Chaotic Recurrent Neural Networks Research Articles

Lyapunov spectra of chaotic recurrent neural networks

Lyapunov spectra of chaotic recurrent neural networks

Finite/fixed‐time synchronization of nonidentical chaotic delayed neural networks with Markovian jump and uncertainties via sliding mode control

AbstractThis article investigates the finite/fixed‐time synchronization problem of Markovian jumping delayed chaotic recurrent neural networks with uncertainties by employing sliding mode control method. In order to cope with Markovian jump and parameter uncertainties, sliding model control is used for its strong robustness and insensitivity character to external disturbances and parameter variations. Above all, two simplified sliding mode surfaces are constructed. Following that, matching controllers are constructed to guarantee the finite/fixed‐time reachability of sliding mode surfaces. Additionally, the dynamics of the sliding mode surfaces can be achieved in a finite/fixed‐time. Based on the Lyapunov stability theory, some sufficient conditions are proposed to guarantee the finite/fixed‐time synchronization. Compared with the conclusions of the existing literature, this article generalizes the corresponding results to Markovian jump, parameter uncertainties, and nonidentical systems. Finally, two numerical examples are given to illustrate the effectiveness of the obtained theoretical results.

Tension: A Python package for FORCE learning.

First-Order, Reduced and Controlled Error (FORCE) learning and its variants are widely used to train chaotic recurrent neural networks (RNNs), and outperform gradient methods on certain tasks. However, there is currently no standard software framework for FORCE learning. We present tension, an object-oriented, open-source Python package that implements a TensorFlow / Keras API for FORCE. We show how rate networks, spiking networks, and networks constrained by biological data can all be trained using a shared, easily extensible high-level API. With the same resources, our implementation outperforms a conventional RNN in loss and published FORCE implementations in runtime. Our work here makes FORCE training chaotic RNNs accessible and simple to iterate, and facilitates modeling of how behaviors of interest emerge from neural dynamics.

Chaotic Recurrent Neural Networks for Financial Forecast

In the past few decades, with the development of artificial intelligence and computer hardware, machine learning has been widely used in various applications including industrial, healthcare, education, finance, etc. Predicting financial time series sequences with effective AI tools for more accurate results has always been one of the hottest topics in finance and AI community. In this paper, the author introduces a new type of recurrent neural network algorithm, called Chaotic Recurrent Neural Network (CRNN), which is based on Dr. Raymond’s original research on Lee-Oscillator and Recurrent Neural Network (RNN) for worldwide financial prediction. We replaced the traditional activation function with a Lee Oscillator Neural Network, which not only can solve the vanishing gradient problem of traditional recurring neural networks during algorithm training, but can also provide an excellent memory correlation mechanism during long-term time series processing. The Experimental results reveal that CRNN outperforms than some popular neural network which widely applied to predict financial data, such as FFBPN, RNN, LSTM, in terms of forecast accuracy in certain cases. The experimental environment is based on Pytorch and Python 3.8, using 10 years (2010-2020) major financial index data, including DJI, HSI, IXIC, SPX, SSE, SZSE, APPL, to forecast 31th day closing price with previous 30 days closing price. Besides financial forecasting, our CRNN algorithm also has many potential applications, such as Natural Language Processing, weather forecasting, etc.

A neuromorphic control architecture for a biped robot

A neuromorphic control architecture is introduced to govern the motion of a lightweight humanoid robot. The reference trajectories necessary to perform stable gaits are generated by neural modules represented by Chaotic Recurrent Neural Networks CRNN organized in a hierarchical fashion. In the higher layer a body-coordination module generates the trajectories for the central parts of the robot body, in the middle layer the limb-coordination modules generate the Cartesian trajectories for the end effector of each limb, finally in the lower layer the limb modules control the position of the robot joints. Each neural module consists of a reservoir of N=200 leaky-integrator neurons randomly and sparsely connected with fixed synapses. The adaptation occurs in the synapses of readout units by online learning techniques like the delta rule and the Recursive Least Square algorithm RLS. It is demonstrated that the neural modules can learn and reproduce with enough accuracy the trajectories acquired from the simulation of a humanoid robot in V-REP software. With an optimal initialization of the reservoir connection matrix and by using a low computationally expensive learning algorithm such as the delta rule, Θ(N), the average of MSE over all lower limbs joints is in the order of 0.1. For the lower-limbs-coordination-module the MSE drops to 0.004 by using the more computational expensive RLS, Θ(N2). In case the neural module needs to learn how to adapt the trajectories according to a specific step length and frequency the MSE is 0.06. A comparison between different learning algorithms applied on the CRNN showed better performances by using RLS. This result is confirmed also by a direct comparison with a different neural architecture, the PCPG, however at the expense of a bigger computational complexity. A real test conducted on a small computational unit (Raspberry Pi2) demonstrated that the CRNN can be executed at a frequency of 142 Hz which suffices to feed a PID feedback control loop at the joint level.

