Dynamic Systems Simulation and Control Using Consecutive Recurrent Neural Networks
PES University（PES大学）；Microspin Machine Works Pvt. Ltd.（Microspin机械工程私人有限公司）
Srikanth Chandar, Harsha Sunder
备注：
14 pages, granted for publication in Communications in Computer and Information Science (CCIS) proceedings by Springer Nature, presented in the International Conference on Modelling, Machine Learning and Astronomy (MMLA 2019)
In this paper, we introduce a novel architecture to connecting adaptive learning and neural networks into an arbitrary machine's control system paradigm. Two consecutive Recurrent Neural Networks (RNNs) are used together to accurately model the dynamic characteristics of electromechanical systems that include controllers, actuators and motors. The age-old method of achieving control with the use of the- Proportional, Integral and Derivative constants is well understood as a simplified method that does not capture the complexities of the inherent nonlinearities of complex control systems. In the context of controlling and simulating electromechanical systems, we propose an alternative to PID controllers, employing a sequence of two Recurrent Neural Networks. The first RNN emulates the behavior of the controller, and the second the actuator/motor. The second RNN when used in isolation, potentially serves as an advantageous alternative to extant testing methods of electromechanical systems.
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.
We propose a new deep recurrent neural network (RNN) architecture for sequential signal reconstruction. Our network is designed by unfolding the iterations of the proximal gradient method that solves the l1-l1 minimization problem. As such, our network leverages by design that signals have a sparse representation and that the difference between consecutive signal representations is also sparse. We evaluate the proposed model in the task of reconstructing video frames from compressive measurements and show that it outperforms several state-of-the-art RNN models.
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.
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…
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…
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…
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…
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.
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 …
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…
Science and Technology on Electronic Information Control Laboratory（电子信息控制科技实验室）
A novel and efficient end-to-end learning model for automatic modulation classification is proposed for wireless spectrum monitoring applications, which automatically learns from the time domain in-phase and quadrature data without requiring the design of hand-crafted expert features. With the intuition of convolutional layers with pooling serving as the role of front-end feature distillation and dimensionality reduction, sequential convolutional recurrent neural networks are developed to take complementary advantage of parallel computing capability of convolutional neural networks and tempora…
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…
University of Science and Technology of China（中国科学技术大学）；York University（约克大学）；IFLYTEK Research（科大讯飞研究院）
We introduce a new structure for memory neural networks, called feedforward sequential memory networks (FSMN), which can learn long-term dependency without using recurrent feedback. The proposed FSMN is a standard feedforward neural networks equipped with learnable sequential memory blocks in the hidden layers. In this work, we have applied FSMN to several language modeling (LM) tasks. Experimental results have shown that the memory blocks in FSMN can learn effective representations of long history. Experiments have shown that FSMN based language models can significantly outperform not only fe…
We describe an application of an encoder-decoder recurrent neural network with LSTM units and attention to generating headlines from the text of news articles. We find that the model is quite effective at concisely paraphrasing news articles. Furthermore, we study how the neural network decides which input words to pay attention to, and specifically we identify the function of the different neurons in a simplified attention mechanism. Interestingly, our simplified attention mechanism performs better that the more complex attention mechanism on a held out set of articles.
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 …
UiT The Arctic University of Norway（挪威北极大学）；Universidad Rey Juan Carlos（胡安·卡洛斯国王大学）
Clinical measurements that can be represented as time series constitute an important fraction of the electronic health records and are often both uncertain and incomplete. Recurrent neural networks are a special class of neural networks that are particularly suitable to process time series data but, in their original formulation, cannot explicitly deal with missing data. In this paper, we explore imputation strategies for handling missing values in classifiers based on recurrent neural network (RNN) and apply a recently proposed recurrent architecture, the Gated Recurrent Unit with Decay, spec…
Recurrent neural networks are often used for learning time-series data. Based on a few assumptions we model this learning task as a minimization problem of a nonlinear least-squares cost function. The special structure of the cost function allows us to build a connection to reinforcement learning. We exploit this connection and derive a convergent, policy iteration-based algorithm. Furthermore, we argue that RNN training can be fit naturally into the reinforcement learning framework.
