self training with noisy student improves imagenet classification

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. Then, EfficientNet-L1 is scaled up from EfficientNet-L0 by increasing width. If nothing happens, download Xcode and try again. In our experiments, we use dropout[63], stochastic depth[29], data augmentation[14] to noise the student. Med. The model with Noisy Student can successfully predict the correct labels of these highly difficult images. over the JFT dataset to predict a label for each image. Self-Training With Noisy Student Improves ImageNet Classification @article{Xie2019SelfTrainingWN, title={Self-Training With Noisy Student Improves ImageNet Classification}, author={Qizhe Xie and Eduard H. Hovy and Minh-Thang Luong and Quoc V. Le}, journal={2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)}, year={2019 . The ONCE (One millioN sCenEs) dataset for 3D object detection in the autonomous driving scenario is introduced and a benchmark is provided in which a variety of self-supervised and semi- supervised methods on the ONCE dataset are evaluated. We use stochastic depth[29], dropout[63] and RandAugment[14]. 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. By showing the models only labeled images, we limit ourselves from making use of unlabeled images available in much larger quantities to improve accuracy and robustness of state-of-the-art models. Selected images from robustness benchmarks ImageNet-A, C and P. Test images from ImageNet-C underwent artificial transformations (also known as common corruptions) that cannot be found on the ImageNet training set. These CVPR 2020 papers are the Open Access versions, provided by the. We sample 1.3M images in confidence intervals. Noisy Student Training is based on the self-training framework and trained with 4-simple steps: Train a classifier on labeled data (teacher). We apply dropout to the final classification layer with a dropout rate of 0.5. It implements SemiSupervised Learning with Noise to create an Image Classification. Our model is also approximately twice as small in the number of parameters compared to FixRes ResNeXt-101 WSL. We used the version from [47], which filtered the validation set of ImageNet. and surprising gains on robustness and adversarial benchmarks. We iterate this process by putting back the student as the teacher. During this process, we kept increasing the size of the student model to improve the performance. This way, the pseudo labels are as good as possible, and the noised student is forced to learn harder from the pseudo labels. This work introduces two challenging datasets that reliably cause machine learning model performance to substantially degrade and curates an adversarial out-of-distribution detection dataset called IMAGENET-O, which is the first out- of-dist distribution detection dataset created for ImageNet models. We verify that this is not the case when we use 130M unlabeled images since the model does not overfit the unlabeled set from the training loss. The results also confirm that vision models can benefit from Noisy Student even without iterative training. This work proposes a novel architectural unit, which is term the Squeeze-and-Excitation (SE) block, that adaptively recalibrates channel-wise feature responses by explicitly modelling interdependencies between channels and shows that these blocks can be stacked together to form SENet architectures that generalise extremely effectively across different datasets. We use EfficientNet-B4 as both the teacher and the student. On robustness test sets, it improves ImageNet-A top-1 accuracy from 61.0% to . 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). supervised model from 97.9% accuracy to 98.6% accuracy. Self-training with noisy student improves imagenet classification, in: Proceedings of the IEEE/CVF Conference on Computer . Self-Training With Noisy Student Improves ImageNet Classification. For example, without Noisy Student, the model predicts bullfrog for the image shown on the left of the second row, which might be resulted from the black lotus leaf on the water. By clicking accept or continuing to use the site, you agree to the terms outlined in our. We present Noisy Student Training, a semi-supervised learning approach that works well even when labeled data is abundant. It is expensive and must be done with great care. 