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

Deep neural networks (DNNs) have many hidden layers each of which has many neurons. This greatly increases the total number of parameters in the model and slows down both the training and decoding. In this chapter, we discuss algorithms and engineering techniques that speedup the training and decoding. Specifically, we describe the parallel training algorithms such as pipelined backpropagation algorithm, asynchronous stochastic gradient descend algorithm, and augmented Lagrange multiplier algorithm. We also introduce model size reduction techniques based on low-rank approximation which can speedup both training and decoding, and techniques such as quantization, lazy evaluation, and frame skipping that significantly speedup the decoding.

Training and Decoding Speedup

The Kalman filter is widely used for addressing acoustic echo cancellation (AEC) problems due to their robustness to double-talk and fast convergence. However, the inability to model nonlinearity and the need to tune control parameters cast limitations on such adaptive filtering algorithms. In this paper, we integrate the frequency domain Kalman filter (FDKF) and deep neural networks (DNNs) into a hybrid method, called NeuralKalman, to leverage the advantages of deep learning and adaptive filtering algorithms. Specifically, we employ a DNN to estimate nonlinearly distorted far-end signals, a transition factor, and the nonlinear transition function in the state equation of the FDKF algorithm. Experimental results show that the proposed NeuralKalman improves the performance of FDKF significantly and outperforms strong baseline methods.

NeuralKalman: A Learnable Kalman Filter for Acoustic Echo Cancellation

In this article, a learning-based resilient fault-tolerant control method is proposed for a class of uncertain nonlinear multiagent systems (MASs) to enhance the security and reliability against denial-of-service (DoS) attacks and actuator faults. With the framework of cooperative output regulation, the developed algorithm consists of designing a distributed resilient observer and a decentralized fault-tolerant controller. Specifically, by using the data-driven method, an online resilient learning algorithm is first presented to learn the unknown exosystem matrix in the presence of DoS attacks. Then, a distributed resilient observer is proposed working against DoS attacks. In addition, based on the developed observer, a decentralized adaptive fault-tolerant controller is designed to compensate for actuator faults. Moreover, the convergence of error systems is shown by using the Lyapunov stability theory. The effectiveness of our result is examined by a simulation example.

Cooperative Fault-Tolerant Control for a Class of Nonlinear MASs by Resilient Learning Approach.

To provide application developers with the ability to easily form customized grammars, grammar extensions are provided that allow application developers to selectively include portions of grammar templates and to easily combine grammar elements to form new grammar structures.

Configurable grammar templates

In this work, three lattice-free (LF) discriminative training criteria for purely sequence-trained neural network acoustic models are compared on LVCSR tasks, namely maximum mutual information (MMI), boosted maximum mutual information (bMMI) and state-level minimum Bayes risk (sMBR). We demonstrate that, analogous to LF-MMI, a neural network acoustic model can also be trained from scratch using LF-bMMI or LF-sMBR criteria respectively without the need of cross-entropy pre-training. Furthermore, experimental results on Switchboard-300hrs and Switchboard+Fisher-2100hrs datasets show that models trained with LF-bMMI consistently outperform those trained with plain LF-MMI and achieve a relative word error rate (WER) reduction of 5% over competitive temporal convolution projected LSTM (TDNN-LSTMP) LF-MMI baselines.

Dong Yu

Papers

Training and Decoding Speedup

NeuralKalman: A Learnable Kalman Filter for Acoustic Echo Cancellation

Cooperative Fault-Tolerant Control for a Class of Nonlinear MASs by Resilient Learning Approach.

Configurable grammar templates

A Comparison of Lattice-free Discriminative Training Criteria for Purely Sequence-Trained Neural Network Acoustic Models