Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry

Kernel methods and neural networks are two of the most prevalent and versatile machine learning techniques. While various recent publications focus on invariant or equivariant deep learning algorithms, our goal is to derive kernel-based methods that exploit symmetries. Symmetries play an important role in many research areas such as physics and chemistry [1, 2, 3], but also point cloud classification problems [4] or problems defined on sets [5] are naturally permutation-invariant. One of the most prominent applications is in quantum physics. Systems of bosons require symmetric wave functions, whereas systems of fermions are represented by antisymmetric wave functions. Exploiting such symmetries of the underlying system is a popular and powerful approach that has been used to improve the performance of kernel-based methods as well as deep-learning algorithms.