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Register a new userThe Deep Bootstrap Framework: Good Online Learners are Good Offline Generalizers
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Added by
Preetum Nakkiran
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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We propose a new framework for reasoning about generalization in deep learning. The core idea is to couple the Real World, where optimizers take stochastic gradient steps on the empirical loss, to an Ideal World, where optimizers take steps on the population loss. This leads to an alternate decomposition of test error into: (1) the Ideal World test error plus (2) the gap between the two worlds. If the gap (2) is universally small, this reduces the problem of generalization in offline learning to the problem of optimization in online learning. We then give empirical evidence that this gap between worlds can be small in realistic deep learning settings, in particular supervised image classification. For example, CNNs generalize better than MLPs on image distributions in the Real World, but this is because they optimize faster on the population loss in the Ideal World. This suggests our framework is a useful tool for understanding generalization in deep learning, and lays a foundation for future research in the area.
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We modify the transchromatic character maps to land in a faithfully flat extension of Morava E-theory. Our construction makes use of the interaction between topological and algebraic localization and completion. As an application we prove that centralizers of tuples of commuting prime-power order elements in good groups are good and we compute a new example.
Recently, intermediate feature maps of pre-trained convolutional neural networks have shown significant perceptual quality improvements, when they are used in the loss function for training new networks. It is believed that these features are better at encoding the perceptual quality and provide more efficient representations of input images compared to other perceptual metrics such as SSIM and PSNR. However, there have been no systematic studies to determine the underlying reason. Due to the lack of such an analysis, it is not possible to evaluate the performance of a particular set of features or to improve the perceptual quality even more by carefully selecting a subset of features from a pre-trained CNN. This work shows that the capabilities of pre-trained deep CNN features in optimizing the perceptual quality are correlated with their success in capturing basic human visual perception characteristics. In particular, we focus our analysis on fundamental aspects of human perception, such as the contrast sensitivity and orientation selectivity. We introduce two new formulations to measure the frequency and orientation selectivity of the features learned by convolutional layers for evaluating deep features learned by widely-used deep CNNs such as VGG-16. We demonstrate that the pre-trained CNN features which receive higher scores are better at predicting human quality judgment. Furthermore, we show the possibility of using our method to select deep features to form a new loss function, which improves the image reconstruction quality for the well-known single-image super-resolution problem.
The current success of deep learning depends on large-scale labeled datasets. In practice, high-quality annotations are expensive to collect, but noisy annotations are more affordable. Previous works report mixed empirical results when training with noisy labels: neural networks can easily memorize random labels, but they can also generalize from noisy labels. To explain this puzzle, we study how architecture affects learning with noisy labels. We observe that if an architecture suits the task, training with noisy labels can induce useful hidden representations, even when the model generalizes poorly; i.e., the last few layers of the model are more negatively affected by noisy labels. This finding leads to a simple method to improve models trained on noisy labels: replacing the final dense layers with a linear model, whose weights are learned from a small set of clean data. We empirically validate our findings across three architectures (Convolutional Neural Networks, Graph Neural Networks, and Multi-Layer Perceptrons) and two domains (graph algorithmic tasks and image classification). Furthermore, we achieve state-of-the-art results on image classification benchmarks by combining our method with existing approaches on noisy label training.
Lottery ticket hypothesis suggests that a dense neural network contains a sparse sub-network that can match the test accuracy of the original dense net when trained in isolation from (the same) random initialization. However, the hypothesis failed to generalize to larger dense networks such as ResNet-50. As a remedy, recent studies demonstrate that a sparse sub-network can still be obtained by using a rewinding technique, which is to re-train it from early-phase training weights or learning rates of the dense model, rather than from random initialization. Is rewinding the only or the best way to scale up lottery tickets? This paper proposes a new, simpler and yet powerful technique for re-training the sub-network, called Knowledge Distillation ticket (KD ticket). Rewinding exploits the value of inheriting knowledge from the early training phase to improve lottery tickets in large networks. In comparison, KD ticket addresses a complementary possibility - inheriting useful knowledge from the late training phase of the dense model. It is achieved by leveraging the soft labels generated by the trained dense model to re-train the sub-network, instead of the hard labels. Extensive experiments are conducted using several large deep networks (e.g ResNet-50 and ResNet-110) on CIFAR-10 and ImageNet datasets. Without bells and whistles, when applied by itself, KD ticket performs on par or better than rewinding, while being nearly free of hyperparameters or ad-hoc selection. KD ticket can be further applied together with rewinding, yielding state-of-the-art results for large-scale lottery tickets.
Recent years have witnessed the rapid advance in neural machine translation (NMT), the core of which lies in the encoder-decoder architecture. Inspired by the recent progress of large-scale pre-trained language models on machine translation in a limited scenario, we firstly demonstrate that a single language model (LM4MT) can achieve comparable performance with strong encoder-decoder NMT models on standard machine translation benchmarks, using the same training data and similar amount of model parameters. LM4MT can also easily utilize source-side texts as additional supervision. Though modeling the source- and target-language texts with the same mechanism, LM4MT can provide unified representations for both source and target sentences, which can better transfer knowledge across languages. Extensive experiments on pivot-based and zero-shot translation tasks show that LM4MT can outperform the encoder-decoder NMT model by a large margin.
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