14.04.2025
Encounters: věda, umělá inteligence a umění
Učená společnost České republiky, MFF UK a Interdisciplinární seminář Topologické studie prostoru pořádají mezioborové setkání: Tři mimořádné přednášky propojují matematiku, fyziku, umělou inteligenci i umění a nabízejí nový pohled na současný svět.
- středa 21. 5. ve 14.00
- MFF UK, Malostranské náměstí 25, Refektář
Program:
- 14.00 – Marc Mézard (Bocconi University, Milano): Mathematical Colloquium: Statistical Physics of Generative Diffusion
- 15.15 – Lenka Zdeborová (EPFL Lausanne): Towards Understanding of Scaling, Emergence and Transformers
- 16.15 – Přestávka na kávu
- 16.45 – Annie Cohen-Solal (Bocconi University in Milan): Kramář and Pablo Picasso: A Magical Encounter During the Darkest Times of Cubism in France
Marc Mézard otevře setkání Matematickým kolokviem Statistical Physics of Generative Diffusion. Pomocí metod statistické fyziky zkoumá principy generativní umělé inteligence – technologií schopných vytvářet nový text, obraz či kód. Lenka Zdeborová naváže přednáškou, v níž ukáže, jak statistická fyzika pomáhá porozumět hlubokému učení a jazykovým modelům. Annie Cohen-Solal setkání zakončí pohledem do světa umění v přednášce o Pablu Picassovi jako cizinci ve Francii a o jeho osudovém setkání s českým historikem umění Vincencem Kramářem.
Marc Mézard
Mathematical Colloquium: Statistical Physics of Generative Diffusion
Generative models, in which one trains an algorithm to generate fake samples ‘similar’ to those of a database, is a major new direction developed in machine learning in the recent years. In particular, generative models based on diffusion equations have become the state of the art for image generation. However, the reasons for this spectacular technological success are not well understood, and neither are its limitations.
While the theory of stochastic processes asserts that a perfect guidance of the diffusion should lead back to samples of the database, this “condensation” phenomenon is avoided in practice by the “imperfection” of the algorithms used in machine learning.
After an introduction to this topic, the talk will focus on the behavior of generative diffusion in the high-dimensional limit, where data are formed by a very large number of variables. Using methods from statistical physics, we explain the various dynamical regimes that occur during the generation and show how the condensation phenomenon is related to a glass phase transition.
Lenka Zdeborová
Towards Understanding of Scaling, Emergence, and Transformers
For over four decades, statistical physics has studied exactly solvable models of artificial neural networks. In this talk, we will explore how these models offer insights into deep learning and large language models. Specifically, we will examine a research strategy that trades distributional assumptions about data for precise control over learning behavior in high-dimensional settings.
We will discuss several types of phase transitions that emerge in this limit, particularly as a function of data quantity. In particular, we will highlight how discontinuous phase transitions are linked to algorithmic hardness, impacting the behavior of gradient-based learning algorithms.
Finally, we will cover recent progress in learning from sequences and advances in understanding generalization in modern architectures, including the role of dot-product attention layers in transformers.
Annie Cohen-Solal
Vincenc Kramář and Pablo Picasso: A Magical Encounter During the Darkest Times of Cubism in France
When 19-year-old Pablo Picasso arrived in Paris in 1900, he spoke no French and knew little of the country’s cultural codes. France, shaken by social unrest, was guarded by institutions that sought to protect national identity – through the “Police of Foreigners” and the conservative Académie des beaux-arts. Though critics praised Picasso’s first Paris exhibition in 1901, the police opened a file on him, labeling him an “anarchist under surveillance.” For over four decades, despite global fame, Picasso remained a marginalized foreigner in France.
In 1940, seeking French citizenship to avoid Franco’s regime, his application was rejected – marked by xenophobic prejudice. At a time when cubism was blamed for the “moral and aesthetic decline” of France, Picasso found a rare ally in Czech art historian and collector Vincenc Kramář. Director of Prague’s Picture Gallery and trained in the interdisciplinary Vienna School, Kramář recognized the brilliance of Picasso’s early, radical work – calling Head of a Woman “superb” while others called it “ugly”.
Picasso the Foreigner, based on new archival research, explores the artist’s life through the lens of immigration, nationalism, and identity. It traces his artistic and political evolution across wars and crises, highlighting not just his genius, but also his strategic response to a hostile world.
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