Antisymmetry

About: Antisymmetry is a research topic. Over the lifetime, 214 publications have been published within this topic receiving 7914 citations.

Antisymmetry and word order in double object constructions in Zarma

Abstract: Double Object Construction in Zarma sometimes allows alternations in the order of its internal arguments and the order in some cases may also be fixed. This tendency does not make predictions about a canonical order for the occurrence of Theme and Recipient objects within the VP simple. The same condition applies to monotransitive structures which vary between a complement-head and a head-complement order. It is the aim of this paper to present and analyse the most salient features of the kind of variations found in Zarma word order, particularly the ones associated with the verb that encodes three-participant events. The paper adopts the minimalist program proposed by Chomsky and is complemented with the Antisymmetry Hypothesis proposed by Kayne (1994). The study shows that the language has a uniform linear order where the recipient canonically precedes the theme on the basis of animacy factor. This is particularly common with the pronoun as the recipient in double object structures. Employing different diagnostics, the paper concludes that the recipient only follows the theme when the theme is associated with a more prominent discourse status. It is also argued that asymmetric C-command always occurs between the theme and the recipient. It implies that the language symmetry is altered by movement to designated positions for the purpose of feature checking.

Constant resistance networks generated from Möbius band

Abstract: The nonself-dual one-terminal-pair constant resistance networks can be obtained by dissection of Mobius band with both properties: two-fold rotational antisymmetry and mirror antisymmetry.

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

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.