# Explicitly antisymmetrized neural network layers for variational Monte Carlo simulation arXiv: https://arxiv.org/abs/2112.03491 ยท HTML: https://mlsanity.com/paper/2112.03491/ ## Key facts - Cited by 14 papers in the map (data through 14 Oct 2026). - Builds on 13 of its 57 references that are in the map. - First posted on arXiv 7 Dec 2021. ## Builds on (most cited first, 13 of 13) - [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015) - [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014) - [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017) - [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015) - [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019) - [Universal Invariant and Equivariant Graph Neural Networks](https://mlsanity.com/paper/1905.04943/) (2019) - [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019) - [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019) - [Why does deep and cheap learning work so well?](https://mlsanity.com/paper/1608.08225/) (2016) - [The power of deeper networks for expressing natural functions](https://mlsanity.com/paper/1705.05502/) (2017) - [Universal approximations of permutation invariant/equivariant functions by deep neural networks](https://mlsanity.com/paper/1903.01939/) (2019) - [Phases of two-dimensional spinless lattice fermions with first-quantized deep neural-network quantum states](https://mlsanity.com/paper/2008.00118/) (2020) - [On Representing (Anti)Symmetric Functions](https://mlsanity.com/paper/2007.15298/) (2020) ## Built on by (most cited first, 14 of 14) - [A Self-Attention Ansatz for Ab-initio Quantum Chemistry](https://mlsanity.com/paper/2211.13672/) (2022) - [Gold-standard solutions to the Schr"odinger equation using deep learning: How much physics do we need?](https://mlsanity.com/paper/2205.09438/) (2022) - [A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions](https://mlsanity.com/paper/2401.10190/) (2024) - [Sampling-free Inference for Ab-Initio Potential Energy Surface Networks](https://mlsanity.com/paper/2205.14962/) (2022) - [An ab initio foundation model of wavefunctions that accurately describes chemical bond breaking](https://mlsanity.com/paper/2506.19960/) (2025) - [Neural Wave Functions for Superfluids](https://mlsanity.com/paper/2305.06989/) (2023) - [Improving Energy Natural Gradient Descent through Woodbury, Momentum, and Randomization](https://mlsanity.com/paper/2505.12149/) (2025) - [Neural Pfaffians: Solving Many Many-Electron Schr"odinger Equations](https://mlsanity.com/paper/2405.14762/) (2024) - [Forward Laplacian: A New Computational Framework for Neural Network-based Variational Monte Carlo](https://mlsanity.com/paper/2307.08214/) (2023) - [Highly Accurate Real-space Electron Densities with Neural Networks](https://mlsanity.com/paper/2409.01306/) (2024) - [Anti-symmetric Barron functions and their approximation with sums of determinants](https://mlsanity.com/paper/2303.12856/) (2023) - [Efficient anti-symmetrization of a neural network layer by taming the sign problem](https://mlsanity.com/paper/2205.12250/) (2022) - [A Score-Based Model for Learning Neural Wavefunctions](https://mlsanity.com/paper/2305.16540/) (2023) - [Is Variational Monte Carlo Robust? Sharp Moment Thresholds and Heavy-tailed Stochastic Optimization](https://mlsanity.com/paper/2606.26009/) (2026) ## Abstract (arXiv) The combination of neural networks and quantum Monte Carlo methods has arisen as a path forward for highly accurate electronic structure calculations. Previous proposals have combined equivariant neural network layers with an antisymmetric layer to satisfy the antisymmetry requirements of the electronic wavefunction. However, to date it is unclear if one can represent antisymmetric functions of physical interest, and it is difficult to measure the expressiveness of the antisymmetric layer. This work attempts to address this problem by introducing explicitly antisymmetrized universal neural network layers as a diagnostic tool. We first introduce a generic antisymmetric (GA) layer, which we use to replace the entire antisymmetric layer of the highly accurate ansatz known as the FermiNet. We demonstrate that the resulting FermiNet-GA architecture can yield effectively the exact ground state energy for small systems. We then consider a factorized antisymmetric (FA) layer which more directly generalizes the FermiNet by replacing products of determinants with products of antisymmetrized neural networks. Interestingly, the resulting FermiNet-FA architecture does not outperform the FermiNet. This suggests that the sum of products of antisymmetries is a key limiting aspect of the FermiNet architecture. To explore this further, we investigate a slight modification of the FermiNet called the full determinant mode, which replaces each product of determinants with a single combined determinant. The full single-determinant FermiNet closes a large part of the gap between the standard single-determinant FermiNet and FermiNet-GA. Surprisingly, on the nitrogen molecule at a dissociating bond length of 4.0 Bohr, the full single-determinant FermiNet can significantly outperform the standard 64-determinant FermiNet, yielding an energy within 0.4 kcal/mol of the best available computational benchmark.