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

There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

In this work, we propose recurrent deep neural networks (DNNs) for robust automatic speech recognition (ASR). Full recurrent connections are added to certain hidden layer of a conventional feedforward DNN and allow the model to capture the temporal dependency in deep representations. A new backpropagation through time (BPTT) algorithm is introduced to make the minibatch stochastic gradient descent (SGD) on the proposed recurrent DNNs more efficient and effective. We evaluate the proposed recurrent DNN architecture under the hybrid setup on both the 2
 nd
 CHiME challenge (track 2) and Aurora-4 tasks. Experimental results on the CHiME challenge data show that the proposed system can obtain consistent 7% relative WER improvements over the DNN systems, achieving state-of-the-art performance without front-end preprocessing, speaker adaptive training or multiple decoding passes. For the experiments on Aurora-4, the proposed system achieves 4% relative WER improvement over a strong DNN baseline system.

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Recurrent deep neural networks for robust speech recognition

In this paper, we present our recent development of a model-domain environment-robust adaptation algorithm, which demonstrates high performance in the standard Aurora 2 speech recognition task. The algorithm consists of two main steps. First, the noise and channel parameters are estimated using a nonlinear environment distortion model in the cepstral domain, the speech recognizer's "feedback" information, and the vector-Taylor-series (VTS) linearization technique collectively. Second, the estimated noise and channel parameters are used to adapt the static and dynamic portions of the HMM means and variances. This two-step algorithm enables joint compensation of both additive and convolutive distortions (JAC). In the experimental evaluation using the standard Aurora 2 task, the proposed JAC/VTS algorithm achieves 91.11% accuracy using the clean-trained simple HMM backend as the baseline system for the model adaptation. This represents high recognition performance on this task without discriminative training of the HMM system. Detailed analysis on the experimental results shows that adaptation of the dynamic portion of the HMM mean and variance parameters is critical to the success of our algorithm.

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High-performance hmm adaptation with joint compensation of additive and convolutive distortions via Vector Taylor Series

The recently proposed context-dependent deep neural network hidden Markov models (CD-DNN-HMMs) have been proved highly promising for large vocabulary speech recognition. In this paper, we develop a more advanced type of DNN, which we call the deep tensor neural network (DTNN). The DTNN extends the conventional DNN by replacing one or more of its layers with a double-projection (DP) layer, in which each input vector is projected into two nonlinear subspaces, and a tensor layer, in which two subspace projections interact with each other and jointly predict the next layer in the deep architecture. In addition, we describe an approach to map the tensor layers to the conventional sigmoid layers so that the former can be treated and trained in a similar way to the latter. With this mapping we can consider a DTNN as the DNN augmented with DP layers so that not only the BP learning algorithm of DTNNs can be cleanly derived but also new types of DTNNs can be more easily developed. Evaluation on Switchboard tasks indicates that DTNNs can outperform the already high-performing DNNs with 4-5% and 3% relative word error reduction, respectively, using 30-hr and 309-hr training sets.

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The Deep Tensor Neural Network With Applications to Large Vocabulary Speech Recognition

We study key issues related to multilingual acoustic modeling for automatic speech recognition (ASR) through a series of large-scale ASR experiments. Our study explores shared structures embedded in a large collection of speech data spanning over a number of spoken languages in order to establish a common set of universal phone models that can be used for large vocabulary ASR of all the languages seen or unseen during training. Language-universal and language-adaptive models are compared with language-specific models, and the comparison results show that in many cases it is possible to build general-purpose language-universal and language-adaptive acoustic models that outperform language-specific ones if the set of shared units, the structure of shared states, and the shared acoustic-phonetic properties among different languages can be properly utilized. Specifically, our results demonstrate that when the context coverage is poor in language-specific training, we can use one tenth of the adaptation data to achieve equivalent performance in cross-lingual speech recognition.

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A study on multilingual acoustic modeling for large vocabulary ASR

Recent studies have shown that deep neural networks (DNNs) perform significantly better than shallow networks and Gaussian mixture models (GMMs) on large vocabulary speech recognition tasks. In this paper, we argue that the improved accuracy achieved by the DNNs is the result of their ability to extract discriminative internal representations that are robust to the many sources of variability in speech signals. We show that these representations become increasingly insensitive to small perturbations in the input with increasing network depth, which leads to better speech recognition performance with deeper networks. We also show that DNNs cannot extrapolate to test samples that are substantially different from the training examples. If the training data are sufficiently representative, however, internal features learned by the DNN are relatively stable with respect to speaker differences, bandwidth differences, and environment distortion. This enables DNN-based recognizers to perform as well or better than state-of-the-art systems based on GMMs or shallow networks without the need for explicit model adaptation or feature normalization.

Dong Yu

Papers

Recurrent deep neural networks for robust speech recognition

High-performance hmm adaptation with joint compensation of additive and convolutive distortions via Vector Taylor Series

The Deep Tensor Neural Network With Applications to Large Vocabulary Speech Recognition

A study on multilingual acoustic modeling for large vocabulary ASR

Feature Learning in Deep Neural Networks - Studies on Speech Recognition Tasks.