Renormalization as a Unified Framework for Scalable Prediction: A Practical Short Version for Machine Learning Practitioners

This short version presents a concise formulation of a renormalization-based framework that unifies a wide range of predictive systems, including Solomonoff-style predictors, Bayesian learners, compression-based methods, and modern large-scale neural networks such as Transformers. The core idea is that these systems share a common structural pattern built from four fundamental operators: coarse-graining, invariance projection, Bayesian updating, and compositional merging. Their composition defines a renormalization operator whose Lipschitz constant determines whether predictive structure collapses, diverges, or becomes scale-invariant. The condition 𝐿_𝑅 = 1 characterizes the scale-invariant regime and yields power-law scaling laws for model size, dataset size, and compute. This provides a theoretical foundation for empirical scaling laws observed in large language models and generative models, including those reported by Kaplan, Henighan, and Hoffmann. In addition to the theoretical contribution, this short version emphasizes practical guidance for machine learning practitioners. The framework clarifies how architectural components—such as normalization layers, residual connections, feedforward scaling, attention temperature, and model depth—affect the stability and scalability of Transformer models. These insights allow practitioners to evaluate whether an architecture is likely to scale predictively without requiring extensive large-scale experimentation. Overall, this short version distills the essential elements of the full renormalization framework while providing actionable principles for designing scalable machine learning models.