$O(N^2)$ Universal Antisymmetry in Fermionic Neural Networks
This addresses a scalability issue in quantum chemistry simulations for researchers, offering a more efficient method with proven theoretical guarantees.
The paper tackles the computational bottleneck in Fermionic Neural Networks (FermiNet) by replacing the Slater determinant with a pairwise antisymmetry construction, reducing the cost from O(N^3) to O(N^2) for N electrons, while proving universal representation capability for antisymmetric functions.
Fermionic neural network (FermiNet) is a recently proposed wavefunction Ansatz, which is used in variational Monte Carlo (VMC) methods to solve the many-electron Schrödinger equation. FermiNet proposes permutation-equivariant architectures, on which a Slater determinant is applied to induce antisymmetry. FermiNet is proved to have universal approximation capability with a single determinant, namely, it suffices to represent any antisymmetric function given sufficient parameters. However, the asymptotic computational bottleneck comes from the Slater determinant, which scales with $O(N^3)$ for $N$ electrons. In this paper, we substitute the Slater determinant with a pairwise antisymmetry construction, which is easy to implement and can reduce the computational cost to $O(N^2)$. We formally prove that the pairwise construction built upon permutation-equivariant architectures can universally represent any antisymmetric function. Besides, this universality can be achieved via continuous approximators when we aim to represent ground-state wavefunctions.