This work presents a new algorithm for training recurrent neural networks (although ideas are applicable to feedforward networks as well). The algorithm is derived from a theory in nonconvex optimization related to the diffusion equation. The contributions made in this work are two fold. First, we show how some seemingly disconnected mechanisms used in deep learning such as smart initialization, annealed learning rate, layerwise pretraining, and noise injection (as done in dropout and SGD) arise naturally and automatically from this framework, without manually crafting them into the algorithms. Second, we present some preliminary results on comparing the proposed method against SGD. It turns out that the new algorithm can achieve similar level of generalization accuracy of SGD in much fewer number of epochs.
Several variants of recurrent neural networks (RNNs) with orthogonal or unitary recurrent matrices have recently been developed to mitigate the vanishing/exploding gradient problem and to model long-term dependencies of sequences. However, with the eigenvalues of the recurrent matrix on the unit circle, the recurrent state retains all input information which may unnecessarily consume model capacity. In this paper, we address this issue by proposing an architecture that expands upon an orthogonal/unitary RNN with a state that is generated by a recurrent matrix with eigenvalues in the unit disc.…
Recurrent neural network is a powerful model that learns temporal patterns in sequential data. For a long time, it was believed that recurrent networks are difficult to train using simple optimizers, such as stochastic gradient descent, due to the so-called vanishing gradient problem. In this paper, we show that learning longer term patterns in real data, such as in natural language, is perfectly possible using gradient descent. This is achieved by using a slight structural modification of the simple recurrent neural network architecture. We encourage some of the hidden units to change their s…
Toyota Technological Institute at Chicago（芝加哥丰田技术研究院）；University of Toronto（多伦多大学）；Carnegie Mellon University（卡内基梅隆大学）
We investigate the parameter-space geometry of recurrent neural networks (RNNs), and develop an adaptation of path-SGD optimization method, attuned to this geometry, that can learn plain RNNs with ReLU activations. On several datasets that require capturing long-term dependency structure, we show that path-SGD can significantly improve trainability of ReLU RNNs compared to RNNs trained with SGD, even with various recently suggested initialization schemes.
Beihang University（北京航空航天大学）；University of Ottawa（渥太华大学）
In this paper, we propose a test, called Flagged-1-Bit (F1B) test, to study the intrinsic capability of recurrent neural networks in sequence learning. Four different recurrent network models are studied both analytically and experimentally using this test. Our results suggest that in general there exists a conflict between feature selection and feature memorization in sequence learning. Such a conflict can be resolved either using a gating mechanism as in LSTM, or by increasing the state dimension as in Vanilla RNN. Gated models resolve this conflict by adaptively adjusting their state-update…
ETH Zürich（苏黎世联邦理工学院）；VMWare Research（威睿研究部）；UIUC（伊利诺伊大学厄巴纳-香槟分校）；Hitachi Power Grids Research（日立电网研究院）
We present a scalable and precise verifier for recurrent neural networks, called Prover based on two novel ideas: (i) a method to compute a set of polyhedral abstractions for the non-convex and nonlinear recurrent update functions by combining sampling, optimization, and Fermat's theorem, and (ii) a gradient descent based algorithm for abstraction refinement guided by the certification problem that combines multiple abstractions for each neuron. Using Prover, we present the first study of certifying a non-trivial use case of recurrent neural networks, namely speech classification. To achieve t…
The vanishing and exploding gradient problems are well-studied obstacles that make it difficult for recurrent neural networks to learn long-term time dependencies. We propose a reparameterization of standard recurrent neural networks to update linear transformations in a provably norm-preserving way through Givens rotations. Additionally, we use the absolute value function as an element-wise non-linearity to preserve the norm of backpropagated signals over the entire network. We show that this reparameterization reduces the number of parameters and maintains the same algorithmic complexity as …
UC San Diego（加州大学圣地亚哥分校）；USC（南加州大学）；Children’s Hospital LA（洛杉矶儿童医院）
We present a novel application of LSTM recurrent neural networks to multilabel classification of diagnoses given variable-length time series of clinical measurements. Our method outperforms a strong baseline on a variety of metrics.
