On the enumeration of sentences by compactness
This work addresses the challenge of automated theory discovery in data analysis, though it appears incremental as it builds on existing meta-programming and validation techniques.
The authors tackled the problem of discovering compact theories from data by developing a Julia meta-program that generates candidate theories, validates them, and measures compactness using metrics like space-time derivatives. The method reduces search space through compactness constraints and is applicable to various combinatorics problems.
Presented is a Julia meta-program that discovers compact theories from data if they exist. It writes candidate theories in Julia and then validates: tossing the bad theories and keeping the good theories. Compactness is measured by a metric: such as the number of space-time derivatives. The underlying algorithm is applicable to a wide variety of combinatorics problems and compactness serves to cut down the search space.