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

• URL: http://arxiv.org/abs/2205.13205v1
• Date: Thu, 26 May 2022 07:44:54 GMT
• Title: $O(N^2)$ Universal Antisymmetry in Fermionic Neural Networks
• Authors: Tianyu Pang, Shuicheng Yan, Min Lin
• Abstract summary: We propose permutation-equivariant architectures, on which a determinant Slater 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. We substitute the Slater with a pairwise antisymmetry construction, which is easy to implement and can reduce the computational cost to $O(N2)$.
• Score: 107.86545461433616
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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\"odinger 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 $O(N^2)$. Furthermore, we formally prove that the pairwise construction built upon permutation-equivariant architectures can universally represent any antisymmetric function.

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