Rigor with machine learning from field theory to the Poincaré conjecture

• Published in: Nature reviews physics Vol. 6; no. 5; pp. 310 - 319
• Main Authors: Gukov, Sergei, Halverson, James, Ruehle, Fabian
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group 01.05.2024
• Subjects: Algebra; Algorithms; Approximation; Artificial intelligence; Automation; Errors; Field theory; Games; Geometry; Learning theory; Machine learning; Mathematics; Neural networks; Physics; Quantum field theory; String theory; Subject specialists; Theoretical physics; Topology

Despite their successes, machine learning techniques are often stochastic, error-prone and blackbox. How could they then be used in fields such as theoretical physics and pure mathematics for which error-free results and deep understanding are a must? In this Perspective, we discuss techniques for o...