A Framework for Solving Functional Equations with Neural Networks
In his ,,essay towards a calculus of junctions from 1815 Charles Babbage introduced a branch of mathematics now known as the theory of functional equations 1. But since then finding concrete solutions for a given functional equation remained a hard task in many cases. For one of his examples, the now famous ,,Babbage equation ψ(ψ(x))=x, which solutions ψ are called ,,the roots of identity and the more general equation ψ(ψ(x))=f(x) which defines kind of a ,,square root of some given function fwe have previously shown that this type of equation can be solved approximately by neural networks with a special topology and learning rule. Here we extend that method towards a wider range of functional equations which can be mapped in similar ways to neural networks too. The method is demonstrated on - but not limited tomultilayer perceptrons. We present a first sketch of this ideas here on some important equations.
Lars Kindermann Achim Lewandowski Peter Protzel
Current Adress: Am Jahsberg - 37186 Moringen, Germany After October 2001: RIKEN Brain Science Instit Dept. of Electrical Engineering and Information Technology Chemnitz University of Technology, 09107
国际会议
8th International Conference on Neural Information Processing(ICONIP 2001)(第八届国际神经信息处理大会)
上海
英文
1113-1116
2001-11-14（万方平台首次上网日期，不代表论文的发表时间）