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

Denoising diffusion probabilistic models (DDPMs) have recently achieved leading performances in many generative tasks. However, the inherited iterative sampling process costs hindered their applications to speech synthesis. This paper proposes FastDiff, a fast conditional diffusion model for high-quality speech synthesis. FastDiff employs a stack of time-aware location-variable convolutions of diverse receptive field patterns to efficiently model long-term time dependencies with adaptive conditions. A noise schedule predictor is also adopted to reduce the sampling steps without sacrificing the generation quality. Based on FastDiff, we design an end-to-end text-to-speech synthesizer, FastDiff-TTS, which generates high-fidelity speech waveforms without any intermediate feature (e.g., Mel-spectrogram). Our evaluation of FastDiff demonstrates the state-of-the-art results with higher-quality (MOS 4.28) speech samples. Also, FastDiff enables a sampling speed of 58x faster than real-time on a V100 GPU, making diffusion models practically applicable to speech synthesis deployment for the first time. We further show that FastDiff generalized well to the mel-spectrogram inversion of unseen speakers, and FastDiff-TTS outperformed other competing methods in end-to-end text-to-speech synthesis. Audio samples are available at https://FastDiff.github.io/.

FastDiff: A Fast Conditional Diffusion Model for High-Quality Speech Synthesis

We propose a new framework and the associated maximum-likelihood and discriminative training algorithms for the variable-parameter hidden Markov model (VPHMM) whose mean and variance parameters vary as functions of additional environment-dependent conditioning parameters. Our framework differs from the VPHMM proposed by Cui and Gong (2007) in that piecewise spline interpolation instead of global polynomial regression is used to represent the dependency of the HMM parameters on the conditioning parameters, and a more effective functional form is used to model the variances. Our framework unifies and extends the conventional discrete VPHMM. It no longer requires quantization in estimating the model parameters and can support both parameter sharing and instantaneous conditioning parameters naturally. We investigate the strengths and weaknesses of the model on the Aurora-3 corpus. We show that under the well-matched condition the proposed discriminatively trained VPHMM outperforms the conventional HMM trained in the same way with relative word error rate (WER) reduction of 19% and 15%, respectively, when only mean is updated and when both mean and variances are updated.

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A Novel Framework and Training Algorithm for Variable-Parameter Hidden Markov Models

We extend our earlier work on deep-structured conditional random field (DCRF) and develop deep-structured hidden conditional random field (DHCRF). We investigate the use of this new sequential deep-learning model for phonetic recognition. DHCRF is a hierarchical model in which the final layer is a hidden conditional random field (HCRF) and the intermediate layers are zero-th-order conditional random fields (CRFs). Parameter estimation and sequence inference in the DHCRF are developed in this work. They are carried out layer by layer so that the time complexity is linear to the number of layers. In the DHCRF, the training label is available only at the final layer and the state boundary is unknown. This difficulty is addressed by using unsupervised learning for the intermediate layers and lattice-based supervised learning for the final layer. Experiments on the standard TIMIT phone recognition task show small performance improvement of a three-layer DHCRF over a two-layer DHCRF; both are significantly better than the single-layer DHCRF and are superior to the discriminatively trained tri-phone hidden Markov model (HMM) using identical input features.

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Deep-structured hidden conditional random fields for phonetic recognition.

Long Short-Term Memory (LSTM) is a particular type of recurrent neural network (RNN) that can model long term temporal dynamics. Recently it has been shown that LSTM-RNNs can achieve higher recognition accuracy than deep feed-forword neural networks (DNNs) in acoustic modelling. However, speaker adaption for LSTM-RNN based acoustic models has not been well investigated. In this paper, we study the LSTM-RNN speaker-aware training that incorporates the speaker information during model training to normalise the speaker variability. We first present several speaker-aware training architectures, and then empirically evaluate three types of speaker representation: I-vectors, bottleneck speaker vectors and speaking rate. Furthermore, to factorize the variability in the acoustic signals caused by speakers and phonemes respectively, we investigate the speaker-aware and phone-aware joint training under the framework of multi-task learning. In AMI meeting speech transcription task, speaker-aware training of LSTM-RNNs reduces word error rates by 6.5% relative to a very strong LSTM-RNN baseline, which uses FMLLR features.

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Speaker-aware training of LSTM-RNNS for acoustic modelling

Deep Neural Network (DNN) training technique embodiments are presented that train a DNN while exploiting the sparseness of non-zero hidden layer interconnection weight values. Generally, a fully connected DNN is initially trained by sweeping through a full training set a number of times. Then, for the most part, only the interconnections whose weight magnitudes exceed a minimum weight threshold are considered in further training. This minimum weight threshold can be established as a value that results in only a prescribed maximum number of interconnections being considered when setting interconnection weight values via an error back-propagation procedure during the training. It is noted that the continued DNN training tends to converge much faster than the initial training.

Dong Yu

Papers

FastDiff: A Fast Conditional Diffusion Model for High-Quality Speech Synthesis

A Novel Framework and Training Algorithm for Variable-Parameter Hidden Markov Models

Deep-structured hidden conditional random fields for phonetic recognition.

Speaker-aware training of LSTM-RNNS for acoustic modelling

Exploiting sparseness in training deep neural networks