A note on chaotic behavior in simple neural networks
Neural Networks
Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations
An introduction to neural computing
An introduction to neural computing
Agent-Based Social Simulation in Markets
Electronic Commerce Research - Special issue on agents in electronic commerce
International Journal of Advanced Media and Communication
Injecting Chaos in Feedforward Neural Networks
Neural Processing Letters
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In training feed-forward neural networks using the backpropagation algorithm, a sensitivity to the values of the parameters of the algorithm hasbeen observed. In particular, it has been observed that this sensitivity with respect to the values of the parameters, such as thelearning rate, plays an important role in the final outcome. In thistutorial paper, we will look at neural networks from a dynamical systemspoint of view andexamine its properties. To this purpose, we collect results regarding chaostheory as well as the backpropagation algorithmand establish a relationship between them. We study in detail as an example the learning of the exclusive OR,an elementary Boolean function. The following conclusions hold for our XOR neural network: no chaos appears for learning rates lower than 5, when chaosoccurs, it disappears as learning progresses. For non-chaotic learning rates, the network learns faster than for other learning rates for which chaos occurs.