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

Long short-term memory (LSTM) acoustic models have recently achieved state-of-the-art results on speech recognition tasks. As a type of recurrent neural network, LSTMs potentially have the ability to model long-span phenomena relating the spectral input to linguistic units. However, it has not been clear whether their observed performance is actually due to this capability, or instead if it is due to a better modeling of short term dynamics through the recurrence. In this paper. we answer this question by applying a windowed (truncated) LSTM to conversational speech transcription, and find that a limited context is adequate, and that it is not necessaary to scan the entire utterance. The sliding window approach allows not only incremental (online) recognition with a bidirectional model, but also frame-wise randomization (as opposed to utterance randomization), which results in faster convergence. On the SWBD/Fisher corpus, applying bidirectional LSTM RNNs to spectral windows of about 0.5s improves WER on the Hub5'00 benchmark set by 16% relative compared to our best sequence-trained DNN. On an extended 3850h training set that that also includes lectures, the relative gain becomes 28% (Hub5'00 WER 9.2%). In-house conversational data improves by 12 to 17% relative.

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Deep bi-directional recurrent networks over spectral windows

This paper presents a new spectral modeling method for statistical parametric speech synthesis. In contrast to the conventional methods in which high-level spectral parameters, such as mel-cepstra or line spectral pairs, are adopted as the features for hidden Markov model (HMM) based parametric speech synthesis, our new method directly models the distribution of the lower-level, un-transformed or raw spectral envelopes. Instead of using single Gaussian distributions, we adopt restricted Boltzmann machines (RBM) to represent the distribution of the spectral envelopes at each HMM state. We anticipate these will give superior performance in modeling the joint distribution of high-dimensional stochastic vectors. The spectral parameters are derived from the spectral envelope corresponding to the estimated mode of each context-dependent RBM and act as the Gaussian mean vector in the parameter generation procedure at synthesis time. Our experimental results show that the RBM is able to model the distribution of the spectral envelopes with better accuracy and generalization ability than the Gaussian mixture model. As a result, our proposed method can significantly improve the naturalness of the conventional HMM-based speech synthesis system using mel-cepstra.

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Modeling spectral envelopes using restricted Boltzmann machines for statistical parametric speech synthesis

We present a novel language identification technique using our recently developed deep-structured conditional random fields (CRFs). The deep-structured CRF is a multi-layer CRF model in which each higher layer's input observation sequence consists of the lower layer's observation sequence and the resulting lower layer's frame-level marginal probabilities. In this paper we extend the original deep-structured CRF by allowing for distinct state representations at different layers and demonstrate its benefits. We propose an unsupervised algorithm to pre-train the intermediate layers by casting it as a multi-objective programming problem that is aimed at minimizing the average frame-level conditional entropy while maximizing the state occupation entropy. Empirical evaluation on a seven-language/dialect voice mail routing task showed that our approach can achieve a routing accuracy (RA) of 86.4% and average equal error rate (EER) of 6.6%. These results are significantly better than the 82.5% RA and 7.5% average EER obtained using the Gaussian mixture model trained with the maximum mutual information criterion but slightly worse than the 87.7% RA and 6.4% EER achieved using the support vector machine with model pushing on the Gaussian super vector (GSV).

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Language recognition using deep-structured conditional random fields

Hybrid systems which integrate the deep neural network (DNN) and hidden Markov model (HMM) have recently achieved remarkable performance in many large vocabulary speech recognition tasks. These systems, however, remain to rely on the HMM and estimate the acoustic scores for the (windowed) frames independently of each other, suffering from the same difficulty as in the previous GMM-HMM systems. In this paper, we propose the deep segmental neural network (DSNN), a segmental model that uses DNNs to estimate the acoustic scores of phonemic or sub-phonemic segments with variable lengths. This allows the DSNN to represent each segment as a single unit, in which frames are made dependent on each other. We describe the architecture of the DSNN, as well as its learning and decoding algorithms. Our evaluation experiments demonstrate that the DSNN can outperform the DNN/HMM hybrid systems and two existing segmental models including the segmental conditional random field and the shallow segmental neural network.

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Deep segmental neural networks for speech recognition.

We develop and describe a novel deep architecture, the Tensor Deep Stacking Network (T-DSN), where multiple blocks are stacked one on top of another and where a bilinear mapping from hidden representations to the output in each block is used to incorporate higher-order statistics of the input features. A learning algorithm for the T-DSN is presented, in which the main parameter estimation burden is shifted to a convex sub-problem with a closed-form solution. Using an efficient and scalable parallel implementation, we train a T-DSN to discriminate standard three-state monophones in the TIMIT database. The T-DSN outperforms an alternative pretrained Deep Neural Network (DNN) architecture in frame-level classification (both state and phone) and in the cross-entropy measure. For continuous phonetic recognition, T-DSN performs equivalently to a DNN but without the need for a hard-to-scale, sequential fine-tuning step.

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Dong Yu

Papers

Deep bi-directional recurrent networks over spectral windows

Modeling spectral envelopes using restricted Boltzmann machines for statistical parametric speech synthesis

Language recognition using deep-structured conditional random fields

Deep segmental neural networks for speech recognition.

A deep architecture with bilinear modeling of hidden representations: Applications to phonetic recognition