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. Noisy Student improves adversarial robustness against an FGSM attack though the model is not optimized for adversarial robustness. C. Szegedy, S. Ioffe, V. Vanhoucke, and A. This attack performs one gradient descent step on the input image[20] with the update on each pixel set to . Noise Self-training with Noisy Student 1. We investigate the importance of noising in two scenarios with different amounts of unlabeled data and different teacher model accuracies. Noisy StudentImageNetEfficientNet-L2state-of-the-art. Code for Noisy Student Training. This accuracy is 1.0% better than the previous state-of-the-art ImageNet accuracy which requires 3.5B weakly labeled Instagram images. During the generation of the pseudo labels, the teacher is not noised so that the pseudo labels are as accurate as possible. Different kinds of noise, however, may have different effects. 10687-10698 Abstract Self-training with Noisy Student. Apart from self-training, another important line of work in semi-supervised learning[9, 85] is based on consistency training[6, 4, 53, 36, 70, 45, 41, 51, 10, 12, 49, 2, 38, 72, 74, 5, 81]. We use our best model Noisy Student with EfficientNet-L2 to teach student models with sizes ranging from EfficientNet-B0 to EfficientNet-B7. Sun, Z. Liu, D. Sedra, and K. Q. Weinberger, Y. Huang, Y. Cheng, D. Chen, H. Lee, J. Ngiam, Q. V. Le, and Z. Chen, GPipe: efficient training of giant neural networks using pipeline parallelism, A. Iscen, G. Tolias, Y. Avrithis, and O. We then select images that have confidence of the label higher than 0.3. We obtain unlabeled images from the JFT dataset [26, 11], which has around 300M images. Here we study if it is possible to improve performance on small models by using a larger teacher model, since small models are useful when there are constraints for model size and latency in real-world applications. unlabeled images. Their noise model is video specific and not relevant for image classification. Noisy Student Training 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. Here we use unlabeled images to improve the state-of-the-art ImageNet accuracy and show that the accuracy gain has an outsized impact on robustness. Self-training with Noisy Student improves ImageNet classification. The algorithm is iterated a few times by treating the student as a teacher to relabel the unlabeled data and training a new student. 3.5B weakly labeled Instagram images. During the generation of the pseudo labels, the teacher is not noised so that the pseudo labels are as accurate as possible. Although the images in the dataset have labels, we ignore the labels and treat them as unlabeled data. In both cases, we gradually remove augmentation, stochastic depth and dropout for unlabeled images, while keeping them for labeled images. CLIP (Contrastive Language-Image Pre-training) builds on a large body of work on zero-shot transfer, natural language supervision, and multimodal learning.The idea of zero-data learning dates back over a decade [^reference-8] but until recently was mostly studied in computer vision as a way of generalizing to unseen object categories. The results are shown in Figure 4 with the following observations: (1) Soft pseudo labels and hard pseudo labels can both lead to great improvements with in-domain unlabeled images i.e., high-confidence images. We iterate this process by putting back the student as the teacher. IEEE Trans. We then train a larger EfficientNet as a student model on the We call the method self-training with Noisy Student to emphasize the role that noise plays in the method and results. After testing our models robustness to common corruptions and perturbations, we also study its performance on adversarial perturbations. 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. Self-training with Noisy Student improves ImageNet classificationCVPR2020, Codehttps://github.com/google-research/noisystudent, Self-training, 1, 2Self-training, Self-trainingGoogleNoisy Student, Noisy Studentstudent modeldropout, stochastic depth andaugmentationteacher modelNoisy Noisy Student, Noisy Student, 1, JFT3ImageNetEfficientNet-B00.3130K130K, EfficientNetbaseline modelsEfficientNetresnet, EfficientNet-B7EfficientNet-L0L1L2, batchsize = 2048 51210242048EfficientNet-B4EfficientNet-L0l1L2350epoch700epoch, 2EfficientNet-B7EfficientNet-L0, 3EfficientNet-L0EfficientNet-L1L0, 4EfficientNet-L1EfficientNet-L2, student modelNoisy, noisystudent modelteacher modelNoisy, Noisy, Self-trainingaugmentationdropoutstochastic depth, Our largest model, EfficientNet-L2, needs to be trained for 3.5 days on a Cloud TPU v3 Pod, which has 2048 cores., 12/self-training-with-noisy-student-f33640edbab2, EfficientNet-L0EfficientNet-B7B7, EfficientNet-L1EfficientNet-L0, EfficientNetsEfficientNet-L1EfficientNet-L2EfficientNet-L2EfficientNet-B75. Our study shows that using unlabeled data improves accuracy and general robustness. This invariance constraint reduces the degrees of freedom in the model. For smaller models, we set the batch size of unlabeled images to be the same as the batch size of labeled images. 