Generalisation of A Class of Continuous Neural Networks

We propose a way of using boolean circuits to perform real valued computation in a way that naturally extends their boolean functionality. The functionality of multiple fan in threshold gates in this model is shown to mimic that of a hardware implementation of continuous Neural Networks. A Vapnik-Chervonenkis dimension and sample size analysis for the system is performed giving best known sample sizes for a real valued Neural Network. Experimental results confirm the conclusion that the sample sizes required for the networks are significantly smaller that for sigmoidal networks. Category: Theory: Computational Learning Theory. 1 Introduction Recent developments in complexity theory have addressed the question of complexity of computation over the real numbers [1]. More recently attempts have been made to introduce some computational cost related to the accuracy of the computations [5]. The model proposed in this paper weakens the computational power still further by relying on classic..