We consider the following learning problem: Given sample pairs of input and output signals generated by an unknown nonlinear system (which is not assumed to be causal or time-invariant), we wish to find a continuous-time recurrent neural net with hyperbolic tangent activation function that approximately reproduces the underlying i/o behavior with high confidence. Leveraging earlier work concerned with matching output derivatives up to a given finite order, we reformulate the learning problem in familiar system-theoretic language and derive quantitative guarantees on the sup-norm risk of the learned model in terms of the number of neurons, the sample size, the number of derivatives being matched, and the regularity properties of the inputs, the outputs, and the unknown i/o map.
Deep Recurrent Stochastic Configuration Networks for Modelling Nonlinear Dynamic Systems
Northeastern University（东北大学）；China University of Mining and Technology（中国矿业大学）；State Key Laboratory of Synthetical Automation for Process Industries（过程综合自动化国家重点实验室）；Research Center for Stochastic Configuration Machines（随机配置机器研究中心）
Granger causality is a widely-used criterion for analyzing interactions in large-scale networks. As most physical interactions are inherently nonlinear, we consider the problem of inferring the existence of pairwise Granger causality between nonlinearly interacting stochastic processes from their time series measurements. Our proposed approach relies on modeling the embedded nonlinearities in the measurements using a component-wise time series prediction model based on Statistical Recurrent Units (SRUs). We make a case that the network topology of Granger causal relations is directly inferrabl…
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 …
Generative System Dynamics in Recurrent Neural Networks
Department of Information Engineering and Mathematics, University of Siena（信息工程与数学系，锡耶纳大学）；Department of Information Engineering, University of Florence（信息工程系，佛罗伦萨大学）；IMT School for Advanced Studies Lucca（卢塞恩高级研究学院）
Faculty of Physics and Astronomy, Heidelberg University（海德堡大学物理与天文学学院）；Institute of Neuroinformatics, University of Zurich and ETH Zurich（苏黎世大学与苏黎世联邦理工学院神经信息学研究所）
A major tenet in theoretical neuroscience is that cognitive and behavioral processes are ultimately implemented in terms of the neural system dynamics. Accordingly, a major aim for the analysis of neurophysiological measurements should lie in the identification of the computational dynamics underlying task processing. Here we advance a state space model (SSM) based on generative piecewise-linear recurrent neural networks (PLRNN) to assess dynamics from neuroimaging data. In contrast to many other nonlinear time series models which have been proposed for reconstructing latent dynamics, our mode…
Ladder networks are a notable new concept in the field of semi-supervised learning by showing state-of-the-art results in image recognition tasks while being compatible with many existing neural architectures. We present the recurrent ladder network, a novel modification of the ladder network, for semi-supervised learning of recurrent neural networks which we evaluate with a phoneme recognition task on the TIMIT corpus. Our results show that the model is able to consistently outperform the baseline and achieve fully-supervised baseline performance with only 75% of all labels which demonstrates…
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 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.
We propose a formulation for nonlinear recurrent models that includes simple parametric models of recurrent neural networks as a special case. The proposed formulation leads to a natural estimator in the form of a convex program. We provide a sample complexity for this estimator in the case of stable dynamics, where the nonlinear recursion has a certain contraction property, and under certain regularity conditions on the input distribution. We evaluate the performance of the estimator by simulation on synthetic data. These numerical experiments also suggest the extent at which the imposed theo…
This paper investigates the use of extended Kalman filtering to train recurrent neural networks with rather general convex loss functions and regularization terms on the network parameters, including $\ell_1$-regularization. We show that the learning method is competitive with respect to stochastic gradient descent in a nonlinear system identification benchmark and in training a linear system with binary outputs. We also explore the use of the algorithm in data-driven nonlinear model predictive control and its relation with disturbance models for offset-free closed-loop tracking.
