Benchmarking the tradeoff between neural network accuracy and training time is computationally expensive. Here we show how a multiplicative cyclic learning rate schedule can be used to construct a tradeoff curve in a single training run. We generate cyclic tradeoff curves for combinations of training methods such as Blurpool, Channels Last, Label Smoothing and MixUp, and highlight how these cyclic tradeoff curves can be used to evaluate the effects of algorithmic choices on network training efficiency.

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。

Restart techniques are common in gradient-free optimization to deal with multimodal functions. Partial warm restarts are also gaining popularity in gradientbased optimization to improve the rate of convergence in accelerated gradient schemes to deal with ill-conditioned functions. In this paper, we propose a simple warm restart technique for stochastic gradient descent to improve its anytime performance when training deep neural networks. We empirically study its performance on the CIFAR-10 and CIFAR-100 datasets, where we demonstrate new state-of-the-art results at 3.14% and 16.21%, respectively. We also demonstrate its advantages on a dataset of EEG recordings and on a downsampled version of the ImageNet dataset. Our source code is available at https://github.com/loshchil/SGDR

It is common practice in deep learning to use overparameterized networks and train for as long as possible; there are numerous studies that show, both theoretically and empirically, that such practices surprisingly do not unduly harm the generalization performance of the classifier. In this paper, we empirically study this phenomenon in the setting of adversarially trained deep networks, which are trained to minimize the loss under worst-case adversarial perturbations. We find that overfitting to the training set does in fact harm robust performance to a very large degree in adversarially robust training across multiple datasets (SVHN, CIFAR-10, CIFAR-100, and ImageNet) and perturbation models ( ∞ and 2 ). Based upon this observed effect, we show that the performance gains of virtually all recent algorithmic improvements upon adversarial training can be matched by simply using early stopping. We also show that effects such as the double descent curve do still occur in adversarially trained models, yet fail to explain the observed overfitting. Finally, we study several classical and modern deep learning remedies for overfitting, including regularization and data augmentation, and find that no approach in isolation improves significantly upon the gains achieved by early stopping. All code for reproducing the experiments as well as pretrained model weights and training logs can be found at https://github.com/ locuslab/robust_overfitting.

L 2 regularization and weight decay regularization are equivalent for standard stochastic gradient descent (when rescaled by the learning rate), but as we demonstrate this is not the case for adaptive gradient algorithms, such as Adam. While common implementations of these algorithms employ L 2 regularization (often calling it "weight decay" in what may be misleading due to the inequivalence we expose), we propose a simple modification to recover the original formulation of weight decay regularization by decoupling the weight decay from the optimization steps taken w.r.t. the loss function. We provide empirical evidence that our proposed modification (i) decouples the optimal choice of weight decay factor from the setting of the learning rate for both standard SGD and Adam and (ii) substantially improves Adam's generalization performance, allowing it to compete with SGD with momentum on image classification datasets (on which it was previously typically outperformed by the latter). Our proposed decoupled weight decay has already been adopted by many researchers, and the community has implemented it in TensorFlow and PyTorch; the complete source code for our experiments is

It is known that the learning rate is the most important hyper-parameter to tune for training deep neural networks. This paper describes a new method for setting the learning rate, named cyclical learning rates, which practically eliminates the need to experimentally find the best values and schedule for the global learning rates. Instead of monotonically decreasing the learning rate, this method lets the learning rate cyclically vary between reasonable boundary values. Training with cyclical learning rates instead of fixed values achieves improved classification accuracy without a need to tune and often in fewer iterations. This paper also describes a simple way to estimate "reasonable bounds" -linearly increasing the learning rate of the network for a few epochs. In addition, cyclical learning rates are demonstrated on the CIFAR-10 and CIFAR-100 datasets with ResNets, Stochastic Depth networks, and DenseNets, and the ImageNet dataset with the AlexNet and GoogLeNet architectures. These are practical tools for everyone who trains neural networks.

在神经网络的经验风险景观中扁平最小值的性质已经讨论了一段时间。越来越多的证据表明他们对尖锐物质具有更好的泛化能力。首先，我们讨论高斯混合分类模型，并分析显示存在贝叶斯最佳点估算器，其对应于属于宽平区域的最小值。可以通过直接在分类器（通常是独立的）或学习中使用的可分解损耗函数上应用最大平坦度算法来找到这些估计器。接下来，我们通过广泛的数值验证将分析扩展到深度学习场景。使用两种算法，熵-SGD和复制-SGD，明确地包括在优化目标中，所谓的非局部平整度措施称为本地熵，我们一直提高常见架构的泛化误差（例如Resnet，CeffectnNet）。易于计算的平坦度测量显示与测试精度明确的相关性。

