Learning Nonlinearity of Boolean Functions: An Experimentation with Neural Networks
This work addresses a specific challenge in computational learning theory for researchers, but it is incremental as it builds on existing methods with limited scalability.
The paper tackles the problem of learning the nonlinearity property of Boolean functions using neural networks, achieving over 95% accuracy in predicting nonlinearity for functions with 4 and 5 variables.
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.