Recurrent neural networks are a powerful tool for modeling sequential data, but the dependence of each timestep's computation on the previous timestep's output limits parallelism and makes RNNs unwieldy for very long sequences. We introduce quasi-recurrent neural networks (QRNNs), an approach to neural sequence modeling that alternates convolutional layers, which apply in parallel across timesteps, and a minimalist recurrent pooling function that applies in parallel across channels. Despite lacking trainable recurrent layers, stacked QRNNs have better predictive accuracy than stacked LSTMs of …
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.
The ALTA Institute（ALTA研究所）；Computer Laboratory（计算机实验室）；University of Cambridge（剑桥大学）
We investigate an extension of continuous online learning in recurrent neural network language models. The model keeps a separate vector representation of the current unit of text being processed and adaptively adjusts it after each prediction. The initial experiments give promising results, indicating that the method is able to increase language modelling accuracy, while also decreasing the parameters needed to store the model along with the computation required at each step.
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.
Oxford-Man Institute of Quantitative Finance（牛津-曼氏定量金融学研究所）
Despite the recent popularity of deep generative state space models, few comparisons have been made between network architectures and the inference steps of the Bayesian filtering framework -- with most models simultaneously approximating both state transition and update steps with a single recurrent neural network (RNN). In this paper, we introduce the Recurrent Neural Filter (RNF), a novel recurrent autoencoder architecture that learns distinct representations for each Bayesian filtering step, captured by a series of encoders and decoders. Testing this on three real-world time series dataset…
Recurrent neural networks (RNNs) with Long Short-Term memory cells currently hold the best known results in unconstrained handwriting recognition. We show that their performance can be greatly improved using dropout - a recently proposed regularization method for deep architectures. While previous works showed that dropout gave superior performance in the context of convolutional networks, it had never been applied to RNNs. In our approach, dropout is carefully used in the network so that it does not affect the recurrent connections, hence the power of RNNs in modeling sequence is preserved. E…
Learning long-term dependencies is a key long-standing challenge of recurrent neural networks (RNNs). Hierarchical recurrent neural networks (HRNNs) have been considered a promising approach as long-term dependencies are resolved through shortcuts up and down the hierarchy. Yet, the memory requirements of Truncated Backpropagation Through Time (TBPTT) still prevent training them on very long sequences. In this paper, we empirically show that in (deep) HRNNs, propagating gradients back from higher to lower levels can be replaced by locally computable losses, without harming the learning capabil…
In this paper, we investigate the use of prediction-adaptation-correction recurrent neural networks (PAC-RNNs) for low-resource speech recognition. A PAC-RNN is comprised of a pair of neural networks in which a {\it correction} network uses auxiliary information given by a {\it prediction} network to help estimate the state probability. The information from the correction network is also used by the prediction network in a recurrent loop. Our model outperforms other state-of-the-art neural networks (DNNs, LSTMs) on IARPA-Babel tasks. Moreover, transfer learning from a language that is similar …
Predicting smartphone users activity using WiFi fingerprints has been a popular approach for indoor positioning in recent years. However, such a high dimensional time-series prediction problem can be very tricky to solve. To address this issue, we propose a novel deep learning model, the convolutional mixture density recurrent neural network (CMDRNN), which combines the strengths of convolutional neural networks, recurrent neural networks and mixture density networks. In our model, the CNN sub-model is employed to detect the feature of the high dimensional input, the RNN sub-model is utilized …
CIMS, New York University（纽约大学库朗数学科学研究所）；CSAIL & IMES, Massachusetts Institute of Technology（麻省理工学院计算机科学与人工智能实验室及医学工程与科学研究所）
In this work, we present the Grounded Recurrent Neural Network (GRNN), a recurrent neural network architecture for multi-label prediction which explicitly ties labels to specific dimensions of the recurrent hidden state (we call this process "grounding"). The approach is particularly well-suited for extracting large numbers of concepts from text. We apply the new model to address an important problem in healthcare of understanding what medical concepts are discussed in clinical text. Using a publicly available dataset derived from Intensive Care Units, we learn to label a patient's diagnoses a…
Université de Montréal（蒙特利尔大学）；Microsoft Research（微软研究院）
In this paper, we explore different neural network architectures that can predict if a speaker of a given utterance is asking a question or making a statement. We com- pare the outcomes of regularization methods that are popularly used to train deep neural networks and study how different context functions can affect the classification performance. We also compare the efficacy of gated activation functions that are favorably used in recurrent neural networks and study how to combine multimodal inputs. We evaluate our models on two multimodal datasets: MSR-Skype and CALLHOME.
