Semantic Information G Theory for Range Control with Tradeoff between Purposiveness and Efficiency

TL;DR

This paper introduces the semantic information G theory, a new framework based on Shannon-Lu theory, to optimize the tradeoff between purposiveness and efficiency in range control, with potential applications in deep learning and reinforcement learning.

Contribution

The paper proposes the semantic information G measure and the R(G) function, providing a general method to enhance information efficiency and optimize range control tradeoffs.

Findings

Parametric solution of R(G) improves range control optimization.

Examples demonstrate tradeoff management between semantic mutual information and efficiency.

R(G) function offers a theoretical basis for IMM methods.

Abstract

Recent advances in deep learning suggest that we need to maximize and minimize two different kinds of information simultaneously. The Information Max-Min (IMM) method has been used in deep learning, reinforcement learning, and maximum entropy control. Shannon's information rate-distortion function is the theoretical basis of Minimizing Mutual Information (MMI) and data compression, but it is not enough to solve the IMM problem. The author has proposed the semantic information G theory (i.e., Shannon-Lu theory), including the semantic information G measure and the information rate fidelity function R(G) (R is the MMI for the given G of semantic mutual information). The parameter solution of the R(G) function provides a general method to improve the information efficiency, G/R. This paper briefly introduces the semantic information G measure and the parametric solution of the R(G) function. Two examples reveal that the parametric solution can help us optimize range control with the tradeoff between purposiveness (i.e., semantic mutual information) and information efficiency. It seems that the R(G) function can serve as the theoretical basis of IMM methods, but we still need further research in combination with deep learning, reinforcement learning, and constraint control.