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. Noisy Student Training is based on the self-training framework and trained with 4 simple steps: For ImageNet checkpoints trained by Noisy Student Training, please refer to the EfficientNet github. Due to the large model size, the training time of EfficientNet-L2 is approximately five times the training time of EfficientNet-B7. But training robust supervised learning models is requires this step. We have also observed that using hard pseudo labels can achieve as good results or slightly better results when a larger teacher is used. During the generation of the pseudo Specifically, we train the student model for 350 epochs for models larger than EfficientNet-B4, including EfficientNet-L0, L1 and L2 and train the student model for 700 epochs for smaller models. However, the additional hyperparameters introduced by the ramping up schedule and the entropy minimization make them more difficult to use at scale. Noisy Student leads to significant improvements across all model sizes for EfficientNet. For example, with all noise removed, the accuracy drops from 84.9% to 84.3% in the case with 130M unlabeled images and drops from 83.9% to 83.2% in the case with 1.3M unlabeled images. The top-1 and top-5 accuracy are measured on the 200 classes that ImageNet-A includes. We then train a larger EfficientNet as a student model on the combination of labeled and pseudo labeled images. In other words, small changes in the input image can cause large changes to the predictions. Proceedings of the eleventh annual conference on Computational learning theory, Proceedings of the IEEE conference on computer vision and pattern recognition, Empirical Methods in Natural Language Processing (EMNLP), Imagenet classification with deep convolutional neural networks, Domain adaptive transfer learning with specialist models, Thirty-Second AAAI Conference on Artificial Intelligence, Regularized evolution for image classifier architecture search, Inception-v4, inception-resnet and the impact of residual connections on learning. We also list EfficientNet-B7 as a reference. Self-training first uses labeled data to train a good teacher model, then use the teacher model to label unlabeled data and finally use the labeled data and unlabeled data to jointly train a student model. For this purpose, we use a much larger corpus of unlabeled images, where some images may not belong to any category in ImageNet. Prior works on weakly-supervised learning require billions of weakly labeled data to improve state-of-the-art ImageNet models. We present Noisy Student Training, a semi-supervised learning approach that works well even when labeled data is abundant. Self-training 1 2Self-training 3 4n What is Noisy Student? Whether the model benefits from more unlabeled data depends on the capacity of the model since a small model can easily saturate, while a larger model can benefit from more data. 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition. The hyperparameters for these noise functions are the same for EfficientNet-B7, L0, L1 and L2. First, we run an EfficientNet-B0 trained on ImageNet[69]. On ImageNet-P, it leads to an mean flip rate (mFR) of 17.8 if we use a resolution of 224x224 (direct comparison) and 16.1 if we use a resolution of 299x299.111For EfficientNet-L2, we use the model without finetuning with a larger test time resolution, since a larger resolution results in a discrepancy with the resolution of data and leads to degraded performance on ImageNet-C and ImageNet-P. However, in the case with 130M unlabeled images, with noise function removed, the performance is still improved to 84.3% from 84.0% when compared to the supervised baseline. On ImageNet, we first train an EfficientNet model on labeled images and use it as a teacher to generate pseudo labels for 300M unlabeled images. Train a classifier on labeled data (teacher). However, manually annotating organs from CT scans is time . Noisy Student Training seeks to improve on self-training and distillation in two ways. 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. In the following, we will first describe experiment details to achieve our results. