Saturating Scaling Laws for Equational Discovery: A Phenomenology of Growth Dynamics in Three Toy Substrates with Two Real-World Replications
Researchers have explored growth dynamics in deterministic equational discovery, finding that short-range substrate sizes often follow a power-law relationship. This relationship, however, is sensitive to architecture and does not transfer across different substrates like arithmetic, boolean, or list domains. A proposed heuristic model suggests a saturating power-law, which appears to be a more accurate long-range approximation, particularly for real-world growth proxies like Mathlib file additions. AI
IMPACT This research provides a new framework for understanding growth dynamics in equational discovery, potentially informing future AI development.