Surface Geometry of Data Manifolds Predicts Optimal Regularization in Neural Networks

We show that four measurable geometric properties of a data manifold — intrinsic dimension, curvature, density variation, and codimension ratio — predict the optimal weight decay for neural networks with R² = 0.196 (p < 0.001) and capture 84% of oracle grid-search performance on held-out domains (40 wins, 19 ties, 1 loss across 60 test manifolds). The key finding is that interaction terms between surface properties — particularly the product of intrinsic dimension and density variation (ID×DCV) — carry the dominant signal, while individual properties alone are weak predictors. This result emerges only when self-regularizing mechanisms (early stopping) are absent, confirming that surface geometry governs explicit regularization specifically. These findings derive from the Tension-Dissipation Framework (TDF), a cosmological theory that identifies three conservation laws (energy, angular momentum, dissipation) as the minimal set producing observed structure at every physical scale. We map these three "legs" to machine learning — compute (Leg 1), gradient flow (Leg 2), and regularization (Leg 3) — and demonstrate that the framework's predictions about the role of dissipation extend from astrophysics to artificial intelligence. All experiments run on a consumer laptop (Surface Pro 7) using standard Python libraries. Code and data are publicly available.