Learning both hierarchical and temporal representation has been among the long-standing challenges of recurrent neural networks. Multiscale recurrent neural networks have been considered as a promising approach to resolve this issue, yet there has been a lack of empirical evidence showing that this type of models can actually capture the temporal dependencies by discovering the latent hierarchical structure of the sequence. In this paper, we propose a novel multiscale approach, called the hierarchical multiscale recurrent neural networks, which can capture the latent hierarchical structure in …
We describe recurrent neural networks (RNNs), which have attracted great attention on sequential tasks, such as handwriting recognition, speech recognition and image to text. However, compared to general feedforward neural networks, RNNs have feedback loops, which makes it a little hard to understand the backpropagation step. Thus, we focus on basics, especially the error backpropagation to compute gradients with respect to model parameters. Further, we go into detail on how error backpropagation algorithm is applied on long short-term memory (LSTM) by unfolding the memory unit.
We observe that the standard log likelihood training objective for a Recurrent Neural Network (RNN) model of time series data is equivalent to a variational Bayesian training objective, given the proper choice of generative and inference models. This perspective may motivate extensions to both RNNs and variational Bayesian models. We propose one such extension, where multiple particles are used for the hidden state of an RNN, allowing a natural representation of uncertainty or multimodality.
McGill University（麦吉尔大学）；Pennsylvania State University（宾夕法尼亚州立大学）
Rule extraction from black-box models is critical in domains that require model validation before implementation, as can be the case in credit scoring and medical diagnosis. Though already a challenging problem in statistical learning in general, the difficulty is even greater when highly non-linear, recursive models, such as recurrent neural networks (RNNs), are fit to data. Here, we study the extraction of rules from second-order recurrent neural networks trained to recognize the Tomita grammars. We show that production rules can be stably extracted from trained RNNs and that in certain case…
This paper compares recurrent neural networks (RNNs) with different types of gated cells for forecasting time series with multiple seasonality. The cells we compare include classical long short term memory (LSTM), gated recurrent unit (GRU), modified LSTM with dilation, and two new cells we proposed recently, which are equipped with dilation and attention mechanisms. To model the temporal dependencies of different scales, our RNN architecture has multiple dilated recurrent layers stacked with hierarchical dilations. The proposed RNN produces both point forecasts and predictive intervals (PIs) …
Sun Yat-sen University（中山大学）；Guangdong University of Technology（广东工业大学）
More and more empirical and theoretical evidence shows that deepening neural networks can effectively improve their performance under suitable training settings. However, deepening the backbone of neural networks will inevitably and significantly increase computation and parameter size. To mitigate these problems, we propose a simple-yet-effective Recurrent Attention Strategy (RAS), which implicitly increases the depth of neural networks with lightweight attention modules by local parameter sharing. The extensive experiments on three widely-used benchmark datasets demonstrate that RAS can impr…
Time series forecasting is difficult. It is difficult even for recurrent neural networks with their inherent ability to learn sequentiality. This article presents a recurrent neural network based time series forecasting framework covering feature engineering, feature importances, point and interval predictions, and forecast evaluation. The description of the method is followed by an empirical study using both LSTM and GRU networks.
University of Southern California（南加州大学）；California Institute of Technology（加州理工学院）
Spatiotemporal forecasting has various applications in neuroscience, climate and transportation domain. Traffic forecasting is one canonical example of such learning task. The task is challenging due to (1) complex spatial dependency on road networks, (2) non-linear temporal dynamics with changing road conditions and (3) inherent difficulty of long-term forecasting. To address these challenges, we propose to model the traffic flow as a diffusion process on a directed graph and introduce Diffusion Convolutional Recurrent Neural Network (DCRNN), a deep learning framework for traffic forecasting …
In this paper we compare different types of recurrent units in recurrent neural networks (RNNs). Especially, we focus on more sophisticated units that implement a gating mechanism, such as a long short-term memory (LSTM) unit and a recently proposed gated recurrent unit (GRU). We evaluate these recurrent units on the tasks of polyphonic music modeling and speech signal modeling. Our experiments revealed that these advanced recurrent units are indeed better than more traditional recurrent units such as tanh units. Also, we found GRU to be comparable to LSTM.
