Starts 15 Jun 2026
Ends 26 Jun 2026
Central European Time
Summer Graduate School on Mathematics for Machine Learning | (smr 4222)
ICTP
Budinich Lecture Hall (LB)
Adriatico Guest House Riva Massimiliano e Carlotta, Grignano I - 34151 Trieste (Italy)
The call for application is open. Please click on APPLY HERE on the left, in order to submit your application
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'.
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:
Andrea Montanari
Basil Saeed
"Rigorous approaches to modern machine learning"
Francesca Mignacco
Davide Ghio
"Statistical physics approach to high-dimensional learning problems"
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.
Participants: The school can be of interest for a very broad range of students basically from all areas of Pure and Applied Mathematics. Indeed, on one hand the topics of the school are specially addressed to those that are working in disciplines directly involved with Machine Learning (such as mathematical statistics, probability, information theory, numerical analysis, statistical mechanics); on the other hand, the lectures are developed starting from a limited requested background in these specific disciplines, so that students with good mathematical foundations in other areas could attend as well. Hence this school could provide the occasion for students with a different background to get into an exciting new area of research, either to find new connections at the theoretical level or to gain further skills which are on extremely high-demand at every level. The school may also be suitable for students who are not enrolled in a mathematical PhD but are working in related areas, such as statistics, computer science, engineering.
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
It is also recommended to read the Chapter 24 of the book Spin Glass Theory and Far Beyond, 2023, pp.477-497, Neural Networks: From the Perceptron to Deep Nets, also available on arXiv as
https://arxiv.org/pdf/2304.06636
https://arxiv.org/pdf/2304.06636
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.
Deadline for applicants in person requesting financial and/or visa support is 1 March 2026; deadline for other participation is 1 May 2026.
**DEADLINE: 01/05/2026**
Organizers
Claudio Arezzo (ICTP), Jean Barbier (ICTP), Filippo Bracci (Rome Tor Vergata and INdAM), Domenico Marinucci (Rome Tor Vergata and INdAM), Cristina Trombetti (Napoli Federico II and INdAM), Local Organiser: Jean Barbier (ICTP)
