The author explores the shift in modern machine learning towards handling non-Euclidean data, contrasting with the traditional focus on Euclidean geometry. Complex data structures like space-time curvature, brain neuron interactions, and physical system symmetries require a broader mathematical approach, similar to the 19th-century non-Euclidean geometry breakthroughs. The review offers a comprehensive overview of this evolving field, outlining challenges and opportunities for further development. A graphical taxonomy is proposed to unify recent advances, making the subject more accessible. This emerging research aims to adapt classical machine learning methods to unconventional data types, emphasizing geometry, topology, and algebraic considerations.
https://www.arxiv.org/abs/2407.09468