We introduce Residue Hyperdimensional Computing, a computing framework that unifies residue number systems with an algebra defined over random, high-dimensional vectors. We show how residue numbers can be represented as high-dimensional vectors in a manner that allows algebraic operations to be performed with component-wise, parallelizable operations on the vector elements. The resulting framework, when combined with an efficient method for factorizing high-dimensional vectors, can represent and operate on numerical values over a large dynamic range using vastly fewer resources than previous methods, and it exhibits impressive robustness to noise. We demonstrate the potential for this framework to solve computationally difficult problems in visual perception and combinatorial optimization, showing improvement over baseline methods. More broadly, the framework provides a possible account for the computational operations of grid cells in the brain, and it suggests new machine learning architectures for representing and manipulating numerical data.

提出了残差超维计算，这是一种将残差数系统与在随机高维向量上定义的代数结合的计算框架。展示了如何将残差数表示为高维向量，从而可以通过对向量元素进行分量并行操作来进行代数运算。结合高维向量分解的有效方法，该框架能够使用比之前方法更少的资源来表示和操作具有大动态范围的数值，并表现出良好的噪声鲁棒性。在视觉感知和组合优化问题中展示了该框架解决计算困难问题的潜力，并显示优于基准方法。除此之外，该框架提供了关于脑中网格细胞计算操作的可能解释，并提出了用于表示和操作数值数据的新的机器学习架构。

高维表示中的余数计算