Learning Nonlinearity of Boolean Functions: An Experimentation with Neural Networks

TL;DR

This paper explores the ability of neural networks to learn the nonlinearity property of Boolean functions, demonstrating high accuracy for small functions but highlighting challenges for larger ones.

Contribution

It presents the first empirical analysis of neural networks predicting Boolean function nonlinearity, showing promising results for small functions and discussing limitations for larger cases.

Findings

Neural networks achieve over 95% accuracy for 4- and 5-variable functions.

Extending to higher variables remains challenging and uncertain in efficiency.

Discipline analysis of neural network learnability for Boolean properties is introduced.

Abstract

This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of functions in the form of a truth table and their corresponding nonlinearity values. We report empirical results to show that deep neural networks are able to learn to predict the property for functions in 4 and 5 variables with an accuracy above 95%. While these results are positive and a disciplined analysis is being presented for the first time in this regard, we should also underline the statutory warning that it seems quite challenging to extend the idea to higher number of variables, and it is also not clear whether one can get advantage in terms of time and space complexity over the existing combinatorial algorithms.