Machine learning and artificial intelligence now permeate nearly every aspect of contemporary life. Yet, despite their widespread impact, the theoretical understanding of why and when these methods work still lags behind practice—leaving important conceptual gaps that call for sustained effort from the research community.

This summer school offers an introduction to modern theoretical ideas developed to explain machine-learning algorithms and to clarify their domains of applicability. The emphasis will be on proof techniques and broadly useful mathematical tools. The lectures will be delivered by two internationally recognized experts. By the end of the school, participants should have an up-to-date view of the key conceptual and technical toolbox—drawing from statistics and statistical physics—needed to engage with current questions in the theory of machine learning.

Lecturers and topics:


Key words: Statistical Learning; Empirical risk minimization and empirical process theory; Interpolation; Kernel methods; Random features and neural tangent models; Random matrix theory; Feature learning; Sampling and generative methods.
Prerequisites: The school is addressed to a wide audience, but nevertheless some previous knowledge of mathematical statistics, probability and machine learning ideas is essential to benefit fully from the content of the course. Such background can be given for instance by classical books on statistical learning theory, i.e. Hastie, James, Tibshirani and Witten, An Introduction to Statistical Learning, 2023, first 3 chapters. Further material on machine learning, for instance the basic notions of excess risk, empirical risk minimization, Bayes estimators, together with regression problems, can be found in the first three chapters of the book "Learning Theory from First Principles", to be published soon by MIT Press and currently available online as

https://www.di.ens.fr/~fbach/ltfp_book.pdf
Poster abstracts: In the application form, all applicants are requested to submit a brief research abstract for a poster presentation. A limited number of abstracts will be selected for the poster session. Please use ICTP templates available for download here or below under 'Material'.

Grants: A limited number of grants are available to support the attendance of selected participants, with priority given to participants from developing countries. There is no registration fee.