Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations
A toolkit for manipulating indefinite summations with application to neural networks
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
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The theoretical analysis and derivation of artificial neural systems, which consists essentially of manipulating symbolic mathematical objects according to certain mathematical and biological knowledge, can be done more efficiently with computer assistance by using and extending methods and systems of symbolic computation. After presenting the mathematical characteristics of neural systems and a brief review on Lyapunov stability theory, the authors present some features and capabilities of existing systems and the extension for manipulating objects occurring in the analysis of neural systems. Some strategies and a toolkit developed in MACSYMA for computer-aided analysis and derivation are described. A concrete example is given to demonstrate the derivation of a hybrid neural system, i.e. a system which in its learning rule combines elements of supervised and unsupervised learning. Future work and research directions are indicated.