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.

Adam: A Method for Stochastic Optimization

Deep learning allows computational models that are composed of multiple processing layers to learn representations of data with multiple levels of abstraction. These methods have dramatically improved the state-of-the-art in speech recognition, visual object recognition, object detection and many other domains such as drug discovery and genomics. Deep learning discovers intricate structure in large data sets by using the backpropagation algorithm to indicate how a machine should change its internal parameters that are used to compute the representation in each layer from the representation in the previous layer. Deep convolutional nets have brought about breakthroughs in processing images, video, speech and audio, whereas recurrent nets have shone light on sequential data such as text and speech.

Deep learning

We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to ½ everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.

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Generative Adversarial Nets

Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

Deep Learning

Most current speech recognition systems use hidden Markov models (HMMs) to deal with the temporal variability of speech and Gaussian mixture models (GMMs) to determine how well each state of each HMM fits a frame or a short window of frames of coefficients that represents the acoustic input. An alternative way to evaluate the fit is to use a feed-forward neural network that takes several frames of coefficients as input and produces posterior probabilities over HMM states as output. Deep neural networks (DNNs) that have many hidden layers and are trained using new methods have been shown to outperform GMMs on a variety of speech recognition benchmarks, sometimes by a large margin. This article provides an overview of this progress and represents the shared views of four research groups that have had recent successes in using DNNs for acoustic modeling in speech recognition.

Deep Neural Networks for Acoustic Modeling in Speech Recognition: The Shared Views of Four Research Groups

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Deep Neural Networks for Acoustic Modeling in Speech Recognition

Both Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) have shown improvements over Deep Neural Networks (DNNs) across a wide variety of speech recognition tasks. CNNs, LSTMs and DNNs are complementary in their modeling capabilities, as CNNs are good at reducing frequency variations, LSTMs are good at temporal modeling, and DNNs are appropriate for mapping features to a more separable space. In this paper, we take advantage of the complementarity of CNNs, LSTMs and DNNs by combining them into one unified architecture. We explore the proposed architecture, which we call CLDNN, on a variety of large vocabulary tasks, varying from 200 to 2,000 hours. We find that the CLDNN provides a 4–6% relative improvement in WER over an LSTM, the strongest of the three individual models.

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Convolutional, Long Short-Term Memory, fully connected Deep Neural Networks

Recently, pre-trained deep neural networks (DNNs) have outperformed traditional acoustic models based on Gaussian mixture models (GMMs) on a variety of large vocabulary speech recognition benchmarks. Deep neural nets have also achieved excellent results on various computer vision tasks using a random “dropout” procedure that drastically improves generalization error by randomly omitting a fraction of the hidden units in all layers. Since dropout helps avoid over-fitting, it has also been successful on a small-scale phone recognition task using larger neural nets. However, training deep neural net acoustic models for large vocabulary speech recognition takes a very long time and dropout is likely to only increase training time. Neural networks with rectified linear unit (ReLU) non-linearities have been highly successful for computer vision tasks and proved faster to train than standard sigmoid units, sometimes also improving discriminative performance. In this work, we show on a 50-hour English Broadcast News task that modified deep neural networks using ReLUs trained with dropout during frame level training provide an 4.2% relative improvement over a DNN trained with sigmoid units, and a 14.4% relative improvement over a strong GMM/HMM system. We were able to obtain our results with minimal human hyper-parameter tuning using publicly available Bayesian optimization code.

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Improving deep neural networks for LVCSR using rectified linear units and dropout

Convolutional Neural Networks (CNNs) are an alternative type of neural network that can be used to reduce spectral variations and model spectral correlations which exist in signals. Since speech signals exhibit both of these properties, CNNs are a more effective model for speech compared to Deep Neural Networks (DNNs). In this paper, we explore applying CNNs to large vocabulary speech tasks. First, we determine the appropriate architecture to make CNNs effective compared to DNNs for LVCSR tasks. Specifically, we focus on how many convolutional layers are needed, what is the optimal number of hidden units, what is the best pooling strategy, and the best input feature type for CNNs. We then explore the behavior of neural network features extracted from CNNs on a variety of LVCSR tasks, comparing CNNs to DNNs and GMMs. We find that CNNs offer between a 13-30% relative improvement over GMMs, and a 4-12% relative improvement over DNNs, on a 400-hr Broadcast News and 300-hr Switchboard task.

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Tara N. Sainath

Papers

Deep Neural Networks for Acoustic Modeling in Speech Recognition: The Shared Views of Four Research Groups

Deep Neural Networks for Acoustic Modeling in Speech Recognition

Convolutional, Long Short-Term Memory, fully connected Deep Neural Networks

Improving deep neural networks for LVCSR using rectified linear units and dropout

Deep convolutional neural networks for LVCSR