Sampling and Learning for Boolean Function (2001.07317v1)

Abstract: In this article, we continue our study on universal learning machine by introducing new tools. We first discuss boolean function and boolean circuit, and we establish one set of tools, namely, fitting extremum and proper sampling set. We proved the fundamental relationship between proper sampling set and complexity of boolean circuit. Armed with this set of tools, we then introduce much more effective learning strategies. We show that with such learning strategies and learning dynamics, universal learning can be achieved, and requires much less data.