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

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 KalmanNet, 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 KalmanNet improves the performance of FDKF signiﬁcantly and outperforms strong baseline methods.

KalmanNet: A Learnable Kalman Filter for Acoustic Echo Cancellation

In previous chapters we have discussed various deep learning models for automatic speech recognition (ASR). In this chapter we introduce the computational network (CN), a unified framework for describing a wide range of arbitrary learning machines, such as deep neural networks (DNNs), convolutional neural networks (CNNs), recurrent neural networks (RNNs) including its long short term memory (LSTM) version, logistic regression, and maximum entropy models. All these learning machines can be formulated and illustrated as a series of computational steps. A CN is a directed graph in which each leaf node represents an input value or a parameter and each non-leaf node represents a matrix operation acting upon its children. We describe algorithms to carry out forward computation and gradient calculation in the CN and introduce most popular computation node types used in a typical CN.

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A Computational Network

This article is concerned with developing a featured multi-instant Luenberger-like observer of discrete-time Takagi–Sugeno fuzzy systems with unmeasurable state variables, that is, not only to reduce the conservatism but also (at the same time) to alleviate the computational complexity over the recent approach reported in the literature. Contrary to previous approaches, an enhanced gain-scheduling mechanism is proposed for constructing much abundant working modes by online evaluating the updated variation information of normalized fuzzy weighting functions across two adjacent sampling instants and, thus, a different group of observer gain matrices with less conservatism is designed in order to employ the exclusive features for each working mode. Moreover, all the redundant terms containing both surplus and unknown system information are discriminated and removed in this study and, thus, the required computational complexity is reduced to a certain extent than the counterpart one. Finally, numerical examples are provided to illustrate the superiority of the developed approach.

Multi-Instant Observer Design of Discrete-Time Fuzzy Systems via An Enhanced Gain-Scheduling Mechanism

Self-supervised learning (SSL) has drawn an increased attention in the field of speech processing. Recent studies have demonstrated that contrastive learning is able to learn discriminative speaker embeddings in a self-supervised manner. However, base contrastive self-supervised learning (CSSL) assumes that the pairs generated from a view of $anchor$ instance and any view of other instances are all negative, which introduces many false negative pairs in constructing the loss function. The problem is referred as $class$-$collision$, which remains as one major issue that impedes the CSSL based speaker verification (SV) systems from achieving better performances. In the meanwhile, studies reveal that negative sample free SSL frameworks perform well in learning speaker or image representations. In this study, we investigate SSL techniques that lead to an improved SV performance. We first analyse the impact of false negative pairs in the CSSL systems. Then, a multi-stage Class-Collision Correction (C3) method is proposed (e.g., false negative pair filtering, InfoNCE re-weighting and ProtoNCE), which leads to the state-of-the-art (SOTA) CSSL based speaker embedding system. On the basis of the pretrained CSSL model, we further propose to employ a negative sample free SSL objective (i.e., DINO) to fine-tune the speaker embedding network. The resulting speaker embedding system (C3-DINO) achieves 2.5% Equal Error Rate (EER) with a simple Cosine Distance Scoring (CDS) method on Voxceleb1 test set, which outperforms the previous SOTA SSL system (4.86%) by a significant +45% relative improvement. With speaker clustering and pseudo labeling on Voxceleb2 training set, a LDA/CDS back-end applying on the C3-DINO speaker embeddings is able to further push the EER to 2.2%. Comprehensive experimental investigations of the Voxceleb benchmarks and our internal dataset demonstrate the effectiveness of our proposed methods, and the performance gap between the SSL SV and the supervised counterpart narrows further.

C3-DINO: Joint Contrastive and Non-Contrastive Self-Supervised Learning for Speaker Verification

In this paper, we present a speech enhancement framework that leverages phonetic information obtained from the acoustic model. It consists of two separate components: (i) a long short-term memory recurrent neural network (LSTM-RNN) based speech enhancement model that takes the combination of log-power spectra (LPS) and phonetic embedding features as input to predict the complex ideal ratio mask (cIRM); and (ii) a convolutional, long short-term memory and fully connected deep neural network (CLDNN) based acoustic model that extracts the phonetic feature vector in the hidden units of its LSTM layer. Our experimental results show that the proposed framework outperforms both the conventional and phoneme-dependent speech enhancement systems under various noisy conditions, generalizes well to unseen conditions, and performs robustly to the speech interference. We further demonstrate its superior enhancement performance on unvoiced speech and report a preliminary yet promising recognition experiment on real test data.

Dong Yu

Papers

KalmanNet: A Learnable Kalman Filter for Acoustic Echo Cancellation

A Computational Network

Multi-Instant Observer Design of Discrete-Time Fuzzy Systems via An Enhanced Gain-Scheduling Mechanism

C3-DINO: Joint Contrastive and Non-Contrastive Self-Supervised Learning for Speaker Verification

Improving Speech Enhancement with Phonetic Embedding Features