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.

/pdf/generative-adversarial-nets-1ofhan3sbf.pdf

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

We apply Context-Dependent Deep-Neural-Network HMMs, or CD-DNN-HMMs, to the real-life problem of audio indexing of data across various sources. Recently, we had shown that on the Switchboard benchmark on speaker-independent transcription of phone calls, CD-DNN-HMMs with 7 hidden layers reduce the word error rate by as much as one-third, compared to discriminatively trained Gaussian-mixture HMMs, and by one-fourth if the GMM-HMM also uses fMPE features. This paper takes CD-DNN-HMM based recognition into a real-life deployment for audio indexing. We find that for our best speaker-independent CD-DNN-HMM, with 32k senones trained on 2000h of data, the one-fourth reduction does carry over to inhomogeneous field data (video podcasts and talks). Compared to a speaker-adaptive GMM system, the relative improvement is 18%, at very similar end-to-end runtime. In system building, we find that DNNs can benefit from a larger number of senones than the GMM-HMM; and that DNN likelihood evaluation is a sizeable runtime factor even in our wide-beam context of generating rich lattices: Cutting the model size by 60% reduces runtime by one-third at a 5% relative WER loss.

https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/0000143.pdf

Context-dependent Deep Neural Networks for audio indexing of real-life data

Conventional word embeddings represent words with fixed vectors, which are usually trained based on co-occurrence patterns among words. In doing so, however, the power of such representations is limited, where the same word might be functionalized separately under different syntactic relations. To address this limitation, one solution is to incorporate relational dependencies of different words into their embeddings. Therefore, in this paper, we propose a multiplex word embedding model, which can be easily extended according to various relations among words. As a result, each word has a center embedding to represent its overall semantics, and several relational embeddings to represent its relational dependencies. Compared to existing models, our model can effectively distinguish words with respect to different relations without introducing unnecessary sparseness. Moreover, to accommodate various relations, we use a small dimension for relational embeddings and our model is able to keep their effectiveness. Experiments on selectional preference acquisition and word similarity demonstrate the effectiveness of the proposed model, and a further study of scalability also proves that our embeddings only need 1/20 of the original embedding size to achieve better performance.

Multiplex Word Embeddings for Selectional Preference Acquisition

In this paper, we extend our previous work on direct recognition of single-channel multi-talker mixed speech using permutation invariant training (PIT) We propose to adapt the PIT models with auxiliary features such as pitch and i-vector, and to exploit the gender information with multi-task learning which jointly optimizes for the speech recognition and speaker-pair prediction We also compare CNN-BLSTMs against BLSTM-RNNs used in our previous PIT-ASR model The experimental results on the artificially mixed two-talker AMI data indicate that our proposed model improvements can reduce word error rate (WER) by ~ 100% relative to our previous work for both speakers in the mixed speech Our results also confirm that PIT can be easily combined with advanced techniques to improve the performance on multi-talker speech recognition

Adaptive Permutation Invariant Training with Auxiliary Information for Monaural Multi-Talker Speech Recognition

We present a structured speech model that is equipped with the capability of jointly representing incomplete articulation and long-span co-articulation in natural human speech. Central to this model is compact statistical parameterization of the highly regular dynamic patterns (exhibited in the hidden vocal-tract-resonance domain) that are driven by the stochastic segmental targets. We provide a rigorous mathematical description of this model, and present novel algorithms for learning the full set of model parameters using the cepstral data of speech. In particular, the gradient ascend techniques for learning variance parameters (for both resonance targets and cepstral prediction residuals) are described in detail. Phonetic recognition experiments are carried out using two paradigms of N-best rescoring and lattice search. Both sets of results demonstrate higher recognition accuracy achieved by the new model compared with the best HMM system. The higher accuracy is consistently observed, with and without combining HMM scores, and with and without including the references in the N-best lists and lattices. Further, the new model with rich parameter-free structure uses only the context-independent, single-modal Gaussian parameters, which are fewer than one percent of the parameters in the context-dependent HMM system with mixture distributions

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A long-contextual-span model of resonance dynamics for speech recognition: parameter learning and recognizer evaluation

In this paper we propose to use utterance-level Permutation Invariant Training (uPIT) for speaker independent multi-talker speech separation and denoising, simultaneously. Specifically, we train deep bi-directional Long Short-Term Memory (LSTM) Recurrent Neural Networks (RNNs) using uPIT, for single-channel speaker independent multi-talker speech separation in multiple noisy conditions, including both synthetic and real-life noise signals. We focus our experiments on generalizability and noise robustness of models that rely on various types of a priori knowledge e.g. in terms of noise type and number of simultaneous speakers. We show that deep bi-directional LSTM RNNs trained using uPIT in noisy environments can improve the Signal-to-Distortion Ratio (SDR) as well as the Extended Short-Time Objective Intelligibility (ESTOI) measure, on the speaker independent multi-talker speech separation and denoising task, for various noise types and Signal-to-Noise Ratios (SNRs). Specifically, we first show that LSTM RNNs can achieve large SDR and ESTOI improvements, when evaluated using known noise types, and that a single model is capable of handling multiple noise types with only a slight decrease in performance. Furthermore, we show that a single LSTM RNN can handle both two-speaker and three-speaker noisy mixtures, without a priori knowledge about the exact number of speakers. Finally, we show that LSTM RNNs trained using uPIT generalize well to noise types not seen during training.

Dong Yu

Papers

Context-dependent Deep Neural Networks for audio indexing of real-life data

Multiplex Word Embeddings for Selectional Preference Acquisition

Adaptive Permutation Invariant Training with Auxiliary Information for Monaural Multi-Talker Speech Recognition

A long-contextual-span model of resonance dynamics for speech recognition: parameter learning and recognizer evaluation

Joint Separation and Denoising of Noisy Multi-talker Speech using Recurrent Neural Networks and Permutation Invariant Training