性，不确定度估计，鲁棒性和效率相比表现出显着的全面改进。 FreeTickets在ImageNet上只使用后者所需的四分之一的培训拖鞋，可以轻松地表达Naive Deep EndleBe。我们的结果提供了对稀疏神经网络的强度的见解，并表明稀疏性的好处超出了通常预期的推理效率。

We study whether a neural network optimizes to the same, linearly connected minimum under different samples of SGD noise (e.g., random data order and augmentation). We find that standard vision models become stable to SGD noise in this way early in training. From then on, the outcome of optimization is determined to a linearly connected region. We use this technique to study iterative magnitude pruning (IMP), the procedure used by work on the lottery ticket hypothesis to identify subnetworks that could have trained in isolation to full accuracy. We find that these subnetworks only reach full accuracy when they are stable to SGD noise, which either occurs at initialization for small-scale settings (MNIST) or early in training for large-scale settings (ResNet-50 and Inception-v3 on ImageNet).

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.

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。

野外的深度学习（DL）的成功采用需要模型：（1）紧凑，（2）准确，（3）强大的分布换档。不幸的是，同时满足这些要求的努力主要是不成功的。这提出了一个重要问题：无法创建紧凑，准确，强大的深神经网络（卡）基础？为了回答这个问题，我们对流行的模型压缩技术进行了大规模分析，该技术揭示了几种有趣模式。值得注意的是，与传统的修剪方法相比（例如，微调和逐渐修剪），我们发现“彩票式风格”方法令人惊讶地用于生产卡，包括二进制牌。具体而言，我们能够创建极其紧凑的卡，与其较大的对应物相比，具有类似的测试精度和匹配（或更好）的稳健性 - 仅通过修剪和（可选）量化。利用卡的紧凑性，我们开发了一种简单的域 - 自适应测试时间合并方法（卡片 - 甲板），它使用门控模块根据与测试样本的光谱相似性动态地选择相应的卡片。该拟议的方法建立了一个“赢得胜利”的卡片，即在CiFar-10-C精度（即96.8％标准和92.75％的鲁棒）和CiFar-100- C精度（80.6％标准和71.3％的稳健性），内存使用率比非压缩基线（Https://github.com/robustbench/robustbench提供的预制卡和卡片 - 甲板）。最后，我们为我们的理论支持提供了理论支持经验研究结果。

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.

网络修剪是一种有效的方法，可以通过可接受的性能妥协降低网络复杂性。现有研究通过耗时的重量调谐或具有扩展宽度的网络的复杂搜索来实现神经网络的稀疏性，这极大地限制了网络修剪的应用。在本文中，我们表明，在没有权重调谐的情况下，高性能和稀疏的子网被称为“彩票奖线”，存在于具有膨胀宽度的预先训练的模型中。例如，我们获得了一个只有10％参数的彩票奖金，仍然达到了原始密度Vggnet-19的性能，而无需对CiFar-10的预先训练的重量进行任何修改。此外，我们观察到，来自许多现有修剪标准的稀疏面具与我们的彩票累积的搜索掩码具有高重叠，其中，基于幅度的修剪导致与我们的最相似的掩模。根据这种洞察力，我们使用基于幅度的修剪初始化我们的稀疏掩模，导致彩票累积搜索至少3倍降低，同时实现了可比或更好的性能。具体而言，我们的幅度基彩票奖学金在Reset-50中除去90％的重量，而在ImageNet上仅使用10个搜索时期可以轻松获得超过70％的前1个精度。我们的代码可在https://github.com/zyxxmu/lottery-jackpots获得。

