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 high-dimensional. 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.
Original language | English |
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Article number | 045016 |
Journal | Machine Learning: Science and Technology |
Volume | 2 |
Issue number | 4 |
Early online date | 6 Aug 2021 |
DOIs | |
Publication status | Published - Dec 2021 |
Keywords
- Quantum chemistry
- Quantum physics
- Reproducing kernel Hilbert spaces
- Symmetry and antisymmetry
ASJC Scopus subject areas
- Artificial Intelligence
- Human-Computer Interaction
- Software