PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

The influence of opposite examples and randomness on the generalization complexity of Boolean functions
Leonardo Franco and Martin Anthony
(2003) Technical Report. Centre for Discrete and Applicable Mathematics, LSE, London, UK.

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:Monograph (Technical Report)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
ID Code:115
Deposited By:Martin Anthony
Deposited On:22 May 2004