Continuous Time Recurrent Neural Network Research Articles

Walking Speed Learning and Generalization Using Seq2Seq Gated and Adaptive Continuous-Time Recurrent Neural Network (S2S-GACTRNN) for a Hip Exoskeleton

The objective of this article is to provide a new approach for walking speed learning and generalization in the speed-adaptation control of exoskeletons. By combining the gated and adaptive continuous-time recurrent neural network (GACTRNN), which has the potential to process periodic signals, and the “sequence to sequence” structure, the S2S-GACTRNN model is proposed for walking gait generation at different speeds. The “proactive loop” and “reactive loop” were presented for learning and generalization capability evaluation, respectively, in the experiments of sinusoidal signals and walking gait signals. First, simulation experiments were carried out to evaluate the S2S-GACTRNN's learning and generalization capabilities of sinusoidal signals with different frequencies. Second, in offline experiments, the model was applied to deal with walking gait signals to evaluate the capabilities of learning and generalization of walking speeds. Third, a client-server system was constructed and an online prediction method was proposed for online experiments to further evaluate the trained model's performance in walking speed generalization. The mean absolute errors of S2S-GACTRNN trained using walking data at three speeds were reduced by 24%, 38%, and 24% compared with that trained using walking data at one speed. The results show that the model has learning and generalization potential for gait signals of different walking speeds and may be utilized as a new approach to the adaptive control of walking speeds in the field of exoskeletons.

Strengthened Circle and Popov Criteria for the Stability Analysis of Feedback Systems With ReLU Neural Networks

This paper considers the stability analysis of a Lurie system with a static repeated ReLU (rectified linear unit) nonlinearity. Properties of the ReLU function are leveraged to derive new tailored quadratic constraints (QCs) which are satisfied by the repeated ReLU. These QCs are used to strengthen the Circle and Popov Criteria for this specialised Lurie system. It is shown that the criteria can be cast as a set of linear matrix inequalities (LMIs) with less restrictive conditions on the matrix variables. Many systems involving a neural network (NN) with ReLU activations are important instances of this specialised Lurie system; for example, a continuous time recurrent neural network (RNN) or the interconnection of a linear system with a feedforward NN. Numerical examples show the strengthened criteria strike an appealing balance between reduced conservatism and complexity, compared to existing criteria.

Global bifurcations in a dynamical model of recurrent neural networks

The dynamical behaviour of a continuous time recurrent neural network model with a special weight matrix is studied. The network contains several identical excitatory neurons and a single inhibitory one. This special construction enables us to reduce the dimension of the system and then fully characterize the local and global codimension-one bifurcations. It is shown that besides saddle-node and Andronov-Hopf bifurcations, homoclinic and cycle fold bifurcations may occur. These bifurcation curves divide the plane of weight parameters into nine domains. The phase portraits belonging to these domains are also characterized.

Ordinary differential equation based neural network coupled with random forest in the quality assessment of hand hygiene processes

We describe a novel approach for quality assessment of hand hygiene process based on combination of ordinary differential equation (ODE) neural network and random forest. The continuous-time recurrent neural network (RNN) with ODE hidden nodes is utilized. Unlike traditional continuous-time RNNs, the ODE network in this scheme applies an input-dependent varying time-constant models referred as liquid time-constant (LTC) RNN. It expresses stable and bounded behavior and yields superior expressivity. The random forest is attractive for findings of multiple trees in classification. It is built from multiple LTC networks, each network is corresponding to each tree. The experimental results showed that the proposed approach attains the recognition accuracy of 98.9% for single handwashing step and 78% for the whole handwashing process.

Path classification by stochastic linear recurrent neural networks

We investigate the functioning of a classifying biological neural network from the perspective of statistical learning theory, modelled, in a simplified setting, as a continuous-time stochastic recurrent neural network (RNN) with the identity activation function. In the purely stochastic (robust) regime, we give a generalisation error bound that holds with high probability, thus showing that the empirical risk minimiser is the best-in-class hypothesis. We show that RNNs retain a partial signature of the paths they are fed as the unique information exploited for training and classification tasks. We argue that these RNNs are easy to train and robust and support these observations with numerical experiments on both synthetic and real data. We also show a trade-off phenomenon between accuracy and robustness.

Simulation for a Mems-Based CTRNN Ultra-Low Power Implementation of Human Activity Recognition.

