论文标题
最佳的二次结合，用于矢量符号神经体系结构中的关系推理
Optimal quadratic binding for relational reasoning in vector symbolic neural architectures
论文作者
论文摘要
约束操作是许多认知过程的基础，例如认知图的形成，关系推理和语言理解。在这些过程中，两种不同的方式，例如位置和对象，事件及其上下文提示，单词及其角色，需要结合在一起，但对基本神经机制知之甚少。先前的作品基于结合对的二次函数引入了结合模型，然后是多对的向量求和。基于此框架，我们解决以下问题：哪些二次矩阵对于解码关系结构是最佳的？由此产生的准确性是什么？我们基于Octonion代数的矩阵表示，介绍了新的结合矩阵，该代数是复数的八维扩展。我们表明，当存在少量对时，这些矩阵比以前已知的方法更准确地解开。此外，结合算子的数值优化会收敛到该八元结合。我们还表明，当有大量绑定对时，随机二次结合会执行以及八元和先前所述的结合方法。因此，这项研究为大脑结合操作的潜在神经机制提供了新的见解。
Binding operation is fundamental to many cognitive processes, such as cognitive map formation, relational reasoning, and language comprehension. In these processes, two different modalities, such as location and objects, events and their contextual cues, and words and their roles, need to be bound together, but little is known about the underlying neural mechanisms. Previous works introduced a binding model based on quadratic functions of bound pairs, followed by vector summation of multiple pairs. Based on this framework, we address following questions: Which classes of quadratic matrices are optimal for decoding relational structures? And what is the resultant accuracy? We introduce a new class of binding matrices based on a matrix representation of octonion algebra, an eight-dimensional extension of complex numbers. We show that these matrices enable a more accurate unbinding than previously known methods when a small number of pairs are present. Moreover, numerical optimization of a binding operator converges to this octonion binding. We also show that when there are a large number of bound pairs, however, a random quadratic binding performs as well as the octonion and previously-proposed binding methods. This study thus provides new insight into potential neural mechanisms of binding operations in the brain.
