Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry
Abstract
We derive symmetric and antisymmetric kernels by symmetrizing and antisymmetrizing conventional kernels and analyze their properties. In particular, we compute the feature space dimensions of the resulting polynomial kernels, prove that the reproducing kernel Hilbert spaces induced by symmetric and antisymmetric Gaussian kernels are dense in the space of symmetric and antisymmetric functions, and propose a Slater determinant representation of the antisymmetric Gaussian kernel, which allows for an efficient evaluation even if the state space is highdimensional. Furthermore, we show that by exploiting symmetries or antisymmetries the size of the training data set can be significantly reduced. The results are illustrated with guiding examples and simple quantum physics and chemistry applications.
 Publication:

arXiv eprints
 Pub Date:
 March 2021
 arXiv:
 arXiv:2103.17233
 Bibcode:
 2021arXiv210317233K
 Keywords:

 Quantum Physics;
 Mathematical Physics;
 Physics  Chemical Physics;
 Statistics  Machine Learning
 EPrint:
 Machine Learning: Science and Technology, Volume 2, Number 4, 2021