Rigor with Machine Learning from Field Theory to the Poincar\'e Conjecture

arXiv:2402.13321v1 Announce Type: cross
Abstract: Machine learning techniques are increasingly powerful, leading to many breakthroughs in the natural sciences, but they are often stochastic, error-prone, and blackbox. How, then, should they be utilized in fields such as theoretical physics and pure mathematics that place a premium on rigor and understanding? In this Perspective we discuss techniques for obtaining rigor in the natural sciences with machine learning. Non-rigorous methods may lead to rigorous results via conjecture generation or verification by reinforcement …

abstract arxiv blackbox conjecture cs.lg error fields hep-th machine machine learning machine learning techniques mathematics natural physics stochastic theoretical physics theory type