Library learning with e-graphs on jazz harmony

Humans can acquire a highly structured intuitive understanding of musical patterns, yet these patterns often require multiple iterations of reflection and re-listening to internalize fully. To capture such an internalization process, we present a computational model for the learning of jazz harmonic patterns based on library learning. Given a corpus of harmonic progressions, our model searches over a space of programs composed of primitive harmonic relations in order to discover concise generative explanations of the corpus. The model first enumerates possible programs for each piece, and then jointly learns a library of harmonic patterns and refactored programs. To efficiently navigate the vast joint space of programs and libraries, we integrate deductive parsing with library learning on e-graphs. We explore how well our model captures aspects of human musical pattern learning by evaluating the intuitiveness of both programs and libraries, as well as similarities to human-written harmonic derivations.

A Computational Cognitive Model for Processing Repetitions of Hierarchical Relations

Patterns are fundamental to human cognition, enabling the recognition of structure and regularity across diverse domains. In this work, we focus on structural repeats, patterns that arise from the repetition of hierarchical relations within sequential data, and develop a candidate computational model of how humans detect and understand such structural repeats. Based on a weighted deduction system, our model infers the minimal generative process of a given sequence in the form of a Template program, a formalism that enriches the context-free grammar with repetition combinators. Such representation efficiently encodes the repetition of sub-computations in a recursive manner. As a proof of concept, we demonstrate the expressiveness of our model on short sequences from music and action planning. The proposed model offers broader insights into the mental representations and cognitive mechanisms underlying human pattern recognition.