Owing to their superior modeling capabilities, gated Recurrent Neural Networks, such as Gated Recurrent Units (GRUs) and Long Short-Term Memory networks (LSTMs), have become popular tools for learning dynamical systems. This paper aims to discuss how these networks can be adopted for the synthesis of Internal Model Control (IMC) architectures. To this end, first a gated recurrent network is used to learn a model of the unknown input-output stable plant. Then, a controller gated recurrent network is trained to approximate the model inverse. The stability of these networks, ensured by means of a…
KTH Royal Institute of Technology（瑞典皇家理工学院）；Uppsala University（乌普萨拉大学）
Stochastic nonlinear dynamical systems are ubiquitous in modern, real-world applications. Yet, estimating the unknown parameters of stochastic, nonlinear dynamical models remains a challenging problem. The majority of existing methods employ maximum likelihood or Bayesian estimation. However, these methods suffer from some limitations, most notably the substantial computational time for inference coupled with limited flexibility in application. In this work, we propose DeepBayes estimators that leverage the power of deep recurrent neural networks in learning an estimator. The method consists o…
Centre National de la Recherche Scientifique (CNRS)（法国国家科学研究中心）
The notion of memory capacity, originally introduced for echo state and linear networks with independent inputs, is generalized to nonlinear recurrent networks with stationary but dependent inputs. The presence of dependence in the inputs makes natural the introduction of the network forecasting capacity, that measures the possibility of forecasting time series values using network states. Generic bounds for memory and forecasting capacities are formulated in terms of the number of neurons of the nonlinear recurrent network and the autocovariance function or the spectral density of the input. …
The goal of this paper is to provide sufficient conditions for guaranteeing the Input-to-State Stability (ISS) and the Incremental Input-to-State Stability (δISS) of Gated Recurrent Units (GRUs) neural networks. These conditions, devised for both single-layer and multi-layer architectures, consist of nonlinear inequalities on network's weights. They can be employed to check the stability of trained networks, or can be enforced as constraints during the training procedure of a GRU. The resulting training procedure is tested on a Quadruple Tank nonlinear benchmark system, showing satisfactory mo…
University of West Attica（西阿提卡大学）；University of the Aegean（爱琴大学）
We investigate the complexity and performance of recurrent neural network (RNN) models as post-processing units for the compensation of fibre nonlinearities in digital coherent systems carrying polarization multiplexed 16-QAM and 32-QAM signals. We evaluate three bi-directional RNN models, namely the bi-LSTM, bi-GRU and bi-Vanilla-RNN and show that all of them are promising nonlinearity compensators especially in dispersion unmanaged systems. Our simulations show that during inference the three models provide similar compensation performance, therefore in real-life systems the simplest scheme …
Institute for Parallel and Distributed Systems（并行与分布式系统研究所）；University of Stuttgart（斯图加特大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Stuttgart Center for Simulation Science（斯图加特模拟科学中心）；University of Southampton（南安普顿大学）；Electronics and Computer Science（电子与计算机科学学院）
Recurrent neural networks are capable of learning the dynamics of an unknown nonlinear system purely from input-output measurements. However, the resulting models do not provide any stability guarantees on the input-output mapping. In this work, we represent a recurrent neural network as a linear time-invariant system with nonlinear disturbances. By introducing constraints on the parameters, we can guarantee finite gain stability and incremental finite gain stability. We apply this identification method to learn the motion of a four-degrees-of-freedom ship that is moving in open water and comp…
Brief technical note on linearizing recurrent neural networks (RNNs) before vs after the pointwise nonlinearity
University of Edinburgh（爱丁堡大学）；Ecole Normale Superieure - PSL Research University（巴黎高等师范学院-PSL研究大学）；INSERM（法国国家健康与医学研究院）；Howard Hughes Medical Institute（霍华德·休斯医学研究所）；Princeton University（普林斯顿大学）
In recent years significant progress has been made in successfully training recurrent neural networks (RNNs) on sequence learning problems involving long range temporal dependencies. The progress has been made on three fronts: (a) Algorithmic improvements involving sophisticated optimization techniques, (b) network design involving complex hidden layer nodes and specialized recurrent layer connections and (c) weight initialization methods. In this paper, we focus on recently proposed weight initialization with identity matrix for the recurrent weights in a RNN. This initialization is specifica…
Surrogate testing techniques have been used widely to investigate the presence of dynamical nonlinearities, an essential ingredient of deterministic chaotic processes. Traditional surrogate testing subscribes to statistical hypothesis testing and investigates potential differences in discriminant statistics between the given empirical sample and its surrogate counterparts. The choice and estimation of the discriminant statistics can be challenging across short time series. Also, conclusion based on a single empirical sample is an inherent limitation. The present study proposes a recurrent neur…
Argonne Leadership Computing Facility（阿贡领导力计算设施）；Argonne National Laboratory（阿贡国家实验室）；Mathematics and Computer Science Division（数学与计算机科学部）
Rapid simulations of advection-dominated problems are vital for multiple engineering and geophysical applications. In this paper, we present a long short-term memory neural network to approximate the nonlinear component of the reduced-order model (ROM) of an advection-dominated partial differential equation. This is motivated by the fact that the nonlinear term is the most expensive component of a successful ROM. For our approach, we utilize a Galerkin projection to isolate the linear and the transient components of the dynamical system and then use discrete empirical interpolation to generate…
Recurrent Stochastic Configuration Networks with Hybrid Regularization for Nonlinear Dynamics Modelling
State Key Laboratory of Synthetical Automation for Process Industries（过程工业综合自动化国家重点实验室）；Northeastern University（东北大学）；Research Center for Stochastic Configuration Machines（随机配置机器研究中心）；China University of Mining and Technology（中国矿业大学）
Viewing recurrent neural networks (RNNs) as continuous-time dynamical systems, we propose a recurrent unit that describes the hidden state's evolution with two parts: a well-understood linear component plus a Lipschitz nonlinearity. This particular functional form facilitates stability analysis of the long-term behavior of the recurrent unit using tools from nonlinear systems theory. In turn, this enables architectural design decisions before experimentation. Sufficient conditions for global stability of the recurrent unit are obtained, motivating a novel scheme for constructing hidden-to-hidd…
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…
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…
We study epidemic forecasting on real-world health data by a graph-structured recurrent neural network (GSRNN). We achieve state-of-the-art forecasting accuracy on the benchmark CDC dataset. To improve model efficiency, we sparsify the network weights via transformed-$\ell_1$ penalty and maintain prediction accuracy at the same level with 70% of the network weights being zero.