This paper presents an energy-efficient classification framework that performs human activity recognition (HAR). Typically, HAR classification tasks require a computational platform that includes a processor and memory along with sensors and their interfaces, all of which consume significant power. The presented framework employs microelectromechanical systems (MEMS) based Continuous Time Recurrent Neural Network (CTRNN) to perform HAR tasks very efficiently. In a real physical implementation, we show that the MEMS-CTRNN nodes can perform computing while consuming power on a nano-watts scale compared to the micro-watts state-of-the-art hardware. We also confirm that this huge power reduction doesn't come at the expense of reduced performance by evaluating its accuracy to classify the highly cited human activity recognition dataset (HAPT). Our simulation results show that the HAR framework that consists of a training module, and a network of MEMS-based CTRNN nodes, provides HAR classification accuracy for the HAPT that is comparable to traditional CTRNN and other Recurrent Neural Network (RNN) implantations. For example, we show that the MEMS-based CTRNN model average accuracy for the worst-case scenario of not using pre-processing techniques, such as quantization, to classify 5 different activities is 77.94% compared to 78.48% using the traditional CTRNN.

Evolution of Situated and Abstract Communication in Leader Selection and Borderline Identification Swarm Robotics Problems

The design of robust yet simple communication mechanisms, that allow the cooperation through direct interaction among robots, is an important aspect of swarm robotics systems. In this paper, we analyze how an identical continuous-time recurrent neural network (CTRNN) controller can lead to the emergence of different kinds of communications within the swarm, either abstract or situated, depending on the problem to be faced. More precisely, we address two swarm robotics tasks that require, at some extent, communication to be solved: leader selection and borderline identification. The parameters of the CTRNN are evolved using separable natural evolution strategies. It is shown that, using the same starting conditions and robots’ controllers, the evolution process leads to the emergence of utterly diverging communications. Firstly, an abstract communication, in which the message carries all the information, results from evolution in the leader selection task. Alternatively, a purely situated communication, meaning that only the context is communicative, emerges when dealing with the borderline identification problem. Nonetheless, scalability and robustness properties are successfully validated.

Exploiting Pull-In/Pull-Out Hysteresis in Electrostatic MEMS Sensor Networks to Realize a Novel Sensing Continuous-Time Recurrent Neural Network

The goal of this paper is to provide a novel computing approach that can be used to reduce the power consumption, size, and cost of wearable electronics. To achieve this goal, the use of microelectromechanical systems (MEMS) sensors for simultaneous sensing and computing is introduced. Specifically, by enabling sensing and computing locally at the MEMS sensor node and utilizing the usually unwanted pull in/out hysteresis, we may eliminate the need for cloud computing and reduce the use of analog-to-digital converters, sampling circuits, and digital processors. As a proof of concept, we show that a simulation model of a network of three commercially available MEMS accelerometers can classify a train of square and triangular acceleration signals inherently using pull-in and release hysteresis. Furthermore, we develop and fabricate a network with finger arrays of parallel plate actuators to facilitate coupling between MEMS devices in the network using actuating assemblies and biasing assemblies, thus bypassing the previously reported coupling challenge in MEMS neural networks.

Discrete-Time Recurrent Neural Network for Solving Bound-Constrained Time-Varying Underdetermined Linear System

A typical recurrent neural network (RNN) has been developed for the online solution of a time-varying underdetermined linear system (TVULS) with bound constraint. This article provides a complete investigation by proposing a new discrete-time RNN (DTRNN) model to solve the bound-constrained TVULS. In particular, the continuous-time RNN (CTRNN) model in the existing literature for solving the bound-constrained TVULS is presented. The new DTRNN model is established and investigated by utilizing the Taylor difference formula to discretize the CTRNN model for determining the solution of the TVULS with bound constraint. Theoretical analysis and numerical results are provided to validate the effectiveness and superiority of the proposed DTRNN model. The model applicability is substantiated through the simulations on a PUMA560 robotic manipulator using the proposed DTRNN model.

Combining evolution and self-organization to find natural Boolean representations in unconventional computational media

Designing novel unconventional computing systems often requires the selection of the computational structure as well as choosing the right symbol encoding. Several approaches apply heuristic search and evolutionary algorithms to find both computational structure and symbol encoding, which is time consuming because they depend on each other. Here, we present a novel approach that combines evolution with self-organization, in particular we evolve the computational structure but let the symbol encoding emerge through self-organization. This should not only be more efficient but should also lead to a more “natural“ symbol encoding. We successfully demonstrate the potential of the technique, using an evolutionary algorithm to optimize the parameters of two non-linear media to perform as NAND-gates: a continuous-time recurrent neural network (CTRNN) and a computational model of BZ-droplet-based computing (DropSim). In both cases, the technique identified representations for TRUE and FALSE, and system configurations that performed successfully as NAND-gates. The effectiveness of the evolved NAND gates was further evaluated by their performance in half-adder networks, where again, both evolved systems performed correctly, producing the correct output for all possible inputs and for all possible transitions between inputs. We conclude that beyond the specific applications demonstrated here, combining evolution with self-organization could be a promising strategy widely applicable.

