Fermionic Neural Networks through the lens of Group Theory

We present an overview of the method of Neural Quantum States applied to the many-body problem of atomic nuclei. Through the lens of group representation theory, we focus on the problem of constructing neural-network ansätze that respect physical symmetries. We explicitly prove that determinants, which are among the most common methods to build antisymmetric neural-network wave functions, can be understood as the result of a group convolution. We also identify the reason why this construction is so efficient in practice compared to other group convolutional operations. We conclude that group representation theory is a promising avenue to incorporate explicitly symmetries in Neural Quantum States.