5 papers
A Single Architecture for Representing Invariance Under Any Space Group
Cindy Y. Zhang, Elif Ertekin, Peter Orbanz +1
Incorporating known symmetries in data into machine learning models has consistently improved predictive accuracy, robustness, and generalization. However, achieving exact invarian…
Gaussian universality for approximately polynomial functions of high-dimensional data
Kevin Han Huang, Morgane Austern, Peter Orbanz
Gaussian universality results assert that the properties of many estimators remain unchanged when the input data are replaced by Gaussians. Such results have gained popularity in h…
Gaussian and Non-Gaussian Universality of Data Augmentation
Kevin Han Huang, Peter Orbanz, Morgane Austern
We provide universality results that quantify how data augmentation affects the variance and limiting distribution of estimates through simple surrogates, and analyze several speci…
Diagonal Symmetrization of Neural Network Solvers for the Many-Electron Schrödinger Equation
Kevin Han Huang, Ni Zhan, Elif Ertekin +2
Incorporating group symmetries into neural networks has been a cornerstone of success in many AI-for-science applications. Diagonal groups of isometries, which describe the invaria…
Designing Mechanical Meta-Materials by Learning Equivariant Flows
Mehran Mirramezani, Anne S. Meeussen, Katia Bertoldi +2
Mechanical meta-materials are solids whose geometric structure results in exotic nonlinear behaviors that are not typically achievable via homogeneous materials. We show how to dra…