Comparing variants of Neural Network Backflow and Hidden Fermion Determinant States

Among the variational wave function ansatz for Fermionic Hamiltonians, neural network backflow (NNBF) and hidden fermion determinant states (HFDS) are two prominent classes to provide accurate approximation for the ground states. In this work, we construct and compare a series of NNBF-type neural network states to bridge the relation between these two wave-functions showing how HFDS can be viewed as a form of NNBF. We provide both analytical and numerical results to support these conclusions considering both the limit of a large number of neurons as well as the more practical finite neuron limit.