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators . This result is also a new state-of-the-art and 1% better than the previous best method that used an order of magnitude more weakly labeled data[44, 71]. If nothing happens, download GitHub Desktop and try again. Figure 1(c) shows images from ImageNet-P and the corresponding predictions. Then we finetune the model with a larger resolution for 1.5 epochs on unaugmented labeled images. Please On, International journal of molecular sciences. We vary the model size from EfficientNet-B0 to EfficientNet-B7[69] and use the same model as both the teacher and the student. For instance, on ImageNet-A, Noisy Student achieves 74.2% top-1 accuracy which is approximately 57% more accurate than the previous state-of-the-art model. A tag already exists with the provided branch name. International Conference on Machine Learning, Learning extraction patterns for subjective expressions, Proceedings of the 2003 conference on Empirical methods in natural language processing, A. Roy Chowdhury, P. Chakrabarty, A. Singh, S. Jin, H. Jiang, L. Cao, and E. G. Learned-Miller, Automatic adaptation of object detectors to new domains using self-training, T. Salimans, I. Goodfellow, W. Zaremba, V. Cheung, A. Radford, and X. Chen, Probability of error of some adaptive pattern-recognition machines, W. Shi, Y. Gong, C. Ding, Z. MaXiaoyu Tao, and N. Zheng, Transductive semi-supervised deep learning using min-max features, C. Simon-Gabriel, Y. Ollivier, L. Bottou, B. Schlkopf, and D. Lopez-Paz, First-order adversarial vulnerability of neural networks and input dimension, Very deep convolutional networks for large-scale image recognition, N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, Dropout: a simple way to prevent neural networks from overfitting. A common workaround is to use entropy minimization or ramp up the consistency loss. Next, a larger student model is trained on the combination of all data and achieves better performance than the teacher by itself.OUTLINE:0:00 - Intro \u0026 Overview1:05 - Semi-Supervised \u0026 Transfer Learning5:45 - Self-Training \u0026 Knowledge Distillation10:00 - Noisy Student Algorithm Overview20:20 - Noise Methods22:30 - Dataset Balancing25:20 - Results30:15 - Perturbation Robustness34:35 - Ablation Studies39:30 - Conclusion \u0026 CommentsPaper: https://arxiv.org/abs/1911.04252Code: https://github.com/google-research/noisystudentModels: https://github.com/tensorflow/tpu/tree/master/models/official/efficientnetAbstract:We present Noisy Student Training, a semi-supervised learning approach that works well even when labeled data is abundant. (Submitted on 11 Nov 2019) We present a simple self-training method that achieves 87.4% top-1 accuracy on ImageNet, which is 1.0% better than the state-of-the-art model that requires 3.5B weakly labeled Instagram images. The abundance of data on the internet is vast. augmentation, dropout, stochastic depth to the student so that the noised We determine number of training steps and the learning rate schedule by the batch size for labeled images. https://arxiv.org/abs/1911.04252, Accompanying notebook and sources to "A Guide to Pseudolabelling: How to get a Kaggle medal with only one model" (Dec. 2020 PyData Boston-Cambridge Keynote), Deep learning has shown remarkable successes in image recognition in recent years[35, 66, 62, 23, 69]. We then use the teacher model to generate pseudo labels on unlabeled images. Self-training is a form of semi-supervised learning [10] which attempts to leverage unlabeled data to improve classification performance in the limited data regime. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (pp. The proposed use of distillation to only handle easy instances allows for a more aggressive trade-off in the student size, thereby reducing the amortized cost of inference and achieving better accuracy than standard distillation. to noise the student. At the top-left image, the model without Noisy Student ignores the sea lions and mistakenly recognizes a buoy as a lighthouse, while the model with Noisy Student can recognize the sea lions. These test sets are considered as robustness benchmarks because the test images are either much harder, for ImageNet-A, or the test images are different from the training images, for ImageNet-C and P. For ImageNet-C and ImageNet-P, we evaluate our models on two released versions with resolution 224x224 and 299x299 and resize images to the resolution EfficientNet is trained on. Noisy student-teacher training for robust keyword spotting, Unsupervised Self-training Algorithm Based on Deep Learning for Optical The most interesting image is shown on the right of the first row. A tag already exists with the provided branch name. Similar to[71], we fix the shallow layers during finetuning. For this purpose, we use the recently developed EfficientNet architectures[69] because they have a larger capacity than ResNet architectures[23]. "Self-training with Noisy Student improves ImageNet classification" pytorch