How Semantic Information G Measure Relates to Distortion, Freshness, Purposiveness, and Efficiency

Abstract: To improve communication efficiency and provide more useful information, we need to measure semantic information by combining inaccuracy or distortion, freshness, purposiveness, and efficiency. The author proposed the semantic information G measure before. This measure is more compatible with Shannon information theory than other semantic or generalized information measures and has been applied to machine learning. This paper focuses on semantic predictive information (including observation information) and purposive (or goal-related) information (involving semantic communication and constraint control). The GPS pointer is used as an example to discuss the change of semantic predictive information with inaccuracy and time (age of the information). An example of constraint control (controlling probability distributions) is provided for measuring purposive information and maximizing this information and the information efficiency. The information rate fidelity function (a generalization of the information rate distortion function) is introduced for the optimization. Two computing examples demonstrate how to measure predictive and goal-related information and optimizing information efficiency. The results accord with theoretical conclusions well. The G measure is related to deep learning; its application to machine learning is worth exploring. Communication efficiency also involves utilities or information values; semantic communication optimization combining utilities needs further research.