Saturating Scaling Laws for Equational Discovery: A Phenomenology of Growth Dynamics in Three Toy Substrates with Two Real-World Replications
The article discusses growth dynamics in deterministic equational discovery substrates across three toy domains. It presents a model predicting saturating power-law growth, emphasizing that dynamics are conditional on the substrate used. The findings suggest that the preferred growth model varies by substrate and that the trajectories do not reach saturation in toy data.
- ▪The study investigates growth dynamics in three toy domains: arithmetic, boolean, and higher-order list.
- ▪A heuristic mean-field closure model predicts a saturating power-law growth pattern.
- ▪The dynamics are substrate-conditional, with different preferred functional families for growth observed.
Opening excerpt (first ~120 words) tap to expand
Computer Science > Artificial Intelligence arXiv:2605.23983 (cs) [Submitted on 14 May 2026] Title:Saturating Scaling Laws for Equational Discovery: A Phenomenology of Growth Dynamics in Three Toy Substrates with Two Real-World Replications Authors:Fabio Rovai View a PDF of the paper titled Saturating Scaling Laws for Equational Discovery: A Phenomenology of Growth Dynamics in Three Toy Substrates with Two Real-World Replications, by Fabio Rovai View PDF HTML (experimental) Abstract:We investigate growth dynamics in deterministic equational discovery substrates. Across three toy domains (arithmetic, boolean, higher-order list; n=592 trajectories), short-range substrate sizes fit a power-law N(t) proportional to t^b.
…
Excerpt limited to ~120 words for fair-use compliance. The full article is at arXiv cs.AI.
Discussion
0 commentsMore from arXiv cs.AI