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Advanced Digital Sciences Center（先进数字科学中心）；Zhejiang University（浙江大学）
In this paper, we study the problem of using representation learning to assist information diffusion prediction on graphs. In particular, we aim at estimating the probability of an inactive node to be activated next in a cascade. Despite the success of recent deep learning methods for diffusion, we find that they often underexplore the cascade structure. We consider a cascade as not merely a sequence of nodes ordered by their activation time stamps; instead, it has a richer structure indicating the diffusion process over the data graph. As a result, we introduce a new data model, namely diffus…
In this paper, we introduce Channel-wise recurrent convolutional neural networks (RecNets), a family of novel, compact neural network architectures for computer vision tasks inspired by recurrent neural networks (RNNs). RecNets build upon Channel-wise recurrent convolutional (CRC) layers, a novel type of convolutional layer that splits the input channels into disjoint segments and processes them in a recurrent fashion. In this way, we simulate wide, yet compact models, since the number of parameters is vastly reduced via the parameter sharing of the RNN formulation. Experimental results on the…
Friedrich-Alexander Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）
The brain cortex, which processes visual, auditory and sensory data in the brain, is known to have many recurrent connections within its layers and from higher to lower layers. But, in the case of machine learning with neural networks, it is generally assumed that strict feed-forward architectures are suitable for static input data, such as images, whereas recurrent networks are required mainly for the processing of sequential input, such as language. However, it is not clear whether also processing of static input data benefits from recurrent connectivity. In this work, we introduce and test …
German Aerospace Center (DLR)（德国航空航天中心）；Universidad de Málaga（马拉加大学）
This article introduces Random Error Sampling-based Neuroevolution (RESN), a novel automatic method to optimize recurrent neural network architectures. RESN combines an evolutionary algorithm with a training-free evaluation approach. The results show that RESN achieves state-of-the-art error performance while reducing by half the computational time.
In this paper, we have used Recurrent Neural Networks to capture and model human motion data and generate motions by prediction of the next immediate data point at each time-step. Our RNN is armed with recently proposed Gated Recurrent Units which has shown promising results in some sequence modeling problems such as Machine Translation and Speech Synthesis. We demonstrate that this model is able to capture long-term dependencies in data and generate realistic motions.
Neural processes (NPs) learn stochastic processes and predict the distribution of target output adaptively conditioned on a context set of observed input-output pairs. Furthermore, Attentive Neural Process (ANP) improved the prediction accuracy of NPs by incorporating attention mechanism among contexts and targets. In a number of real-world applications such as robotics, finance, speech, and biology, it is critical to learn the temporal order and recurrent structure from sequential data. However, the capability of NPs capturing these properties is limited due to its permutation invariance inst…
Technische Universität Darmstadt（达姆施塔特工业大学）；Concordia University（康考迪亚大学）
A regression problem with dependent data is considered. Regularity assumptions on the dependency of the data are introduced, and it is shown that under suitable structural assumptions on the regression function a deep recurrent neural network estimate is able to circumvent the curse of dimensionality.
Time series forecasting based on deep architectures has been gaining popularity in recent years due to their ability to model complex non-linear temporal dynamics. The recurrent neural network is one such model capable of handling variable-length input and output. In this paper, we leverage recent advances in deep generative models and the concept of state space models to propose a stochastic adaptation of the recurrent neural network for multistep-ahead time series forecasting, which is trained with stochastic gradient variational Bayes. In our model design, the transition function of the rec…
Recurrent Neural Networks (RNNs) are designed to handle sequential data but suffer from vanishing or exploding gradients. Recent work on Unitary Recurrent Neural Networks (uRNNs) have been used to address this issue and in some cases, exceed the capabilities of Long Short-Term Memory networks (LSTMs). We propose a simpler and novel update scheme to maintain orthogonal recurrent weight matrices without using complex valued matrices. This is done by parametrizing with a skew-symmetric matrix using the Cayley transform. Such a parametrization is unable to represent matrices with negative one eige…
University of British Columbia（不列颠哥伦比亚大学）；Stewart Blusson Quantum Matter Institute（斯图尔特·布鲁森量子物质研究所）；University of Cambridge（剑桥大学）
Recurrent neural networks play an important role in both research and industry. With the advent of quantum machine learning, the quantisation of recurrent neural networks has become recently relevant. We propose fully quantum recurrent neural networks, based on dissipative quantum neural networks, capable of learning general causal quantum automata. A quantum training algorithm is proposed and classical simulations for the case of product outputs with the fidelity as cost function are carried out. We thereby demonstrate the potential of these algorithms to learn complex quantum processes with …
Pedestrian Volume Prediction Using a Diffusion Convolutional Gated Recurrent Unit Model
School of Statistics（统计学院）；Renmin University of China（中国人民大学）；School of Mathematics and Statistics（数学与统计学院）；The University of Melbourne（墨尔本大学）；School of Business, Law and Entrepreneurship（商学、法学与创业学院）；Swinburne University of Technology（斯威本科技大学）
In this paper we investigate the correlation between NFT valuations and various features from three primary categories: public market data, NFT metadata, and social trends data.
