Trained neural kernels reveal hidden geometry of superconducting materials
Learning the Geometry of Materials Space with Trained Neural Tangent Kernels
Machine Learning
Summary
Predicting properties of materials like superconductors can be tricky because even powerful AI models learn complex information that is hard to understand. The authors use a special mathematical tool called the neural tangent kernel (NTK) to peek inside a trained neural network and recover the way it organizes materials. They show that this approach can reproduce the network’s predictions and groups similar superconducting materials together, revealing meaningful patterns. This helps connect the prediction of material properties to how materials relate to each other chemically and physically.
What this means in practice
- •For materials design teams: Use trained neural tangent kernels to identify and cluster promising superconductors based on composition-driven patterns found by AI models.
- •For chemical data analysts: Apply recovered geometry from trained kernels to better organize and understand materials datasets linking chemical and electronic properties.
Tested on one dataset.
Authors
Daniel Kaplan, Gabriel Kotliar, Anirvan M Sengupta
Abstract
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.