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 …
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.
Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling them. While there are many methods for modeling nonlinear dynamical systems, existing techniques face a trade off between offering interpretable descriptions and making accurate predictions. Here, we develop a class of models that aims to achieve both simultaneously, smoothly interpolating between simple descriptions and more complex, yet also more accurate mo…
Technische Universität München（慕尼黑工业大学）；Leibniz Universität Hannover（莱布尼茨汉诺威大学）
Leveraging advances in variational inference, we propose to enhance recurrent neural networks with latent variables, resulting in Stochastic Recurrent Networks (STORNs). The model i) can be trained with stochastic gradient methods, ii) allows structured and multi-modal conditionals at each time step, iii) features a reliable estimator of the marginal likelihood and iv) is a generalisation of deterministic recurrent neural networks. We evaluate the method on four polyphonic musical data sets and motion capture data.
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.
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.
McGill University（麦吉尔大学）；Pennsylvania State University（宾夕法尼亚州立大学）
Understanding recurrent networks through rule extraction has a long history. This has taken on new interests due to the need for interpreting or verifying neural networks. One basic form for representing stateful rules is deterministic finite automata (DFA). Previous research shows that extracting DFAs from trained second-order recurrent networks is not only possible but also relatively stable. Recently, several new types of recurrent networks with more complicated architectures have been introduced. These handle challenging learning tasks usually involving sequential data. However, it remains…
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 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 long term dependencies in recurrent networks is difficult due to vanishing and exploding gradients. To overcome this difficulty, researchers have developed sophisticated optimization techniques and network architectures. In this paper, we propose a simpler solution that use recurrent neural networks composed of rectified linear units. Key to our solution is the use of the identity matrix or its scaled version to initialize the recurrent weight matrix. We find that our solution is comparable to LSTM on our four benchmarks: two toy problems involving long-range temporal structures, a la…
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…
Recurrent networks are trained to memorize their input better, often in the hopes that such training will increase the ability of the network to predict. We show that networks designed to memorize input can be arbitrarily bad at prediction. We also find, for several types of inputs, that one-node networks optimized for prediction are nearly at upper bounds on predictive capacity given by Wiener filters, and are roughly equivalent in performance to randomly generated five-node networks. Our results suggest that maximizing memory capacity leads to very different networks than maximizing predicti…
Washington University School of Medicine（华盛顿大学医学院）
Deep Learning networks have established themselves as providing state of art performance for semantic segmentation. These techniques are widely applied specifically to medical detection, segmentation and classification. The advent of the U-Net based architecture has become particularly popular for this application. In this paper we present the Dense Recurrent Residual Convolutional Neural Network(Dense R2U CNN) which is a synthesis of Recurrent CNN, Residual Network and Dense Convolutional Network based on the U-Net model architecture. The residual unit helps training deeper network, while the…
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 been the dominant models for many speech and language processing tasks. However, we understand little about the behavior and the class of functions recurrent networks can realize. Moreover, the heuristics used during training complicate the analyses. In this paper, we study recurrent networks' ability to learn long-term dependency in the context of speech recognition. We consider two decoding approaches, online and batch decoding, and show the classes of functions to which the decoding approaches correspond. We then draw a connection between batch decoding and a …
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.
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.…
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…
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…
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…
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 …
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.
