# ÒÔÉ«ÁÐÎº×ÈÂüµÄÇàÄêÊýÑ§¼ÒRonen Eldan

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Ronen Eldan Receives 2022 Blavatnik Award for Young Scientists in Israel

Ronen Eldan Receives 2022 Blavatnik Award for Young Scientists in Israel - IAS News | Institute for Advanced Study

Ronen Eldan, current von Neumann Fellow in the School of Mathematics, has received a 2022 Blavatnik Award for his profound contributions to statistics, machine learning, and theoretical computer science.

Eldan is honored for his work solving conjectures in the mathematical theory of high-dimensional phenomena¡ªin addition to his research on high-dimensional probability, the connection between high-dimensional systems and stochastic calculus, the limitations of neural networks in machine learning, and decision-making in artificial intelligence. At the Institute, Eldan is exploring the phenomena that arise when the dimension of the system tends to infinity, manifested in mathematical domains such as probability, analysis, geometry, combinatorics, theoretical computer science, and machine learning.

The Blavatnik Awards for Young Scientists in Israel was established in 2017 as the honor expanded from the United States to include the scientific community of Israel and the United Kingdom. Past recipients have hailed from 48 countries across six continents, with prizes totaling $13.6 million. Previous Blavatnik Laureates include past Visitor in the School of Mathematics Guy Rothblum (2009¨C11) and past Visiting Professor June Huh (2014¨C20) who won in 2017£¨×¢£ºJune HuhÊÇICM2022 Fields½±µÃÖ÷£© Granted by the Blavatnik Family Foundation, the New York Academy of Sciences, and the Israel Academy of Sciences and Humanities, The Blavatnik Awards for Young Scientists in Israel comes with a$100,000 reward and an invitation to join the international community of Blavatnik Science Scholars and the annual Blavatnik Science Symposium.

The Laureates will be formally honored at a ceremony in Tel Aviv-Jaffa on June 8, 2022.

http://blavatnikawards.org/honorees/profile/ronen-eldan

Research Summary:

The work of Ronen Eldan, PhD, has led to breakthroughs in solving mathematical conjectures that have profound impacts on the fields of statistics, machine learning, and theoretical computer science. His research spans several fields of mathematics, with a focus on high dimensional probability. This subject area deals with the understanding of random systems in which the datasets have many variables or sources of randomness. It aims to find ways to tame the ¡°curse of dimensionality¡± which refers to the fact that the number of configutations of a system grows exponentially as the number of variables increases making it difficult to analyze or visualize high-dimensional systems.

One of Eldan¡¯s main research endeavors has been to establish connections between the theory of high dimensional phenomena and stochastic calculus, the theory that explains the motion of diffusing particles. These connections have led to an emerging methodology in the field, referred to as ¡°pathwise analysis¡±. Eldan first developed a new technique, now coined as ¡°Eldan¡¯s stochastic localization¡±, which can be used obtain insights regarding the behavior of high dimensional distributions. This technique has proved essential towards solving two central problems in the field of convex geometry that have remained unsolved since the 1980s. These two problems¡ªthe hyperplane conjecture by Jean Bourgain and the Kannan-Lov¨¢sz-Simonovits conjecture¡ªreveal some of the fundamental facts about the geometry of high dimensional convex sets. This progress not only opens the door to solve other questions in high dimensional probability, but also gives important insights in the theoretical foundation of machine learning and data science. By further developing the ¡°pathwise analysis¡± methodology, Eldan was able to solve two conjectures by prominent mathematician Michel Talagrand, and gain beneficial insights in several fields adjacent to high-dimensional probability such as the theory behind processing of noisy data in statistics, the analysis of Boolean functions¡ªa fundamental object in theoretical computer science ¡ªas well as for understanding the behavior of many interacting particles in mathematical physics.

On the applied side, Eldan has utilized the theory of high-dimensional phenomena in two main directions. One of them is to understand the limitations of neural networks in terms of its ability to express functions and fit data, and the role of a network¡¯s depth in those limitations. The other one is to provid the first optimal algorithm for the ¡°convex bandit optimization¡± problem, a central paradigm for decision-making under uncertainty which combines aspects from optimization and reinforcement learning.

https://blog.sciencenet.cn/blog-1687789-1353633.html

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