Effective learning in recurrent max-min neural networks

Abstract

Max and min operations have interesting properties that facilitate the exchange of information between the symbolic and real-valued domains. As such, neural networks that employ max-rain activation functions have been a subject of interest in recent years. Since max-min functions are not strictly differentiable, we propose a mathematically sound learning method based on using Fourier convergence analysis of side-derivatives to derive a gradient descent technique for max-min error functions. We then propose a novel recurrent max-min neural network model that is trained to perform grammatical inference as an application example. Comparisons made between this model and recurrent sigmoidal neural networks show that our model not only performs better in terms of learning speed and generalization, but that its final weight configuration allows a deterministic finite automation (DFA) to be extracted in a straightforward manner. In essence, we are able to demonstrate that our proposed gradient descent technique does allow max-min neural networks to learn effectively.