https://neckpinch.com/authors/sergei-gukov/New arXiv papers by Sergei Gukov, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2402.13321/arxiv:2402.13321Tue, 20 Feb 2024 00:00:00 GMTSergei Gukov, James Halverson, Fabian Ruehle — 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 learning. We survey applications of these techniques-for-rigor ranging from string theory to the smooth 4d Poincaré conjecture in low-dimensional topology. One can also imagine building direct bridges between machine learning theory and either mathematics or theoretical physics. As examples, we describe a new approach to field theory motivated by neural network theory, and a theory of Riemannian metric flows induced by neural network gradient descent, which encompasses Perelman's formulation of the Ricci flow that was utilized to resolve the 3d Poincaré conjecture.Ricci flowPoincaré conjecturePhysicsDiscrete & graph Ricci