Large-batch SGD is important for scaling training of deep neural networks. However, without fine-tuning hyperparameter schedules, the generalization of the model may be hampered. We propose to use batch augmentation: replicating instances of samples within the same batch with different data augmentations. Batch augmentation acts as a regularizer and an accelerator, increasing both generalization and performance scaling for a fixed budget of optimization steps. We analyze the effect of batch augmentation on gradient variance and show that it empirically improves convergence for a wide variety of networks and datasets. Our results show that batch augmentation reduces the number of necessary SGD updates to achieve the same accuracy as the state-of-the-art. Overall, this simple yet effective method enables faster training and better generalization by allowing more computational resources to be used concurrently. Large batch training of neural networksRecent approaches by [10], [8], [41] and others show that by adapting the optimization regime (i.e., hyperparameter schedule), large batch training can achieve equally good

本文描述了机器学习中“一般周期性训练”的原则，在该原理中，培训以“易于训练”开始和结束，而“硬训练”发生在中间时期。我们提出了几种训练神经网络的表现，包括算法示例（通过超参数和损失功能），基于数据的示例和基于模型的示例。具体而言，我们介绍了几种新技术：周期性重量衰减，周期性批量尺寸，周期性局灶性损失，周期性软度温度，周期性数据增强，周期性梯度剪辑和周期性的半监督学习。此外，我们证明了周期性的重量衰减，周期性软度温度和周期性梯度剪辑（作为该原理的三个示例）对训练有素的模型的测试准确性性能有益。此外，我们从一般周期性培训的角度讨论了基于模型的示例（例如预处理和知识蒸馏），并建议对典型培训方法进行一些更改。总而言之，本文定义了一般的周期性培训概念，并讨论了该概念可以应用于训练神经网络的几种特定方式。本着可重复性的精神，我们的实验中使用的代码可在\ url {https://github.com/lnsmith54/cfl}上获得。

Vision transformer (ViT) models exhibit substandard optimizability. In particular, they are sensitive to the choice of optimizer (AdamW vs. SGD), optimizer hyperparameters, and training schedule length. In comparison, modern convolutional neural networks are easier to optimize. Why is this the case? In this work, we conjecture that the issue lies with the patchify stem of ViT models, which is implemented by a stride-p p×p convolution (p = 16 by default) applied to the input image. This large-kernel plus large-stride convolution runs counter to typical design choices of convolutional layers in neural networks. To test whether this atypical design choice causes an issue, we analyze the optimization behavior of ViT models with their original patchify stem versus a simple counterpart where we replace the ViT stem by a small number of stacked stride-two 3×3 convolutions. While the vast majority of computation in the two ViT designs is identical, we find that this small change in early visual processing results in markedly different training behavior in terms of the sensitivity to optimization settings as well as the final model accuracy. Using a convolutional stem in ViT dramatically increases optimization stability and also improves peak performance (by ∼1-2% top-1 accuracy on ImageNet-1k), while maintaining flops and runtime. The improvement can be observed across the wide spectrum of model complexities (from 1G to 36G flops) and dataset scales (from ImageNet-1k to ImageNet-21k). These findings lead us to recommend using a standard, lightweight convolutional stem for ViT models in this regime as a more robust architectural choice compared to the original ViT model design.

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.

尽管卷积神经网络（CNN）的演变发展，但它们的性能令人惊讶地取决于超参数的选择。但是，由于现代CNN的较长训练时间，有效探索大型超参数搜索空间仍然具有挑战性。多保真优化可以通过提前终止无主张的配置来探索更多的超参数配置。但是，它通常会导致选择亚最佳配置作为训练，并在早期阶段通常会缓慢收敛。在本文中，我们提出了具有重复学习率（MORL）的多余性优化，该率将CNNS的优化过程纳入了多性效率优化。莫尔减轻了缓慢启动的问题，并实现了更精确的低保真近似。我们对一般图像分类，转移学习和半监督学习的全面实验证明了MORL对其他多保真优化方法的有效性，例如连续减半算法（SHA）和HyperBand。此外，它可以在实际预算内进行手工调整的超参数配置的显着性能改进。

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。

Deep neural networks are typically trained by optimizing a loss function with an SGD variant, in conjunction with a decaying learning rate, until convergence. We show that simple averaging of multiple points along the trajectory of SGD, with a cyclical or constant learning rate, leads to better generalization than conventional training. We also show that this Stochastic Weight Averaging (SWA) procedure finds much flatter solutions than SGD, and approximates the recent Fast Geometric Ensembling (FGE) approach with a single model. Using SWA we achieve notable improvement in test accuracy over conventional SGD training on a range of state-of-the-art residual networks, PyramidNets, DenseNets, and Shake-Shake networks on CIFAR-10, CIFAR-100, and ImageNet. In short, SWA is extremely easy to implement, improves generalization, and has almost no computational overhead.

