From the String Landscape to the Mathematical Landscape: a Machine-Learning Outlook

Abstract

We review the recent programme of using machine-learning to explore the landscape of mathematical problems. With this paradigm as a model for human intuition -complementary to and in contrast with the more formalistic approach of automated theorem proving -we highlight some experiments on how AI helps with conjecture formulation, pattern recognition and computation.

Machine Learning Algebraic Geometry for Physics

“…Machine learning has seen a vast array of applications to algebraic geometry in physics, with first introduction to the string landscape in [1][2][3][4][5], and numerous current uses in finding suitable metrics on the landscape [6][7][8][9][10][11][12][13][14][15][15][16][17][18][19][20]. More generally, the question of machinelearning mathematics and using data scientific methods as well as artificial intelligence to help humans to do mathematics is very much in the air [21][22][23][24][25][26][27].…”

“…In the era of big data, the technique of machine learning therefore naturally enters this string landscape. For recent summaries and reviews, see [21,25,27,[36][37][38].…”

Metastable vacua from torsion and machine learning

“…These conditions were inferred after implementing a Machine Learning (ML) algorithm specifically designed to look for dS vacua. The use of ML algorithms and tools has been proven to be prolific (and in a more systematic way) to explore the vacua in string theory compactifications (see for instance [16][17][18][19][20][21][22][23][24][25]). For that, we implemented a hybrid algorithm to explore the minima of a scalar potential of the form 3…”