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

Attention-based encoder-decoder architectures such as Listen, Attend, and Spell (LAS), subsume the acoustic, pronunciation and language model components of a traditional automatic speech recognition (ASR) system into a single neural network. In previous work, we have shown that such architectures are comparable to state-of-the-art ASR systems on dictation tasks, but it was not clear if such architectures would be practical for more challenging tasks such as voice search. In this work, we explore a variety of structural and optimization improvements to our LAS model which significantly improve performance. On the structural side, we show that word piece models can be used instead of graphemes. We also introduce a multi-head attention architecture, which offers improvements over the commonly-used single-head attention. On the optimization side, we explore synchronous training, scheduled sampling, label smoothing, and minimum word error rate optimization, which are all shown to improve accuracy. We present results with a unidirectional LSTM encoder for streaming recognition. On a 12, 500 hour voice search task, we find that the proposed changes improve the WER from 9.2% to 5.6%, while the best conventional system achieves 6.7%; on a dictation task our model achieves a WER of 4.1% compared to 5% for the conventional system.

State-of-the-Art Speech Recognition with Sequence-to-Sequence Models

This paper describes a new model-based speaker adaptation algorithm called the eigenvoice approach. The approach constrains the adapted model to be a linear combination of a small number of basis vectors obtained offline from a set of reference speakers, and thus greatly reduces the number of free parameters to be estimated from adaptation data. These "eigenvoice" basis vectors are orthogonal to each other and guaranteed to represent the most important components of variation between the reference speakers. Experimental results for a small-vocabulary task (letter recognition) given in the paper show that the approach yields major improvements in performance for tiny amounts of adaptation data. For instance, we obtained 16% relative improvement in error rate with one letter of supervised adaptation data, and 26% relative improvement with four letters of supervised adaptation data. After a comparison of the eigenvoice approach with other speaker adaptation algorithms, the paper concludes with a discussion of future work.

Rapid speaker adaptation in eigenvoice space

Deep neural networks have recently become the gold standard for acoustic modeling in speech recognition systems The key computational unit of a deep network is a linear projection followed by a point-wise non-linearity, which is typically a logistic function In this work, we show that we can improve generalization and make training of deep networks faster and simpler by substituting the logistic units with rectified linear units These units are linear when their input is positive and zero otherwise In a supervised setting, we can successfully train very deep nets from random initialization on a large vocabulary speech recognition task achieving lower word error rates than using a logistic network with the same topology Similarly in an unsupervised setting, we show how we can learn sparse features that can be useful for discriminative tasks All our experiments are executed in a distributed environment using several hundred machines and several hundred hours of speech data

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Patrick Nguyen

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

State-of-the-Art Speech Recognition with Sequence-to-Sequence Models

Rapid speaker adaptation in eigenvoice space

On rectified linear units for speech processing