Following up on a previous analysis of graph embeddings, we generalize and expand some results to the general setting of vector symbolic architectures (VSA) and hyperdimensional computing (HDC). Importantly, we explore the mathematical relationship between superposition, orthogonality, and tensor product. We establish the tensor product representation as the central representation, with a suite of unique properties. These include it being the most general and expressive representation, as well as being the most compressed representation that has errorrless unbinding and detection.

翻译：在先前对图嵌入分析的基础上，我们将部分结果推广并扩展到向量符号架构与超维计算的一般设定中。重要的是，我们探究了叠加性、正交性与张量积之间的数学关系。我们将张量积表示确立为核心表示，并赋予其一套独特性质。这些性质包括：它是最具一般性和表达力的表示，同时也是可实现无误差解绑与检测的最紧凑表示。