In this work, we propose a novel recurrent neural network (RNN) architecture. The proposed RNN, gated-feedback RNN (GF-RNN), extends the existing approach of stacking multiple recurrent layers by allowing and controlling signals flowing from upper recurrent layers to lower layers using a global gating unit for each pair of layers. The recurrent signals exchanged between layers are gated adaptively based on the previous hidden states and the current input. We evaluated the proposed GF-RNN with different types of recurrent units, such as tanh, long short-term memory and gated recurrent units, on…
This paper introduces the Deep Recurrent Attentive Writer (DRAW) neural network architecture for image generation. DRAW networks combine a novel spatial attention mechanism that mimics the foveation of the human eye, with a sequential variational auto-encoding framework that allows for the iterative construction of complex images. The system substantially improves on the state of the art for generative models on MNIST, and, when trained on the Street View House Numbers dataset, it generates images that cannot be distinguished from real data with the naked eye.
Recurrent neural networks (RNNs) are very good at modelling the flow of text, but typically need to be trained on a far larger corpus than is available for the PAN 2015 Author Identification task. This paper describes a novel approach where the output layer of a character-level RNN language model is split into several independent predictive sub-models, each representing an author, while the recurrent layer is shared by all. This allows the recurrent layer to model the language as a whole without over-fitting, while the outputs select aspects of the underlying model that reflect their author's …
Real-time classification of Electromyography signals is the most challenging part of controlling a prosthetic hand. Achieving a high classification accuracy of EMG signals in a short delay time is still challenging. Recurrent neural networks (RNNs) are artificial neural network architectures that are appropriate for sequential data such as EMG. In this paper, after extracting features from a hybrid time-frequency domain (discrete Wavelet transform), we utilize a set of recurrent neural network-based architectures to increase the classification accuracy and reduce the prediction delay time. The…
The capability of recurrent neural networks to approximate trajectories of a random dynamical system, with random inputs, on non-compact domains, and over an indefinite or infinite time horizon is considered. The main result states that certain random trajectories over an infinite time horizon may be approximated to any desired accuracy, uniformly in time, by a certain class of deep recurrent neural networks, with simple feedback structures. The formulation here contrasts with related literature on this topic, much of which is restricted to compact state spaces and finite time intervals. The m…
Queen Mary University of London（伦敦玛丽女王大学）；New York University（纽约大学）
We introduce a convolutional recurrent neural network (CRNN) for music tagging. CRNNs take advantage of convolutional neural networks (CNNs) for local feature extraction and recurrent neural networks for temporal summarisation of the extracted features. We compare CRNN with three CNN structures that have been used for music tagging while controlling the number of parameters with respect to their performance and training time per sample. Overall, we found that CRNNs show a strong performance with respect to the number of parameter and training time, indicating the effectiveness of its hybrid st…
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…
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 …
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 …
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.
Escuela Politécnica Superior, Universidad Autónoma de Madrid（马德里自治大学高等理工学院）
We explore a neural network architecture that stacks a recurrent layer and a feedforward layer that is also connected to the input, and compare it to standard Elman and LSTM architectures in terms of accuracy and interpretability. When noise is introduced into the activation function of the recurrent units, these neurons are forced into a binary activation regime that makes the networks behave much as finite automata. The resulting models are simpler, easier to interpret and get higher accuracy on different sample problems, including the recognition of regular languages, the computation of add…
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.
Recent approaches based on artificial neural networks (ANNs) have shown promising results for short-text classification. However, many short texts occur in sequences (e.g., sentences in a document or utterances in a dialog), and most existing ANN-based systems do not leverage the preceding short texts when classifying a subsequent one. In this work, we present a model based on recurrent neural networks and convolutional neural networks that incorporates the preceding short texts. Our model achieves state-of-the-art results on three different datasets for dialog act prediction.
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.
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) …
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…
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.…
