PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

On a generalization complexity measure for Boolean functions
Leonardo Franco and Martin Anthony
In: IJCNN 2004, 26-29 July 2004, Budapest, Hungary.

Abstract

We analyze Boolean functions using a recently proposed measure of their complexity. This complexity measure, motivated by the aim of relating the complexity of the functions with the generalization ability that can be obtained when the functions are implemented in feed-forward neural networks, is the sum of two components. The first of these is related to the `average sensitivity' of the function and the second is, in a sense, a measure of the `randomness' or lack of structure of the function. In this paper, we investigate the importance of using the second term in the complexity measure. We also explore the existence of very complex Boolean functions, considering, in particular, the symmetric Boolean functions.

EPrint Type:Conference or Workshop Item (Poster)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
ID Code:112
Deposited By:Martin Anthony
Deposited On:22 May 2004