摘要翻译：
全息约化表示(HRR)是基于卷积界的$N$-元组的叠加，但是$N$-元组不能被视为向量，因为它的形式依赖于基。这就是为什么HRR不能与几何结构联系在一起。用几何积代替卷积，就得到了类似于HRR但可以用几何解释的简化表示。在HRR及其几何类似物中发生的可变结合在数学上对应于$Z_2\×…\×Z_2$（二元$N$-元组的加法组，加法模为2）的两种不同表示。与标准HRR相反，通过几何积执行的变量绑定允许计算所有非零向量的精确逆，这一过程甚至比HRR中使用的近似逆更简单。新的简化表示的形式结构类似于卡通计算，一种量子计算的几何模拟。
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英文标题：
《Geometric Analogue of Holographic Reduced Representation》
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作者：
Diederik Aerts, Marek Czachor, Bart De Moor
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最新提交年份：
2007
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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一级分类：Physics        物理学
二级分类：Quantum Physics        量子物理学
分类描述：Description coming soon
描述即将到来
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英文摘要：
  Holographic reduced representations (HRR) are based on superpositions of convolution-bound $n$-tuples, but the $n$-tuples cannot be regarded as vectors since the formalism is basis dependent. This is why HRR cannot be associated with geometric structures. Replacing convolutions by geometric products one arrives at reduced representations analogous to HRR but interpretable in terms of geometry. Variable bindings occurring in both HRR and its geometric analogue mathematically correspond to two different representations of $Z_2\times...\times Z_2$ (the additive group of binary $n$-tuples with addition modulo 2). As opposed to standard HRR, variable binding performed by means of geometric product allows for computing exact inverses of all nonzero vectors, a procedure even simpler than approximate inverses employed in HRR. The formal structure of the new reduced representation is analogous to cartoon computation, a geometric analogue of quantum computation.
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PDF链接：
https://arxiv.org/pdf/0710.2611