Foundation Model Training Bounds: A Formally Verified Framework for Generalization and Scaling
Mathematics verified. Core theorems are machine-checked in Lean 4.
Prose and presentation may not have been human-reviewed.
Abstract
We present a formally verified framework for analyzing foundation model training dynamics through the lens of generalization bounds and scaling laws. The framework establishes fundamental relationships between training loss, validation loss, generalization gap, and model size, providing rigorous guarantees for certificate-based quality metrics. All 12 core theorems are machine-verified in the Platonic proof system with 0 axioms beyond standard real arithmetic, ensuring the mathematical foundations are sound. The results connect training dynamics to spectral properties, offering a unified view of model scaling and generalization.
Keywords: foundation models, generalization bounds, scaling laws, formal verification, machine learning theory
Length
1,500 words
Status
draft