Fitting a recurrent dynamical neural network to neural spiking data: tackling the sigmoidal gain function issues

This is a continuation of a recent study (Doruk RO, Zhang K. Fitting of dynamic recurrent neural network models to sensory stimulus-response data. J Biol Phys 2018; 44: 449-469), where a continuous time dynamical recurrent neural network is fitted to neural spiking data. In this research, we address the issues arising from the inclusion of sigmoidal gain function parameters to the estimation algorithm. The neural spiking data will be obtained from the same model as that of Doruk and Zhang, but we propose a different model for identification. This will also be a continuous time recurrent neural network, but with generic sigmoidal gains. The simulation framework and estimation algorithms are kept similar to that of Doruk and Zhang so that we can have a solid base to compare the results. We evaluate the estimation performance in two different ways. First, we compare the firing rate responses of the original and the estimated model. We find that responses of both models to the same stimuli are similar. Secondly, we evaluate variations of the standard deviations of the estimates against a number of samples and stimulus parameters. They show a similar pattern to that of Doruk and Zhang. We thus conclude that our model serves as a reasonable alternative provided that firing rate is the response of interest (to any stimulus).

A Noise-Suppressing Neural Algorithm for Solving the Time-Varying System of Linear Equations: A Control-Based Approach

It has been found that there exists an essential similarity between solving equations and controlling dynamic systems: Both errors are expected to decrease to zero (or an acceptably tiny value) as soon as possible. By exploiting such a similarity, researchers have presented and investigated continuous-time recurrent neural network models for solving time-varying problems. To be compatible with digital computers, it is desirable to develop discrete-time neural algorithms from the control perspective for performance improvement. In this paper, a discrete-time zeroing neural algorithm is proposed for the solving system of linear equations with the aid of control techniques. To lay a basis for theoretical analyses, the proposed zeroing neural algorithm with nonlinearity is converted into a second-order linear system plus a residual term, and then, analyzed using the control theory. Theoretical results and numerical experiments are provided, which illustrate that the proposed neural algorithm possesses an improved performance compared to the existing solutions.

Self-Optimization in Continuous-Time Recurrent Neural Networks.

A recent advance in complex adaptive systems has revealed a new unsupervised learning technique called self-modeling or self-optimization. Basically, a complex network that can form an associative memory of the state configurations of the attractors on which it converges will optimize its structure: it will spontaneously generalize over these typically suboptimal attractors and thereby also reinforce more optimal attractors—even if these better solutions are normally so hard to find that they have never been previously visited. Ideally, after sufficient self-optimization the most optimal attractor dominates the state space, and the network will converge on it from any initial condition. This technique has been applied to social networks, gene regulatory networks, and neural networks, but its application to less restricted neural controllers, as typically used in evolutionary robotics, has not yet been attempted. Here we show for the first time that the self-optimization process can be implemented in a continuous-time recurrent neural network with asymmetrical connections. We discuss several open challenges that must still be addressed before this technique could be applied in actual robotic scenarios.

Interactive natural language acquisition in a multi-modal recurrent neural architecture

ABSTRACTFor the complex human brain that enables us to communicate in natural language, we gathered good understandings of principles underlying language acquisition and processing, knowledge about sociocultural conditions, and insights into activity patterns in the brain. However, we were not yet able to understand the behavioural and mechanistic characteristics for natural language and how mechanisms in the brain allow to acquire and process language. In bridging the insights from behavioural psychology and neuroscience, the goal of this paper is to contribute a computational understanding of appropriate characteristics that favour language acquisition. Accordingly, we provide concepts and refinements in cognitive modelling regarding principles and mechanisms in the brain and propose a neurocognitively plausible model for embodied language acquisition from real-world interaction of a humanoid robot with its environment. In particular, the architecture consists of a continuous time recurrent neural network, where parts have different leakage characteristics and thus operate on multiple timescales for every modality and the association of the higher level nodes of all modalities into cell assemblies. The model is capable of learning language production grounded in both, temporal dynamic somatosensation and vision, and features hierarchical concept abstraction, concept decomposition, multi-modal integration, and self-organisation of latent representations.

Neural networks for computing best rank-one approximations of tensors and its applications

This paper presents the neural dynamical network to compute a best rank-one approximation of a real-valued tensor. We implement the neural network model by the ordinary differential equations (ODE), which is a class of continuous-time recurrent neural network. Several new properties of solutions for the neural network are established. We prove that the locally asymptotic stability of solutions for ODE by constructive an appropriate Lyapunov function under mild conditions. Furthermore, we also discuss how to use the proposed neural networks for solving the tensor eigenvalue problem including the tensor H-eigenvalue problem, the tensor Z-eigenvalue problem, and the generalized eigenvalue problem with symmetric-definite tensor pairs. Finally, we generalize the proposed neural networks to the computation of the restricted singular values and the associated restricted singular vectors of real-valued tensors. We illustrate and validate theoretical results via numerical simulations.

