(Re)discovering Laws of Music Theory Using Information Lattice Learning

Abstract

Information lattice learning (ILL) is a novel framework for knowledge discovery based on group-theoretic and information-theoretic foundations, which can rediscover the rules of music as known in the canon of music theory and also discover new rules that have remained unexamined. Such probabilistic rules are further demonstrated to be human-interpretable. ILL itself is a rediscovery and generalization of Shannon’s lattice theory of information, where probability measures are not given but are learned from training data. This article explains the basics of the ILL framework, including both how to construct a lattice-structured abstraction universe that specifies the structural possibilities of rules, and how to find the most informative rules by performing statistical learning through an iterative student–teacher algorithmic architecture that optimizes information functionals. The ILL framework is finally shown to support both pedagogy and novel patterns of music co-creativity.