## \$O(N^2)\$ Universal Antisymmetry in Fermionic Neural Networks

21 May 2022, 02:42 (modified: 05 Jul 2022, 07:34)ICML-AI4Science PosterReaders: Everyone
Keywords: Universal Antisymmetry, Fermionic Neural Networks
TL;DR: We develop a simple \$O(N^2)\$ Ansatz based on Fermionic Neural Networks, whose model family is universal to represent any antisymmetric function.
Abstract: Fermionic neural network (FermiNet) is a recently proposed wavefunction Ansatz, which is used in variational Monte Carlo (VMC) methods to solve the many-electron Schr\"{o}dinger 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.
Track: Original Research Track
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