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：继先前对图嵌入的分析之后，我们将部分结论推广并扩展至向量符号架构（VSA）和超维计算（HDC）的一般框架。重点探讨了叠加、正交性与张量积之间的数学关系。我们确立了张量积表征作为核心表征的地位，该表征具有一系列独特性质：它是最具普适性与表达力的表征形式，同时也是能够在无误差解绑与检测条件下实现最高压缩率的表征。