1. 1 Introduction to Neural Networks Recurrent Neural Networks

2. 2 Recurrent neural networks are neural networks with feedback loops. Why recurrent neural networks? –A new approach to problem solving (via neurodynamics). –A better way for long-term prediction (e.g., financial forecasting).

3. 3 Hopfield Neural Networks (RNNs with fixed-points)

4. 4 Hopfield Network Architecture

5. 5 Hopfield Network Formulation

6. 6 Hopfield Network for Pattern Associative Memory

7. 7 Stability analysis

8. 8 Trend of change in energy due to the change in state x k :

9. 9 Recurrent Multilayer Perceptron

10. 10 Recurrent Multilayer Perceptron Network Architecture

11. 11 Formulation and Learning Algorithm

12. 12 Main Applications of Hopfield Networks Pattern Association Optimisation Time-series modelling and prediction, with better performance than feedforward MLP.