Statistical Physics and Machine Learning

Course objectives

GENERAL OBJECTIVES: The course is an advanced module aimed at guiding the students through a journey at the boundary between statistical physics and machine learning by introducing advanced concepts of equilibrium and out of equilibrium statistical mechanics and by illustrating their applications to learning models and development of artificial intelligence. SPECIFIC OBJECTIVES: A - Knowledge and understanding OF 1) To acquire the main methods of statistical mechanics, probability and information theory relevant to applications in machine learning and inference, such as the replica approach, message passing, mutual information, data compression, Bayesian approaches OF 2) To understand the different physical behaviour shown by inference and artificial learning procedures (curse of dimensionality, metastability, presence of multiple thermodynamic states) B - Application skills OF 3) To know how to apply an analytical technique to a given inference or learning setting to study its physical behavior C - Autonomy of judgment OF 4) Be able to recognize to which class of disordered systems a given inference or learning setting belongs D - Communication skills OF 5) Ability to learn from oral presentation of research results on topics similar to those introduced during the course OF 6) Ability to present the course topics orally in a non-technical language that allows understanding even by those who have not yet taken the course E - Ability to learn OF 7) To be able to read scientific texts and articles in order to independently investigate the topics introduced during the course

Channel 1
CHIARA CAMMAROTA Lecturers' profile

Program - Frequency - Exams

Course program
The first part of the module is devoted to introduction to Machine Learning, its termonology and examples of implementations, as well as to a recap of basic concepts of statistical physics [10 ore] The second part of the module is devoted to the illustration of methods of statistical physics of equilibrium and out of equilibrium for the study of simple models of learning [38 ore] The third part is devoted to the discussion of perspectives for the study of more complex models of learning [12 ore]
Prerequisites
a) It is fundamental to have basic knowledge of statistical physics and probability theory b) It is important to have basic knowledge on phase transition and critical phenomena c) It is useful to have some knowledge of physics of complex systems
Books
Engel and C. Van den Broeck, Statistical Mechanics of Learning
Teaching mode
Mainly frontal lectures, with the possible addition of training sessions and group works. The acquiring of knowledges, mainly allowed by frontal lectures, covers an important part of the education objectives of the module. Achieving independence in the application of analitical tools introduced and the exploration of the implications of learning processes will be favoured by training sessions and group works, which will also offer the occasion for the development of communication and collaborative skills.
Frequency
Attendance to the lectures is not mandatory but strongly recommended.
Exam mode
To pass the exam it is needed to obtain a mark higher or equal to 18/30: it is needed to show the acquisition of a sufficient knlwledge of the main topics discussed during lectures and to present them without logic inconsistencies or gaps. To gain a mark of 30/30 cum laude, the student must show having acquired an excellent knowledge of all topics discussed during lectures and to be able to discuss them in a logic, consistent and critical manner.
Bibliography
Additional material, mainly research or review papers, will be suggested and made available during the module
Lesson mode
Mainly frontal lectures, with the possible addition of training sessions to develop critical thinking skills. The acquiring of knowledges, mainly allowed by frontal lectures, covers an important part of the education objectives of the module. Achieving independence in the application of analitical tools introduced and the exploration of the implications of learning processes will be favoured by training sessions, which will also offer the occasion for the development of communication and collaborative skills.
  • Lesson code10599959
  • Academic year2025/2026
  • CoursePhysics
  • CurriculumCondensed matter physics: Theory and experiment (Percorso valido anche fini del conseguimento del titolo multiplo italo-francese-portoghese-canadese) - in lingua inglese
  • Year2nd year
  • Semester1st semester
  • SSDFIS/02
  • CFU6