The loss functions of deep neural networks are complex and their geometric properties are not well understood. We show that the optima of these complex loss functions are in fact connected by simple curves over which training and test accuracy are nearly constant. We introduce a training procedure to discover these high-accuracy pathways between modes. Inspired by this new geometric insight, we also propose a new ensembling method entitled Fast Geometric Ensembling (FGE). Using FGE we can train high-performing ensembles in the time required to train a single model. We achieve improved performance compared to the recent state-of-the-art Snapshot Ensembles, on CIFAR-10, CIFAR-100, and ImageNet. * Equal contribution. 1 Suppose we have three weight vectors w1, w2, w3. We set u = (w2 − w1), v = (w3 − w1) − w3 − w1, w2 − w1 / w2 − w1 2 • (w2 − w1). Then the normalized vectors û = u/ u , v = v/ v form an orthonormal basis in the plane containing w1, w2, w3. To visualize the loss in this plane, we define a Cartesian grid in the basis û, v and evaluate the networks corresponding to each of the points in the grid. A point P with coordinates (x, y) in the plane would then be given by P = w1 + x • û + y • v.

Much of the recent progress made in image classification research can be credited to training procedure refinements, such as changes in data augmentations and optimization methods. In the literature, however, most refinements are either briefly mentioned as implementation details or only visible in source code. In this paper, we will examine a collection of such refinements and empirically evaluate their impact on the final model accuracy through ablation study. We will show that, by combining these refinements together, we are able to improve various CNN models significantly. For example, we raise ResNet-50's top-1 validation accuracy from 75.3% to 79.29% on ImageNet. We will also demonstrate that improvement on image classification accuracy leads to better transfer learning performance in other application domains such as object detection and semantic segmentation.

The vast majority of successful deep neural networks are trained using variants of stochastic gradient descent (SGD) algorithms. Recent attempts to improve SGD can be broadly categorized into two approaches: (1) adaptive learning rate schemes, such as AdaGrad and Adam, and (2) accelerated schemes, such as heavy-ball and Nesterov momentum. In this paper, we propose a new optimization algorithm, Lookahead, that is orthogonal to these previous approaches and iteratively updates two sets of weights. Intuitively, the algorithm chooses a search direction by looking ahead at the sequence of "fast weights" generated by another optimizer. We show that Lookahead improves the learning stability and lowers the variance of its inner optimizer with negligible computation and memory cost. We empirically demonstrate Lookahead can significantly improve the performance of SGD and Adam, even with their default hyperparameter settings on ImageNet, CIFAR-10/100, neural machine translation, and Penn Treebank.

观察到在训练期间重新定位神经网络，以改善最近的作品中的概括。然而，它既不在深度学习实践中被广泛采用，也不经常用于最先进的培训方案中。这就提出了一个问题，即何时重新定位起作用，以及是否应与正规化技术一起使用，例如数据增强，体重衰减和学习率计划。在这项工作中，我们对标准培训的经验比较进行了广泛的经验比较，并选择了一些重新定位方法来回答这个问题，并在各种图像分类基准上培训了15,000多个模型。我们首先确定在没有任何其他正则化的情况下，这种方法对概括始终有益。但是，当与其他经过精心调整的正则化技术一起部署时，重新定位方法几乎没有给予概括，尽管最佳的概括性能对学习率和体重衰减超参数的选择不太敏感。为了研究重新定位方法对嘈杂数据的影响，我们还考虑在标签噪声下学习。令人惊讶的是，在这种情况下，即使在存在其他经过精心调整的正则化技术的情况下，重新定位也会显着改善标准培训。

对敌对训练（AT）作为最小值优化问题，可以有效地增强模型对对抗攻击的鲁棒性。现有的AT方法主要集中于操纵内部最大化，以生成质量对抗性变体或操纵外部最小化以设计有效的学习目标。然而，始终表现出与准确性和跨界混合物问题存在的鲁棒性的经验结果，这激发了我们研究某些标签随机性以使AT受益。首先，我们分别对AT的内部最大化和外部最小化进行彻底研究嘈杂的标签（NLS）注射，并获得有关NL注射益处AT何时的观察结果。其次，根据观察结果，我们提出了一种简单但有效的方法 - Noilin将NLS随机注入每个训练时期的训练数据，并在发生强大的过度拟合后动态提高NL注入率。从经验上讲，Noilin可以显着减轻AT的不良过度拟合的不良问题，甚至进一步改善了最新方法的概括。从哲学上讲，Noilin阐明了与NLS学习的新观点：NLS不应总是被视为有害的，即使在培训集中没有NLS的情况下，我们也可以考虑故意注射它们。代码可在https://github.com/zjfheart/noilin中找到。

作为标签噪声，最受欢迎的分布变化之一，严重降低了深度神经网络的概括性能，具有嘈杂标签的强大训练正在成为现代深度学习中的重要任务。在本文中，我们提出了我们的框架，在子分类器（ALASCA）上创造了自适应标签平滑，该框架提供了具有理论保证和可忽略的其他计算的可靠特征提取器。首先，我们得出标签平滑（LS）会产生隐式Lipschitz正则化（LR）。此外，基于这些推导，我们将自适应LS（ALS）应用于子分类器架构上，以在中间层上的自适应LR的实际应用。我们对ALASCA进行了广泛的实验，并将其与以前的几个数据集上的噪声燃烧方法相结合，并显示我们的框架始终优于相应的基线。