CMSA New Technologies in Mathematics: Some exactly solvable models for machine learning via Statistical physics
Florent Krzakala - Univ. Pierre et Marie Curie
The increasing dimensionality of data in the modern machine learning age presents new challenges and opportunities. The high-dimensional settings allow one to use powerful asymptotic methods from probability theory and statistical physics to obtain precise characterizations and develop new algorithmic approaches. Statistical mechanics approaches, in particular, are very well suited for such problems. I will give examples of recent works in our group that build on powerful methods of statistical physics of disordered systems to analyze some relevant questions in machine learning and neural networks, including overparameterization, kernel methods, and the behavior gradient descent algorithm in a high dimensional non-convex landscape.