Recurrent neural networks have shown excellent performance in many applications, however they require increased complexity in hardware or software based implementations. The hardware complexity can be much lowered by minimizing the word-length of weights and signals. This work analyzes the fixed-point performance of recurrent neural networks using a retrain based quantization method. The quantization sensitivity of each layer in RNNs is studied, and the overall fixed-point optimization results minimizing the capacity of weights while not sacrificing the performance are presented. A language mo…
National Physical Laboratory（国家物理实验室）；Mathematical Institute（数学研究所）；University of Oxford（牛津大学）；IIIT Delhi（德里印度理工学院）
We propose to use stochastic Riemannian coordinate descent on the orthogonal group for recurrent neural network training. The algorithm rotates successively two columns of the recurrent matrix, an operation that can be efficiently implemented as a multiplication by a Givens matrix. In the case when the coordinate is selected uniformly at random at each iteration, we prove the convergence of the proposed algorithm under standard assumptions on the loss function, stepsize and minibatch noise. In addition, we numerically demonstrate that the Riemannian gradient in recurrent neural network trainin…
We propose ThalNet, a deep learning model inspired by neocortical communication via the thalamus. Our model consists of recurrent neural modules that send features through a routing center, endowing the modules with the flexibility to share features over multiple time steps. We show that our model learns to route information hierarchically, processing input data by a chain of modules. We observe common architectures, such as feed forward neural networks and skip connections, emerging as special cases of our architecture, while novel connectivity patterns are learned for the text8 compression t…
We investigate sequence machine learning techniques on raw radio signal time-series data. By applying deep recurrent neural networks we learn to discriminate between several application layer traffic types on top of a constant envelope modulation without using an expert demodulation algorithm. We show that complex protocol sequences can be learned and used for both classification and generation tasks using this approach.
The emergence of brain-inspired neuromorphic computing as a paradigm for edge AI is motivating the search for high-performance and efficient spiking neural networks to run on this hardware. However, compared to classical neural networks in deep learning, current spiking neural networks lack competitive performance in compelling areas. Here, for sequential and streaming tasks, we demonstrate how a novel type of adaptive spiking recurrent neural network (SRNN) is able to achieve state-of-the-art performance compared to other spiking neural networks and almost reach or exceed the performance of c…
MILA, Université de Montréal（蒙特利尔大学 MILA）；University of Toronto（多伦多大学）；Institut des Hautes Études Scientifiques, France（法国高等科学研究所）；Carnegie Mellon University（卡内基梅隆大学）
In this paper, we systematically analyze the connecting architectures of recurrent neural networks (RNNs). Our main contribution is twofold: first, we present a rigorous graph-theoretic framework describing the connecting architectures of RNNs in general. Second, we propose three architecture complexity measures of RNNs: (a) the recurrent depth, which captures the RNN's over-time nonlinear complexity, (b) the feedforward depth, which captures the local input-output nonlinearity (similar to the "depth" in feedforward neural networks (FNNs)), and (c) the recurrent skip coefficient which captures…
Reservoir characterization involves the estimation petrophysical properties from well-log data and seismic data. Estimating such properties is a challenging task due to the non-linearity and heterogeneity of the subsurface. Various attempts have been made to estimate petrophysical properties using machine learning techniques such as feed-forward neural networks and support vector regression (SVR). Recent advances in machine learning have shown promising results for recurrent neural networks (RNN) in modeling complex sequential data such as videos and speech signals. In this work, we propose an…
IRIDIA（IRIDIA实验室）；Université Libre de Bruxelles（布鲁塞尔自由大学）
We show that collaborative filtering can be viewed as a sequence prediction problem, and that given this interpretation, recurrent neural networks offer very competitive approach. In particular we study how the long short-term memory (LSTM) can be applied to collaborative filtering, and how it compares to standard nearest neighbors and matrix factorization methods on movie recommendation. We show that the LSTM is competitive in all aspects, and largely outperforms other methods in terms of item coverage and short term predictions.
