Algebraic Expression of Subjective Spatial and Temporal Patterns

TL;DR

This paper extends the algebraic framework of subjective spatial patterns to include temporal patterns, providing a mathematical foundation for understanding how machines learn and represent complex data over space and time.

Contribution

It introduces an algebraic expression for subjective spatial and temporal patterns within the universal learning machine framework, advancing the mathematical modeling of machine learning processes.

Findings

Developed algebraic expressions for spatial and temporal patterns

Enhanced understanding of subjective pattern representation in machine learning

Provides a foundation for future mathematical analysis of learning processes

Abstract

Universal learning machine is a theory trying to study machine learning from mathematical point of view. The outside world is reflected inside an universal learning machine according to pattern of incoming data. This is subjective pattern of learning machine. In [2,4], we discussed subjective spatial pattern, and established a powerful tool -- X-form, which is an algebraic expression for subjective spatial pattern. However, as the initial stage of study, there we only discussed spatial pattern. Here, we will discuss spatial and temporal patterns, and algebraic expression for them.