Title: Separations in symmetric and antisymmetric neural ansatze
Abstract: Many particle systems appear across several areas of physics and chemistry, and often their governing equations exhibit invariances to particle permutations, motivating the study of function approximation under particle symmetries. For instance, the Hamiltonian in classical mechanics is permutation invariant, while the wavefunction in fermionic systems is invariant up to permutation signs. In this talk, we will describe the ability of certain neural network architectures to approximate symmetric and antisymmetric functions. Specifically, we study the approximation benefits of `self-attention’ in symmetric networks, and the benefits of the Jastrow ansatz over the simpler Slater determinant, establishing the first quantitative separations. Joint work with Aaron Zweig.