China University of Political Science and Law（中国政法大学）；Institute of High Performance Computing（高性能计算研究所）
A deep learning approach has been widely applied in sequence modeling problems. In terms of automatic speech recognition (ASR), its performance has significantly been improved by increasing large speech corpus and deeper neural network. Especially, recurrent neural network and deep convolutional neural network have been applied in ASR successfully. Given the arising problem of training speed, we build a novel deep recurrent convolutional network for acoustic modeling and then apply deep residual learning to it. Our experiments show that it has not only faster convergence speed but better recog…
In this report, two commonly used data-driven models for predicting well production under a waterflood setting: the capacitance resistance model (CRM) and recurrent neural networks (RNN) are compared. Both models are completely data-driven and are intended to learn the reservoir behavior during a water flood from historical data. This report serves as a technical guide to the python-based implementation of the CRM model available from the associated GitHub repository.
Hypercomplex-valued neural networks, including quaternion-valued neural networks, can treat multi-dimensional data as a single entity. In this paper, we present the quaternion-valued recurrent projection neural networks (QRPNNs). Briefly, QRPNNs are obtained by combining the non-local projection learning with the quaternion-valued recurrent correlation neural network (QRCNNs). We show that QRPNNs overcome the cross-talk problem of QRCNNs. Thus, they are appropriate to implement associative memories. Furthermore, computational experiments reveal that QRPNNs exhibit greater storage capacity and …
University Politechnica of Bucharest（布加勒斯特理工大学）；Academy of Romanian Scientists（罗马尼亚科学院）
Diacritics restoration is a mandatory step for adequately processing Romanian texts, and not a trivial one, as you generally need context in order to properly restore a character. Most previous methods which were experimented for Romanian restoration of diacritics do not use neural networks. Among those that do, there are no solutions specifically optimized for this particular language (i.e., they were generally designed to work on many different languages). Therefore we propose a novel neural architecture based on recurrent neural networks that can attend information at different levels of ab…
In this work we compare different batch construction methods for mini-batch training of recurrent neural networks. While popular implementations like TensorFlow and MXNet suggest a bucketing approach to improve the parallelization capabilities of the recurrent training process, we propose a simple ordering strategy that arranges the training sequences in a stochastic alternatingly sorted way. We compare our method to sequence bucketing as well as various other batch construction strategies on the CHiME-4 noisy speech recognition corpus. The experiments show that our alternated sorting approach…
The study of deep neural networks (DNNs) in the infinite-width limit, via the so-called neural tangent kernel (NTK) approach, has provided new insights into the dynamics of learning, generalization, and the impact of initialization. One key DNN architecture remains to be kernelized, namely, the recurrent neural network (RNN). In this paper we introduce and study the Recurrent Neural Tangent Kernel (RNTK), which provides new insights into the behavior of overparametrized RNNs. A key property of the RNTK should greatly benefit practitioners is its ability to compare inputs of different length. T…
Graph processes model a number of important problems such as identifying the epicenter of an earthquake or predicting weather. In this paper, we propose a Graph Convolutional Recurrent Neural Network (GCRNN) architecture specifically tailored to deal with these problems. GCRNNs use convolutional filter banks to keep the number of trainable parameters independent of the size of the graph and of the time sequences considered. We also put forward Gated GCRNNs, a time-gated variation of GCRNNs akin to LSTMs. When compared with GNNs and another graph recurrent architecture in experiments using both…
Universidad de Málaga（马拉加大学）；Massachusetts Institute of Technology（麻省理工学院）
Recurrent neural networks are a powerful tool, but they are very sensitive to their hyper-parameter configuration. Moreover, training properly a recurrent neural network is a tough task, therefore selecting an appropriate configuration is critical. Varied strategies have been proposed to tackle this issue. However, most of them are still impractical because of the time/resources needed. In this study, we propose a low computational cost model to evaluate the expected performance of a given architecture based on the distribution of the error of random samples of the weights. We empirically vali…