implementation. The method, named self-training with Noisy Student, also benefits from the large capacity of EfficientNet family. The performance drops when we further reduce it. Finally, we iterate the algorithm a few times by treating the student as a teacher to generate new pseudo labels and train a new student. The main difference between our work and prior works is that we identify the importance of noise, and aggressively inject noise to make the student better. This is why "Self-training with Noisy Student improves ImageNet classification" written by Qizhe Xie et al makes me very happy. In other words, the student is forced to mimic a more powerful ensemble model. Self-training with Noisy Student improves ImageNet classication Qizhe Xie 1, Minh-Thang Luong , Eduard Hovy2, Quoc V. Le1 1Google Research, Brain Team, 2Carnegie Mellon University fqizhex, thangluong, qvlg@google.com, hovy@cmu.edu Abstract We present Noisy Student Training, a semi-supervised learning approach that works well even when . In the above experiments, iterative training was used to optimize the accuracy of EfficientNet-L2 but here we skip it as it is difficult to use iterative training for many experiments. Do better imagenet models transfer better? 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. Parthasarathi et al. In Noisy Student, we combine these two steps into one because it simplifies the algorithm and leads to better performance in our preliminary experiments. ImageNet-A test set[25] consists of difficult images that cause significant drops in accuracy to state-of-the-art models. The width. Since we use soft pseudo labels generated from the teacher model, when the student is trained to be exactly the same as the teacher model, the cross entropy loss on unlabeled data would be zero and the training signal would vanish. We evaluate our EfficientNet-L2 models with and without Noisy Student against an FGSM attack. Models are available at https://github.com/tensorflow/tpu/tree/master/models/official/efficientnet. Hence, whether soft pseudo labels or hard pseudo labels work better might need to be determined on a case-by-case basis. Train a larger classifier on the combined set, adding noise (noisy student). Noisy Student Training is a semi-supervised learning method which achieves 88.4% top-1 accuracy on ImageNet (SOTA) and surprising gains on robustness and adversarial benchmarks. A self-training method that better adapt to the popular two stage training pattern for multi-label text classification under a semi-supervised scenario by continuously finetuning the semantic space toward increasing high-confidence predictions, intending to further promote the performance on target tasks. Astrophysical Observatory. To intuitively understand the significant improvements on the three robustness benchmarks, we show several images in Figure2 where the predictions of the standard model are incorrect and the predictions of the Noisy Student model are correct. Finally, the training time of EfficientNet-L2 is around 2.72 times the training time of EfficientNet-L1. As shown in Figure 3, Noisy Student leads to approximately 10% improvement in accuracy even though the model is not optimized for adversarial robustness. to use Codespaces. Yalniz et al. Our experiments showed that self-training with Noisy Student and EfficientNet can achieve an accuracy of 87.4% which is 1.9% higher than without Noisy Student. . et al. . The total gain of 2.4% comes from two sources: by making the model larger (+0.5%) and by Noisy Student (+1.9%). In contrast, changing architectures or training with weakly labeled data give modest gains in accuracy from 4.7% to 16.6%. Hence, a question that naturally arises is why the student can outperform the teacher with soft pseudo labels. Noisy Students performance improves with more unlabeled data. In particular, we first perform normal training with a smaller resolution for 350 epochs. We iterate this process by putting back the student as the teacher. Scripts used for our ImageNet experiments: Similar scripts to run predictions on unlabeled data, filter and balance data and train using the filtered data. ImageNet . As stated earlier, we hypothesize that noising the student is needed so that it does not merely learn the teachers knowledge. possible. This article demonstrates the first tool based on a convolutional Unet++ encoderdecoder architecture for the semantic segmentation of in vitro angiogenesis simulation images followed by the resulting mask postprocessing for data analysis by experts. As a comparison, our method only requires 300M unlabeled images, which is perhaps more easy to collect. A novel random matrix theory based damping learner for second order optimisers inspired by linear shrinkage estimation is developed, and it is demonstrated that the derived method works well with adaptive gradient methods such as Adam. Qizhe Xie, Eduard Hovy, Minh-Thang Luong, Quoc V. Le. