Abstract

The paper presents the concept and basis for the apparatus of a new mathematical object—spots, which follows the concept of “mental images” in psychology and corresponds to the idea of vague geometric objects. Since mental images are semantic ones, spots appear to be an adequate mathematical object, promising for solving problems of artificial intelligence (AI), including the knowledge representation and modeling of the processes of human reasoning. A possible new architecture of constructing neural networks using the introduced elementary relations of spots, as well as application of vectors and matrices in which the elementary relations of spots play the role of numerical values, are considered. Variants of the implementation of a new mathematical model at the hardware level for creating neuromorphic systems based on new promising components of memristors and FeFETs, which have non-volatile memory, extremely low switching losses and faster read/write operations, are also proposed. The suggested concept seems to be important both in the theoretical aspect, as section of the Qualitative Mathematics, and for its application in many areas of AI.

中文翻译：

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人工智能问题的斑点概念和神经形态系统算法

摘要

本文介绍了一种新的数学对象-点的设备的概念和基础，该点遵循心理学中的“心理图像”概念，并且对应于模糊的几何对象。由于心理图像是语义图像，因此斑点似乎是适当的数学对象，有望解决人工智能（AI）问题，包括知识表示和人类推理过程的建模。考虑了使用引入的点的基本关系构建神经网络的可能的新架构，以及其中点的基本关系起着数值作用的向量和矩阵的应用。还提出了一种新的数学模型在硬件上实现的变体，用于基于忆阻器和FeFET的新的有希望的组件来创建神经形态系统，这些组件具有非易失性存储器，极低的开关损耗和更快的读/写操作。作为定性数学的一部分，建议的概念在理论方面似乎都很重要，对于在AI的许多领域中的应用也很重要。