Recent neural networks demonstrated impressively accurate approximations of electronic ground-state wave functions. Such neural networks typically consist of a permutation-equivariant neural network followed by a permutation-antisymmetric operation to enforce the electronic exchange symmetry. While accurate, such neural networks are computationally expensive. In this work, we explore the flipped approach, where we first compute antisymmetric quantities based on the electronic coordinates and then apply sign equivariant neural networks to preserve the antisymmetry. While this approach promises acceleration thanks to the lower-dimensional representation, we demonstrate that it reduces to a Jastrow factor, a commonly used permutation-invariant multiplicative factor in the wave function. Our empirical results support this further, finding little to no improvements over baselines. We conclude with neither theoretical nor empirical advantages of sign equivariant functions for representing electronic wave functions within the evaluation of this work.

翻译：近期，神经网络在近似电子基态波函数方面展现了令人瞩目的精度。此类神经网络通常由置换等变神经网络与置换反对称操作组成，以强制实现电子交换对称性。尽管精度较高，但其计算成本高昂。在本工作中，我们探索了一种逆向方法：首先基于电子坐标计算反对称量，随后应用符号等变神经网络保持反对称性。虽然该方法因采用更低维的表示而有望提升计算速度，但我们证明了它实际上退化为了Jastrow因子——即波函数中常用的置换不变乘性因子。实验结果进一步佐证了这一点：相较于基线方法，该方法几乎没有带来改进。基于本研究的评估，我们得出结论：在表示电子波函数方面，符号等变函数既无理论优势，也无实证优势。