Visual motor integration of robot’s drawing behavior using recurrent neural network

Drawing is a way of visually expressing our feelings, knowledge, and situation. People draw pictures to share information with other human beings. This study investigates visuomotor memory (VM), which is a reusable memory storing drawing behavioral data. We propose a neural network-based model for acquiring a computational memory that can replicate VM through self-organized learning of a robot’s actual drawing experiences. To design the model, we assume that VM has the following two characteristics: (1) it is formed by bottom-up learning and integration of temporal drawn pictures and motion data, and (2) it allows the observers to associate drawing motions from pictures. The proposed model comprises a deep neural network for dimensionally compressing temporal drawn images and a continuous-time recurrent neural network for integration learning of drawing motions and temporal drawn images. Two experiments are conducted on unicursal shape learning to investigate whether the proposed model can learn the function without any shape information for visual processing. Based on the first experiment, the model can learn 15 drawing sequences for three types of pictures, acquiring associative memory for drawing motions through the bottom-up learning process. Thus, it can associate drawing motions from untrained drawn images. In the second experiment, four types of pictures are trained, with four distorted variations per type. In this case, the model can organize the different shapes based on their distortions by utilizing both the image information and the drawing motions, even if visual characteristics are not shared.

영구자석 동기모터를 위한 CTRNN모델 기반 적응형 PI 제어기 설계

In many industrial applications that use the electric motors robust controllers are needed. The method using a neural network in order to design a robust controller when a disturbance occurs is studied. Backpropagation algorithm, which is used in a conventional neural network controller is used in many areas, but when the number of neurons in the input layer, hidden layer and output layer of the neural network increases the processing speed of the learning process is slow. In this paper an adaptive PI(Proportional and Integral) controller based on CTRNN(Continuous Time Recurrent Neural Network) for permanent magnet synchronous motors is presented. By varying the load and the speed the validity of the proposed method is verified through simulation and experiments.

Active Shape Discrimination with Compliant Bodies as Reservoir Computers.

Compliant bodies with complex dynamics can be used both to simplify control problems and to lead to adaptive reflexive behavior when engaged with the environment in the sensorimotor loop. By revisiting an experiment introduced by Beer and replacing the continuous-time recurrent neural network therein with reservoir computing networks abstracted from compliant bodies, we demonstrate that adaptive behavior can be produced by an agent in which the body is the main computational locus. We show that bodies with complex dynamics are capable of integrating, storing, and processing information in meaningful and useful ways, and furthermore that with the addition of the simplest of nervous systems such bodies can generate behavior that could equally be described as reflexive or minimally cognitive.

Parameter inference of general nonlinear dynamical models of gene regulatory networks from small and noisy time series

A new inference approach to general dynamic models of gene regulatory networks (GRN) is introduced. The methodology is based on a Maximum a Posteriori (MAP) smoothing of time series data from which mean field variables of the dynamics are estimated. The interactions are modeled by a Continuous Time Recurrent Neural Network (CTRNN). Parameter estimation of the CTRNN is performed without the need to numerically solve the system of nonlinear differential equations. The method is tested on a benchmark of real genetic networks and displays superior performance, in terms of the mean squared error of the expression dynamics, compared to other formalisms.

Energy-Aware Multipath Routing Scheme Based on Particle Swarm Optimization in Mobile Ad Hoc Networks.

Mobile ad hoc network (MANET) is a collection of autonomous mobile nodes forming an ad hoc network without fixed infrastructure. Dynamic topology property of MANET may degrade the performance of the network. However, multipath selection is a great challenging task to improve the network lifetime. We proposed an energy-aware multipath routing scheme based on particle swarm optimization (EMPSO) that uses continuous time recurrent neural network (CTRNN) to solve optimization problems. CTRNN finds the optimal loop-free paths to solve link disjoint paths in a MANET. The CTRNN is used as an optimum path selection technique that produces a set of optimal paths between source and destination. In CTRNN, particle swarm optimization (PSO) method is primly used for training the RNN. The proposed scheme uses the reliability measures such as transmission cost, energy factor, and the optimal traffic ratio between source and destination to increase routing performance. In this scheme, optimal loop-free paths can be found using PSO to seek better link quality nodes in route discovery phase. PSO optimizes a problem by iteratively trying to get a better solution with regard to a measure of quality. The proposed scheme discovers multiple loop-free paths by using PSO technique.