Canalizing Boolean Functions Maximize the Mutual Information

TL;DR

This paper demonstrates that canalizing Boolean functions optimize mutual information between inputs and outputs, with proofs covering both uniform and product distributed inputs, advancing understanding in biologically inspired information processing.

Contribution

It proves that canalizing functions maximize mutual information in Boolean networks, a novel insight supported by Fourier analysis and applicable to various input distributions.

Findings

Canalizing functions maximize mutual information

Proofs cover uniform and product input distributions

Enhances understanding of information processing in biological networks

Abstract

The ability of information processing in biologically motivated Boolean networks is of interest in recent information theoretic research. One measure to quantify this ability is the well known mutual information. Using Fourier analysis we show that canalizing functions maximize the mutual information between an input variable and the outcome of the function. We proof our result for Boolean functions with uniform distributed as well as product distributed input variables.