# Towards Antisymmetric Neural Ansatz Separation

arXiv: https://arxiv.org/abs/2208.03264 · HTML: https://mlsanity.com/paper/2208.03264/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 32 references that are in the map.
- First posted on arXiv 5 Aug 2022.

## Builds on (most cited first, 14 of 14)

- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [A simple neural network module for relational reasoning](https://mlsanity.com/paper/1706.01427/) (2017)
- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [The Power of Depth for Feedforward Neural Networks](https://mlsanity.com/paper/1512.03965/) (2015)
- [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019)
- [On the Limitations of Representing Functions on Sets](https://mlsanity.com/paper/1901.09006/) (2019)
- [Universal Approximation of Functions on Sets](https://mlsanity.com/paper/2107.01959/) (2021)
- [Depth Separation for Neural Networks](https://mlsanity.com/paper/1702.08489/) (2017)
- [Optimization-Based Separations for Neural Networks](https://mlsanity.com/paper/2112.02393/) (2021)
- [On Representing (Anti)Symmetric Functions](https://mlsanity.com/paper/2007.15298/) (2020)
- [Exponential Separations in Symmetric Neural Networks](https://mlsanity.com/paper/2206.01266/) (2022)
- [Quantitative approximation results for complex-valued neural networks](https://mlsanity.com/paper/2102.13092/) (2021)

## Built on by (most cited first, 2 of 2)

- [Anti-symmetric Barron functions and their approximation with sums of determinants](https://mlsanity.com/paper/2303.12856/) (2023)
- [Uniform Ck Approximation of G-Invariant and Antisymmetric Functions, Embedding Dimensions, and Polynomial Representations](https://mlsanity.com/paper/2403.01339/) (2024)

## Abstract (arXiv)

We study separations between two fundamental models (or Ans"atze) of antisymmetric functions, that is, functions f of the form f(xσ(1), ldots, xσ(N)) = sign(σ)f(x1, ldots, xN), where σ is any permutation. These arise in the context of quantum chemistry, and are the basic modeling tool for wavefunctions of Fermionic systems. Specifically, we consider two popular antisymmetric Ans"atze: the Slater representation, which leverages the alternating structure of determinants, and the Jastrow ansatz, which augments Slater determinants with a product by an arbitrary symmetric function. We construct an antisymmetric function in N dimensions that can be efficiently expressed in Jastrow form, yet provably cannot be approximated by Slater determinants unless there are exponentially (in N2) many terms. This represents the first explicit quantitative separation between these two Ans"atze.