Physical and Evolutionary Constraints on Machine Learning Priors: Reconciling No Free Lunch with Real-World Generalization

The No Free Lunch (NFL) theorems formally demonstrate that, averaged over all mathematically possible target functions, no learning algorithm can systematically outperform random guessing. While these theorems establish rigorous bounds for optimization across arbitrary spaces, the sustained empirical success of highly generalized architectures (such as Transformers) indicates that real-world problems occupy a remarkably structured, low-complexity subset of functions. In this paper, we bridge this theoretical gap by establishing physical, evolutionary, and algorithmic foundations for real-world machine learning priors. First, we formalize an Incremental Universal Machine Learning framework, proving that sequential task dependencies yield substantial computational transfer speedups bounded by conditional Kolmogorov complexity $K^{\prime }({\mathcal{D}}_{<i})$, and proving that uniform NFL sampling is mathematically isomorphic to an incompressible Chaitin-random data stream with zero transfer mutual information. Second, we derive an Evolutionary Zeta Process via Yule-Simon master equations (formalizing Chaitin's metabiology), and prove the $q$-Coverage Bit-Budget Theorem; applying this theoretical framework, we estimate that co-evolution concentrates $90\%$ of real-world task mass into compact description budgets ($15-60$ bits for human-scale problem instances, detailed in Appendix H). Third, combining physical entropy bounds (Bekenstein bound, Brudno's theorem) with a graphical model of computation, we introduce Minimum Machine Volume Complexity, proving it is an adequate, objective measure that resolves the classical $O(1)$ compiler subjectivity of universal induction. Finally, we synthesize these priors into a discretized PAC-Bayes generalization bound and empirical Cellular Automata evaluations, demonstrating why general-purpose neural architectures systematically succeed in our universe.