Spots Concept for Problems of Artificial Intelligence and Algorithms of Neuromorphic Systems

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.