Automatic Concept Learning via Information Lattices

Concept learning is about distilling interpretable rules and concepts from data, a prelude to more advanced knowledge discovery and problem solving in creative domains such as art and science. While concept learning is pervasive in humans, current AI systems are mostly good at either applying human-distilled rules (rule-based AI) or capturing patterns in a task-driven fashion (pattern recognition), but not at learning patterns in a human-interpretable way similar to human-induced theory and knowledge (pattern theory). We propose a new learning paradigm---automatic concept learning---which places self-exploration and self-explanation as the focus, so that people can leverage the learned rules and concepts to solve tasks thereafter. Woven around the core idea of abstraction, we formalize the entire automatic concept learning framework as a generalization of Shannon's information lattice that brings learning into the picture. The core idea of abstraction is cast as a hierarchical, interpretable, data-free, and task-free clustering problem, seeded from universal priors such as symmetries. We present both a theoretical and algorithmic foundation of abstraction generation, and further couple abstractions with statistics in a teacher-student learning loop to distill customizable traces of rules that well-summarize and explain the data. As its first use case, in the domain of music, we build an automatic music theorist MUS-ROVER to distill, from sheet music, compositional rules that resemble many music theory textbooks. The MUS-ROVER web application can further deliver personalized lessons on music composition.