Learning the Geometry of Materials Space with Trained Neural Tangent Kernels

Daniel Kaplan, Gabriel Kotliar, Anirvan M Sengupta

Neural networks trained to predict materials properties learn representations whose physical content can be difficult to extract. We use the neural tangent kernel (NTK), evaluated at trained parameters, to recover 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 predictive performance and substantially outperforms regression with the initial kernel. Spectral analysis and multidimensional scaling reveal a geometry dominated by a small number of directions. Clustering and local neighborhood analysis organize compounds into recognizable superconducting families and connect materials with related chemical and correlated-electron properties despite substantial differences in $T_c$. These results establish trained tangent kernels as practical probes of learned materials representations, connecting property prediction with the exploration of materials space.