Open AccessProceedings Article
Adam: A Method for Stochastic Optimization
Diederik P. Kingma,Jimmy Ba +1 more
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This work introduces Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments, and provides a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework.Abstract:
We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and/or parameters. The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients. The hyper-parameters have intuitive interpretations and typically require little tuning. Some connections to related algorithms, on which Adam was inspired, are discussed. We also analyze the theoretical convergence properties of the algorithm and provide a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Empirical results demonstrate that Adam works well in practice and compares favorably to other stochastic optimization methods. Finally, we discuss AdaMax, a variant of Adam based on the infinity norm.read more
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References
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Proceedings Article
ImageNet Classification with Deep Convolutional Neural Networks
TL;DR: The state-of-the-art performance of CNNs was achieved by Deep Convolutional Neural Networks (DCNNs) as discussed by the authors, which consists of five convolutional layers, some of which are followed by max-pooling layers, and three fully-connected layers with a final 1000-way softmax.
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Auto-Encoding Variational Bayes
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TL;DR: A stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case is introduced.
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Reducing the Dimensionality of Data with Neural Networks
TL;DR: In this article, an effective way of initializing the weights that allows deep autoencoder networks to learn low-dimensional codes that work much better than principal components analysis as a tool to reduce the dimensionality of data is described.
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Deep Neural Networks for Acoustic Modeling in Speech Recognition: The Shared Views of Four Research Groups
Geoffrey E. Hinton,Li Deng,Dong Yu,George E. Dahl,Abdelrahman Mohamed,Navdeep Jaitly,Andrew W. Senior,Vincent Vanhoucke,Patrick Nguyen,Tara N. Sainath,Brian Kingsbury +10 more
TL;DR: This article provides an overview of progress and represents the shared views of four research groups that have had recent successes in using DNNs for acoustic modeling in speech recognition.
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Adaptive Subgradient Methods for Online Learning and Stochastic Optimization.
TL;DR: Adaptive subgradient methods as discussed by the authors dynamically incorporate knowledge of the geometry of the data observed in earlier iterations to perform more informative gradient-based learning, which allows us to find needles in haystacks in the form of very predictive but rarely seen features.