最大化模型准确性的常规配方是（1）具有各种超参数的多个模型，以及（2）选择在固定验证集中表现最佳的单个模型，从而丢弃其余部分。在本文中，我们在微调大型预训练的模型的背景下重新审视了该过程的第二步，其中微调模型通常位于单个低误差盆地中。我们表明，平均多种模型的权重以不同的超参数配置进行了微调通常提高准确性和鲁棒性。与传统的合奏不同，我们可能会平均许多模型，而不会产生任何其他推理或记忆成本 - 我们将结果称为“模型汤”。当微调大型预训练的模型，例如夹子，Align和VIT-G在JFT上预先训练的VIT-G时，我们的汤食谱可为ImageNet上的超参数扫描中的最佳模型提供显着改进。所得的VIT-G模型在Imagenet上达到90.94％的TOP-1准确性，实现了新的最新状态。此外，我们表明，模型汤方法扩展到多个图像分类和自然语言处理任务，改善分发性能，并改善新下游任务的零局部性。最后，我们通过分析将权重平衡和与logit浓度的性能相似与预测的损失和信心的平坦度联系起来，并经过经验验证这种关系。代码可从https://github.com/mlfoundations/model-soups获得。

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。

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。

Over-parameterization of deep neural networks (DNNs) has shown high prediction accuracy for many applications. Although effective, the large number of parameters hinders its popularity on resource-limited devices and has an outsize environmental impact. Sparse training (using a fixed number of nonzero weights in each iteration) could significantly mitigate the training costs by reducing the model size. However, existing sparse training methods mainly use either random-based or greedy-based drop-and-grow strategies, resulting in local minimal and low accuracy. In this work, to assist explainable sparse training, we propose important weights Exploitation and coverage Exploration to characterize Dynamic Sparse Training (DST-EE), and provide quantitative analysis of these two metrics. We further design an acquisition function and provide the theoretical guarantees for the proposed method and clarify its convergence property. Experimental results show that sparse models (up to 98\% sparsity) obtained by our proposed method outperform the SOTA sparse training methods on a wide variety of deep learning tasks. On VGG-19 / CIFAR-100, ResNet-50 / CIFAR-10, ResNet-50 / CIFAR-100, our method has even higher accuracy than dense models. On ResNet-50 / ImageNet, the proposed method has up to 8.2\% accuracy improvement compared to SOTA sparse training methods.

预训练是在各种下游任务上转移学习的广泛采用的起点。对彩票假说（LTH）的最新研究表明，这种巨大的预训练模型可以用极稀疏的子网（又称匹配子网络）代替，而无需牺牲可传递性。但是，实际的安全 - 重要应用程序通常在标准转移之外提出了更具挑战性的要求，这也要求这些子网克服对抗性脆弱性。在本文中，我们制定了一个更严格的概念，双赢彩票，其中预训练模型的位置可以在各种下游任务上独立传输，以在两个标准下达到相同的标准和可靠的概括正如完整的预培训模型可以做到的那样，对抗性训练制度。我们全面检查了各种训练机制，发现强大的预训练倾向于制作出更少的双赢彩票，其性能优于标准对应物。例如，在下游CIFAR-10/100数据集上，我们识别出具有标准的，快速的对抗性和对抗性预训练的双赢匹配子网，以89.26％/73.79％，89.26％/79.03％和91.41％的匹配培训。 /83.22%稀疏。此外，我们观察到获得的双赢彩票票可以在实用数据限制（例如1％和10％）下游方案下传输的数据效率更高。我们的结果表明，彩票票务方案以及数据限制的转移设置可以扩大稳健的预训练的好处。代码可在https://github.com/vita-group/double-win-lth上找到。

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.

执行零摄像推理时（即，在特定数据集上不进行微调）时，大型预训练的模型（例如剪辑或ALIGN）在一系列数据分布中提供一致的精度。尽管现有的微调方法显着提高了给定目标分布的准确性，但它们通常会降低分配变化的稳健性。我们通过引入一种简单有效的方法来提高鲁棒性，同时进行微调：结合零拍和微调模型（Wise-ft）的重量。与标准的微调相比，Wise-FT在分配变化下提供了巨大的准确性提高，同时保留了目标分布的高精度。在Imagenet和五个派生的分布变化上，Wise-FT在先前的工作中提高了分布转移的准确性4至6个百分点（PP），同时将Imagenet精度提高1.6pp。Wise-ft的稳健性相似（2至23 pp），明智之前与七个常用的转移学习数据集的标准微调相比，在一组进一步的分配转移的各种集合中，准确性增长率为0.8至3.3 pp。这些改进在微调或推理期间没有任何额外的计算成本。

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.

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。

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.