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

arXiv: https://arxiv.org/abs/2411.05789 · HTML: https://mlsanity.com/paper/2411.05789/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 19 Oct 2024.

## Builds on (most cited first, 7 of 7)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)
- [A Max-Min Entropy Framework for Reinforcement Learning](https://mlsanity.com/paper/2106.10517/) (2021)
- [Semantic Information G Theory and Logical Bayesian Inference for Machine Learning](https://mlsanity.com/paper/1809.01577/) (2018)
- [Understanding and Accelerating EM Algorithm's Convergence by Fair Competition Principle and Rate-Verisimilitude Function](https://mlsanity.com/paper/2104.12592/) (2021)
- [Reviewing Evolution of Learning Functions and Semantic Information Measures for Understanding Deep Learning](https://mlsanity.com/paper/2305.14397/) (2023)

## Abstract (arXiv)

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.