Design and Modeling of a Lightweight and Low Power Consumption Full-Scale Biped Robot

This paper introduces the design methodology, the modeling and the power consumption tests for a newly developed biped robot equipped with 12 DOFs. The robot is 1.1 meters tall (lower limbs) which makes it comparable in dimension with other state-of-the-art full-scale humanoids. By using a combination of 3D printing techniques and lightweight materials, the system weighs only 10.8[Formula: see text]kg (without batteries) while retaining high links strength and rigidity. Without compromising the workspace dimension, the robot presents a very low weight-to-height ratio (9.8[Formula: see text]kg/m) that translates into a safer operation and reduced energy consumption. To perform elementary locomotion primitives, e.g., changing the support from one foot to the other or lifting its body, the robot prototype consumes only 65 watts. Simulation results demonstrate the suitability of the robot’s kinematics to perform walking motion and predict an average power consumption of 200 watts. The direct kinematics of the robot is presented together with its inverse dynamics based on a Chaotic Recurrent Neural Network (CRNN). The adaptive model is identified using a recursive least squares algorithm that allows the CRNN to predict the torques at different step lengths with a MSE of 0.0057 on normalized data.

Exponential adaptive synchronization of stochastic memristive chaotic recurrent neural networks with time-varying delays

This paper is focused on the global exponential adaptive synchronization problem of two stochastic memristive chaotic neural networks with both stochastic disturbance and time-varying delays. First, in order to develop the guaranteed cost control, a periodically alternate adaptive rule is designed. Then, by constructing appropriate Lyapunov–Krasovskii functionals, several easily verified synchronization criteria are derived to guarantee exponential adaptive synchronization of drive-response stochastic memristive chaotic recurrent neural networks. Lastly, a numerical simulation is carried out to demonstrate the effectiveness of the proposed results.

Exponential Synchronization of Memristive Chaotic Recurrent Neural Networks Via Alternate Output Feedback Control

AbstractThis paper considers the global exponential synchronization problem of two memristive chaotic recurrent neural networks with time‐varying delays using periodically alternate output feedback control. First, the periodically alternate output feedback control rule is designed for the global exponential synchronization of two memristive chaotic recurrent neural networks. Then, according to the Lyapunov stability theory, we construct an appropriate Lyapunov‐Krasovskii functional to derive several new sufficient conditions guaranteeing exponential synchronization of two memristive chaotic recurrent neural networks under periodically alternate output feedback control. Compared with existing results on synchronization conditions on the basis of linear matrix inequalities of memristive chaotic recurrent neural networks, the derived results complement, extend earlier related results, and are also easy to validate in this paper. An illustrative example is provided to illustrate the effectiveness of the synchronization criteria.

Development of a neuromorphic control system for a lightweight humanoid robot

A neuromorphic control system for a lightweight middle size humanoid biped robot built using 3D printing techniques is proposed. The control architecture consists of different modules capable to learn and autonomously reproduce complex periodic trajectories. Each module is represented by a chaotic Recurrent Neural Network (RNN) with a core of dynamic neurons randomly and sparsely connected with fixed synapses. A set of read-out units with adaptable synapses realize a linear combination of the neurons output in order to reproduce the target signals. Different experiments were conducted to find out the optimal initialization for the RNN’s parameters. From simulation results, using normalized signals obtained from the robot model, it was proven that all the instances of the control module can learn and reproduce the target trajectories with an average RMS error of 1.63 and variance 0.74.

Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control

In this paper, a new method to synchronize two identical chaotic recurrent neural networks is proposed. Using the drive-response concept, a nonlinear feedback control law is derived to achieve the state synchronization of the two identical chaotic neural networks. Furthermore, based on the Lyapunov method, a delay independent sufficient synchronization condition in terms of linear matrix inequality (LMI) is obtained. A numerical example with graphical illustrations is given to illuminate the presented synchronization scheme.

Chaotic recurrent neural networks and their application to speech recognition

A new Chaotic Recurrent Neural Network (CRNN) is proposed to improve the learning ability and the application to the speech recognition of Korean spoken digits and Korean monosyllables is discussed. The learning performance of the CRNN is compared to that of the RNN and the influence of refractory parameters on learning is considered. The MFCC (Mel-Frequency Cepstrum Coefficients) is used as an input feature for learning and recall. Speech data are acquired by using A/D board composed of AD574A chip with 8 kHz sampling rate and 12 bit resolution. In the experiment on Korean monosyllables, the classification process and the segmentation process are executed for recognizing many syllables.