Physics

CHIARA CAMMAROTA

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

This 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. We will see how statistical physics influenced the devise and development of machine learning rules and allowed to make analysis and predictions for typical behaviors, beyond worst case scenario.

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

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]

Engel and C. Van den Broeck, Statistical Mechanics of Learning

Additional material, mainly research or review papers, will be suggested and made available during the module

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.

Attendance to the lectures is not mandatory but strongly recommended.

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.