Kymn Christopher J, Kleyko Denis, Frady E Paxon, Bybee Connor, Kanerva Pentti, Sommer Friedrich T, Olshausen Bruno A
Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA 94720, U.S.A.
Centre for Applied Autonomous Sensor Systems, Orebro University, Orebro SE-701 82, Sweden.
Neural Comput. 2024 Dec 12;37(1):1-37. doi: 10.1162/neco_a_01723.
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 resources that scale only logarithmically with the range, a vast improvement over previous methods. It also 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.
我们引入了余数超维计算，这是一种将余数系统与基于随机高维向量定义的代数相结合的计算框架。我们展示了余数如何能够以一种允许对向量元素进行逐分量、可并行化操作来执行代数运算的方式表示为高维向量。当与一种用于分解高维向量的有效方法相结合时，由此产生的框架能够使用仅随范围对数增长的资源来表示和处理大动态范围内的数值，这比以前的方法有了巨大改进。它对噪声也表现出令人印象深刻的鲁棒性。我们展示了这个框架在解决视觉感知和组合优化中计算困难问题方面的潜力，相较于基线方法有了改进。更广泛地说，该框架为大脑中网格细胞的计算操作提供了一种可能的解释，并且它为表示和处理数值数据提出了新的机器学习架构。