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. Self-Training With Noisy Student Improves ImageNet Classification Qizhe Xie, Minh-Thang Luong, Eduard Hovy, Quoc V. Le; Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2020, pp. Noisy Student Training extends the idea of self-training and distillation with the use of equal-or-larger student models and noise added to the student during learning. [57] used self-training for domain adaptation. This paper presents a unique study of transfer learning with large convolutional networks trained to predict hashtags on billions of social media images and shows improvements on several image classification and object detection tasks, and reports the highest ImageNet-1k single-crop, top-1 accuracy to date. As shown in Table3,4 and5, when compared with the previous state-of-the-art model ResNeXt-101 WSL[44, 48] trained on 3.5B weakly labeled images, Noisy Student yields substantial gains on robustness datasets. Lastly, we follow the idea of compound scaling[69] and scale all dimensions to obtain EfficientNet-L2. On ImageNet, we first train an EfficientNet model on labeled images and use it as a teacher to generate pseudo labels for 300M unlabeled images. For simplicity, we experiment with using 1128,164,132,116,14 of the whole data by uniformly sampling images from the the unlabeled set though taking the images with highest confidence leads to better results. The top-1 accuracy is simply the average top-1 accuracy for all corruptions and all severity degrees. Are you sure you want to create this branch? To noise the student, we use dropout[63], data augmentation[14] and stochastic depth[29] during its training. Due to duplications, there are only 81M unique images among these 130M images. Unlike previous studies in semi-supervised learning that use in-domain unlabeled data (e.g, ., CIFAR-10 images as unlabeled data for a small CIFAR-10 training set), to improve ImageNet, we must use out-of-domain unlabeled data. If nothing happens, download GitHub Desktop and try again. This result is also a new state-of-the-art and 1% better than the previous best method that used an order of magnitude more weakly labeled data [ 44, 71]. To achieve strong results on ImageNet, the student model also needs to be large, typically larger than common vision models, so that it can leverage a large number of unlabeled images. Do imagenet classifiers generalize to imagenet? For instance, on the right column, as the image of the car undergone a small rotation, the standard model changes its prediction from racing car to car wheel to fire engine. Self-training with Noisy Student improves ImageNet classification. Our experiments showed that our model significantly improves accuracy on ImageNet-A, C and P without the need for deliberate data augmentation. The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative We first report the validation set accuracy on the ImageNet 2012 ILSVRC challenge prediction task as commonly done in literature[35, 66, 23, 69] (see also [55]). For each class, we select at most 130K images that have the highest confidence. Stochastic Depth is a simple yet ingenious idea to add noise to the model by bypassing the transformations through skip connections. task. The comparison is shown in Table 9. We hypothesize that the improvement can be attributed to SGD, which introduces stochasticity into the training process. We conduct experiments on ImageNet 2012 ILSVRC challenge prediction task since it has been considered one of the most heavily benchmarked datasets in computer vision and that improvements on ImageNet transfer to other datasets. The mapping from the 200 classes to the original ImageNet classes are available online.222https://github.com/hendrycks/natural-adv-examples/blob/master/eval.py. You signed in with another tab or window. Self-Training Noisy Student " " Self-Training . This material is presented to ensure timely dissemination of scholarly and technical work. It has three main steps: train a teacher model on labeled images use the teacher to generate pseudo labels on unlabeled images Scaling width and resolution by c leads to c2 times training time and scaling depth by c leads to c times training time. , have shown that computer vision models lack robustness. [^reference-9] [^reference-10] A critical insight was to . A. Krizhevsky, I. Sutskever, and G. E. 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