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Register a new userWhy are Adaptive Methods Good for Attention Models?
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Added by
Jingzhao Zhang
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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While stochastic gradient descent (SGD) is still the emph{de facto} algorithm in deep learning, adaptive methods like Clipped SGD/Adam have been observed to outperform SGD across important tasks, such as attention models. The settings under which SGD performs poorly in comparison to adaptive methods are not well understood yet. In this paper, we provide empirical and theoretical evidence that a heavy-tailed distribution of the noise in stochastic gradients is one cause of SGDs poor performance. We provide the first tight upper and lower convergence bounds for adaptive gradient methods under heavy-tailed noise. Further, we demonstrate how gradient clipping plays a key role in addressing heavy-tailed gradient noise. Subsequently, we show how clipping can be applied in practice by developing an emph{adaptive} coordinate-wise clipping algorithm (ACClip) and demonstrate its superior performance on BERT pretraining and finetuning tasks.
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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.
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.
Adaptive gradient methods have attracted much attention of machine learning communities due to the high efficiency. However their acceleration effect in practice, especially in neural network training, is hard to analyze, theoretically. The huge gap between theoretical convergence results and practical performances prevents further understanding of existing optimizers and the development of more advanced optimization methods. In this paper, we provide adaptive gradient methods a novel analysis with an additional mild assumption, and revise AdaGrad to radagrad for matching a better provable convergence rate. To find an $epsilon$-approximate first-order stationary point in non-convex objectives, we prove random shuffling radagrad achieves a $tilde{O}(T^{-1/2})$ convergence rate, which is significantly improved by factors $tilde{O}(T^{-1/4})$ and $tilde{O}(T^{-1/6})$ compared with existing adaptive gradient methods and random shuffling SGD, respectively. To the best of our knowledge, it is the first time to demonstrate that adaptive gradient methods can deterministically be faster than SGD after finite epochs. Furthermore, we conduct comprehensive experiments to validate the additional mild assumption and the acceleration effect benefited from second moments and random shuffling.
We provide a theoretical explanation for the effectiveness of gradient clipping in training deep neural networks. The key ingredient is a new smoothness condition derived from practical neural network training examples. We observe that gradient smoothness, a concept central to the analysis of first-order optimization algorithms that is often assumed to be a constant, demonstrates significant variability along the training trajectory of deep neural networks. Further, this smoothness positively correlates with the gradient norm, and contrary to standard assumptions in the literature, it can grow with the norm of the gradient. These empirical observations limit the applicability of existing theoretical analyses of algorithms that rely on a fixed bound on smoothness. These observations motivate us to introduce a novel relaxation of gradient smoothness that is weaker than the commonly used Lipschitz smoothness assumption. Under the new condition, we prove that two popular methods, namely, emph{gradient clipping} and emph{normalized gradient}, converge arbitrarily faster than gradient descent with fixed stepsize. We further explain why such adaptively scaled gradient methods can accelerate empirical convergence and verify our results empirically in popular neural network training settings.
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.
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