Establishing linkages between ML and Differential Geometry is intriguing (to say the least). But I have this nagging sense that "data manifolds" are too rigidly tied to numerical representations for this program to flourish. Differential geometry is all about invariance. Geometric objects have a life of their own so to speak, irrespective of any particular representation. In the broader data science world such an internal structure is not accessible in general. The systems modeled are too complex and their capture in data too superficial to be a reflection of the "true state". In a sense this is analogous to the "blind men touching a elephant in different parts and disagreeing about what it is". Show 1 reply