profound inherent theory. [5] It just can meet the needs of machine learning and describe the procedure of machine learning clearly. So Lie group machine learning is formed. This paper is based on the basic conceptions of machine learning and gives the generalization hypothesis axiom; the partition independence hypothesis axiom; the duality hypothesis axiom and the learning compatibility hypothesis axiom of Lie group machine learning. Index terms—Lie group; machine learning; Lie group machine leaning; hypothesis axiom