Traditional Recurrent Neural Networks assume vectorized data as inputs. However many data from modern science and technology come in certain structures such as tensorial time series data. To apply the recurrent neural networks for this type of data, a vectorisation process is necessary, while such a vectorisation leads to the loss of the precise information of the spatial or longitudinal dimensions. In addition, such a vectorized data is not an optimum solution for learning the representation of the longitudinal data. In this paper, we propose a new variant of tensorial neural networks which d…
Realization Theory Of Recurrent Neural ODEs Using Polynomial System Embeddings
Institut de Recherche Technologique SystemX（SystemX 技术研究院）；Trinov（Trinov 公司）；Centre de Recherche en Informatique, Signal et Automatique de Lille（里尔计算机、信号与自动化研究中心）
Texas A&M University（得克萨斯农工大学）；University of Texas at Austin（得克萨斯大学奥斯汀分校）
Stochastic recurrent neural networks with latent random variables of complex dependency structures have shown to be more successful in modeling sequential data than deterministic deep models. However, the majority of existing methods have limited expressive power due to the Gaussian assumption of latent variables. In this paper, we advocate learning implicit latent representations using semi-implicit variational inference to further increase model flexibility. Semi-implicit stochastic recurrent neural network(SIS-RNN) is developed to enrich inferred model posteriors that may have no analytic d…
Weinberg College of Arts and Sciences, Northwestern University（西北大学温伯格文理学院）；Northwestern University（西北大学）
In a recurrent setting, conventional approaches to neural architecture search find and fix a general model for all data samples and time steps. We propose a novel algorithm that can dynamically search for the structure of cells in a recurrent neural network model. Based on a combination of recurrent and recursive neural networks, our algorithm is able to construct customized cell structures for each data sample and time step, allowing for a more efficient architecture search than existing models. Experiments on three common datasets show that the algorithm discovers high-performance cell archi…
We introduce MinimalRNN, a new recurrent neural network architecture that achieves comparable performance as the popular gated RNNs with a simplified structure. It employs minimal updates within RNN, which not only leads to efficient learning and testing but more importantly better interpretability and trainability. We demonstrate that by endorsing the more restrictive update rule, MinimalRNN learns disentangled RNN states. We further examine the learning dynamics of different RNN structures using input-output Jacobians, and show that MinimalRNN is able to capture longer range dependencies tha…
We present the multiplicative recurrent neural network as a general model for compositional meaning in language, and evaluate it on the task of fine-grained sentiment analysis. We establish a connection to the previously investigated matrix-space models for compositionality, and show they are special cases of the multiplicative recurrent net. Our experiments show that these models perform comparably or better than Elman-type additive recurrent neural networks and outperform matrix-space models on a standard fine-grained sentiment analysis corpus. Furthermore, they yield comparable results to s…
National Research University Higher School of Economics（国立研究大学高等经济学院）；Kaspersky Lab（卡巴斯基实验室）；Lomonosov Moscow State University（莫斯科国立大学）；Yandex
Recurrent neural networks show state-of-the-art results in many text analysis tasks but often require a lot of memory to store their weights. Recently proposed Sparse Variational Dropout eliminates the majority of the weights in a feed-forward neural network without significant loss of quality. We apply this technique to sparsify recurrent neural networks. To account for recurrent specifics we also rely on Binary Variational Dropout for RNN. We report 99.5% sparsity level on sentiment analysis task without a quality drop and up to 87% sparsity level on language modeling task with slight loss o…
Loyola Marymount University（洛约拉马利蒙特大学）；California State University, Long Beach（加州州立大学长滩分校）
We introduce an exceptionally simple gated recurrent neural network (RNN) that achieves performance comparable to well-known gated architectures, such as LSTMs and GRUs, on the word-level language modeling task. We prove that our model has simple, predicable and non-chaotic dynamics. This stands in stark contrast to more standard gated architectures, whose underlying dynamical systems exhibit chaotic behavior.
We study the problem of compressing recurrent neural networks (RNNs). In particular, we focus on the compression of RNN acoustic models, which are motivated by the goal of building compact and accurate speech recognition systems which can be run efficiently on mobile devices. In this work, we present a technique for general recurrent model compression that jointly compresses both recurrent and non-recurrent inter-layer weight matrices. We find that the proposed technique allows us to reduce the size of our Long Short-Term Memory (LSTM) acoustic model to a third of its original size with neglig…
