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 \emph{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 \emph{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 available at this https URL

Decoupled Weight Decay Regularization

Machine learning techniques based on neural networks are achieving remarkable results in a wide variety of domains. Often, the training of models requires large, representative datasets, which may be crowdsourced and contain sensitive information. The models should not expose private information in these datasets. Addressing this goal, we develop new algorithmic techniques for learning and a refined analysis of privacy costs within the framework of differential privacy. Our implementation and experiments demonstrate that we can train deep neural networks with non-convex objectives, under a modest privacy budget, and at a manageable cost in software complexity, training efficiency, and model quality.

Deep Learning with Differential Privacy

Data augmentation is an effective technique for improving the accuracy of modern image classifiers. However, current data augmentation implementations are manually designed. In this paper, we describe a simple procedure called AutoAugment to automatically search for improved data augmentation policies. In our implementation, we have designed a search space where a policy consists of many sub-policies, one of which is randomly chosen for each image in each mini-batch. A sub-policy consists of two operations, each operation being an image processing function such as translation, rotation, or shearing, and the probabilities and magnitudes with which the functions are applied. We use a search algorithm to find the best policy such that the neural network yields the highest validation accuracy on a target dataset. Our method achieves state-of-the-art accuracy on CIFAR-10, CIFAR-100, SVHN, and ImageNet (without additional data). On ImageNet, we attain a Top-1 accuracy of 83.5% which is 0.4% better than the previous record of 83.1%. On CIFAR-10, we achieve an error rate of 1.5%, which is 0.6% better than the previous state-of-the-art. Augmentation policies we find are transferable between datasets. The policy learned on ImageNet transfers well to achieve significant improvements on other datasets, such as Oxford Flowers, Caltech-101, Oxford-IIT Pets, FGVC Aircraft, and Stanford Cars.

/pdf/autoaugment-learning-augmentation-strategies-from-data-1b9ts7ae8u.pdf

AutoAugment: Learning Augmentation Strategies From Data

We present a simple self-training method that achieves 88.4% top-1 accuracy on ImageNet, which is 2.0% better than the state-of-the-art model that requires 3.5B weakly labeled Instagram images. On robustness test sets, it improves ImageNet-A top-1 accuracy from 61.0% to 83.7%, reduces ImageNet-C mean corruption error from 45.7 to 28.3, and reduces ImageNet-P mean flip rate from 27.8 to 12.2. To achieve this result, we first train an EfficientNet model on labeled ImageNet images and use it as a teacher to generate pseudo labels on 300M unlabeled images. We then train a larger EfficientNet as a student model on the combination of labeled and pseudo labeled images. We iterate this process by putting back the student as the teacher. During the generation of the pseudo labels, the teacher is not noised so that the pseudo labels are as accurate as possible. However, during the learning of the student, we inject noise such as dropout, stochastic depth and data augmentation via RandAugment to the student so that the student generalizes better than the teacher.

/pdf/self-training-with-noisy-student-improves-imagenet-mpoijz8hnv.pdf

Self-Training With Noisy Student Improves ImageNet Classification

Adaptive optimization methods, which perform local optimization with a metric constructed from the history of iterates, are becoming increasingly popular for training deep neural networks. Examples include AdaGrad, RMSProp, and Adam. We show that for simple overparameterized problems, adaptive methods often find drastically different solutions than gradient descent (GD) or stochastic gradient descent (SGD). We construct an illustrative binary classification problem where the data is linearly separable, GD and SGD achieve zero test error, and AdaGrad, Adam, and RMSProp attain test errors arbitrarily close to half. We additionally study the empirical generalization capability of adaptive methods on several state-of-the-art deep learning models. We observe that the solutions found by adaptive methods generalize worse (often significantly worse) than SGD, even when these solutions have better training performance. These results suggest that practitioners should reconsider the use of adaptive methods to train neural networks.

/pdf/the-marginal-value-of-adaptive-gradient-methods-in-machine-3vhfqmyifv.pdf

The Marginal Value of Adaptive Gradient Methods in Machine Learning

Machine learning is currently dominated by largely experimental work focused on improvements in a few key tasks. However, the impressive accuracy numbers of the best performing models are questionable because the same test sets have been used to select these models for multiple years now. To understand the danger of overfitting, we measure the accuracy of CIFAR-10 classifiers by creating a new test set of truly unseen images. Although we ensure that the new test set is as close to the original data distribution as possible, we find a large drop in accuracy (4% to 10%) for a broad range of deep learning models. Yet more recent models with higher original accuracy show a smaller drop and better overall performance, indicating that this drop is likely not due to overfitting based on adaptivity. Instead, we view our results as evidence that current accuracy numbers are brittle and susceptible to even minute natural variations in the data distribution.

Do CIFAR-10 Classifiers Generalize to CIFAR-10?

Adaptive optimization methods, which perform local optimization with a metric constructed from the history of iterates, are becoming increasingly popular for training deep neural networks Examples include AdaGrad, RMSProp, and Adam We show that for simple overparameterized problems, adaptive methods often find drastically different solutions than gradient descent (GD) or stochastic gradient descent (SGD) We construct an illustrative binary classification problem where the data is linearly separable, GD and SGD achieve zero test error, and AdaGrad, Adam, and RMSProp attain test errors arbitrarily close to half We additionally study the empirical generalization capability of adaptive methods on several state-of-the-art deep learning models We observe that the solutions found by adaptive methods generalize worse (often significantly worse) than SGD, even when these solutions have better training performance These results suggest that practitioners should reconsider the use of adaptive methods to train neural networks

We build new test sets for the CIFAR-10 and ImageNet datasets. Both benchmarks have been the focus of intense research for almost a decade, raising the danger of overfitting to excessively re-used test sets. By closely following the original dataset creation processes, we test to what extent current classification models generalize to new data. We evaluate a broad range of models and find accuracy drops of 3% - 15% on CIFAR-10 and 11% - 14% on ImageNet. However, accuracy gains on the original test sets translate to larger gains on the new test sets. Our results suggest that the accuracy drops are not caused by adaptivity, but by the models' inability to generalize to slightly "harder" images than those found in the original test sets.

Do ImageNet Classifiers Generalize to ImageNet

/pdf/do-imagenet-classifiers-generalize-to-imagenet-3xg7p22br9.pdf

Rebecca Roelofs

Papers

The Marginal Value of Adaptive Gradient Methods in Machine Learning

Do CIFAR-10 Classifiers Generalize to CIFAR-10?

The Marginal Value of Adaptive Gradient Methods in Machine Learning

Do ImageNet Classifiers Generalize to ImageNet

Do ImageNet Classifiers Generalize to ImageNet