Convergence Analysis of Recurrent Neural Networks

1. Front Matter

   Pages i-xvii

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2. Introduction

   • Zhang Yi, K. K. Tan

   Pages 1-14

3. Hopfield Recurrent Neural Networks

   • Zhang Yi, K. K. Tan

   Pages 15-32

4. Cellular Neural Networks

   • Zhang Yi, K. K. Tan

   Pages 33-67

5. Recurrent Neural Networks with Unsaturating Piecewise Linear Activation Functions

   • Zhang Yi, K. K. Tan

   Pages 69-89

6. Lotka-Volterra Recurrent Neural Networks with Delays

   • Zhang Yi, K. K. Tan

   Pages 91-117

7. Delayed Recurrent Neural Networks with Global Lipschitz Activation Functions

   • Zhang Yi, K. K. Tan

   Pages 119-170

8. Other Models of Continuous Time Recurrent Neural Networks

   • Zhang Yi, K. K. Tan

   Pages 171-193

9. Discrete Recurrent Neural Networks

   • Zhang Yi, K. K. Tan

   Pages 195-217

10. Back Matter

    Pages 219-233

    PDF

Since the outstanding and pioneering research work of Hopfield on recurrent neural networks (RNNs) in the early 80s of the last century, neural networks have rekindled strong interests in scientists and researchers. Recent years have recorded a remarkable advance in research and development work on RNNs, both in theoretical research as weIl as actual applications. The field of RNNs is now transforming into a complete and independent subject. From theory to application, from software to hardware, new and exciting results are emerging day after day, reflecting the keen interest RNNs have instilled in everyone, from researchers to practitioners. RNNs contain feedback connections among the neurons, a phenomenon which has led rather naturally to RNNs being regarded as dynamical systems. RNNs can be described by continuous time differential systems, discrete time systems, or functional differential systems, and more generally, in terms of non­ linear systems. Thus, RNNs have to their disposal, a huge set of mathematical tools relating to dynamical system theory which has tumed out to be very useful in enabling a rigorous analysis of RNNs.

• calculus
• cognition
• image processing
• linear optimization
• network
• networks
• neural networks
• pattern recognition

• School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, People’s Republic of China

  Zhang Yi

• Department of Electrical and Computer Engineering, The National University of Singapore, Singapore

  K. K. Tan

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