AI and the World's Hard Problems · Chemistry & materials · arXiv · 2026-10-21
Learning the Geometry of Materials Space with Trained Neural Tangent Kernels
Neural networks trained to predict materials properties learn representations whose physical content can be difficult to extract. Using the neural tangent kernel evaluated at trained parameters, this work recovers the geometry learned by a network that predicts superconducting transition temperatures from elemental composition alone: kernel ridge regression with the trained NTK closely reproduces the network's performance and substantially outperforms regression with the initial kernel. Spectral analysis and multidimensional scaling reveal a geometry dominated by a small number of directions, and clustering and local neighborhood analysis organize compounds into recognizable superconducting families, connecting materials with related chemical and correlated-electron properties despite substantial differences in Tc.