Vector Symbolic Architectures combine a high-dimensional vector space with a set of carefully designed operators in order to perform symbolic computations with large numerical vectors. Major goals are the exploitation of their representational power and ability to deal with fuzziness and ambiguity. Over the past years, several VSA implementations have been proposed. The available implementations differ in the underlying vector space and the particular implementations of the VSA operators. This paper provides an overview of eleven available VSA implementations and discusses their commonalities and differences in the underlying vector space and operators. We create a taxonomy of available binding operations and show an important ramification for non self-inverse binding operations using an example from analogical reasoning. A main contribution is the experimental comparison of the available implementations in order to evaluate (1) the capacity of bundles, (2) the approximation quality of non-exact unbinding operations, (3) the influence of combining binding and bundling operations on the query answering performance, and (4) the performance on two example applications: visual place- and language-recognition. We expect this comparison and systematization to be relevant for development of VSAs, and to support the selection of an appropriate VSA for a particular task. The implementations are available.
翻译:矢量控制结构将高维矢量空间与一组精心设计的操作者结合起来,以便与大量矢量矢量进行象征性的计算。主要目标是利用它们的代表性力量和能力来处理模糊性和模糊性。在过去几年中,提出了若干VSA实施建议。在矢量控制空间和VSA操作者的具体实施方面,现有的实施方式各不相同。本文件概述了11项可用的VSA实施方式,并讨论了它们与矢量空间和操作者之间的共同点和差异。我们创建了现有约束性操作的分类,并以模拟推理为例,展示了非自我反约束操作的重要缩放。主要贡献是对现有实施过程的实验性比较,以便评估:(1)捆绑能力,(2)非外形无约束力操作的近似质量,(3)结合捆绑和捆绑操作对答性工作的影响,以及(4)两种实例应用的性能:视觉定位和语言识别。我们期望这种比较和系统化对于VSA的开发具有相关性,并支持为某项特定任务选择适当的VSA。