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Spin Glasses, Learning, and Optimisation in High Dimension

Project description

From spin glasses to smarter AI

Why do some machine learning algorithms work so well, even when they shouldn’t? The answer might lie in spin glasses, strange magnetic materials first studied in the 1980s that puzzled physicists with their disordered, unpredictable behaviour. These systems, where particles ’spin‘ in conflict with one another, have since inspired insights into everything from brain networks to artificial intelligence. But many of their mysteries remain unsolved. Supported by the Marie Skłodowska-Curie Actions programme, the SLOHD project takes on one of the toughest: the phase transition in the mixed Sherrington–Kirkpatrick model. Using a novel dynamic approach, it also explores links to neural networks. By uniting physics and machine learning, SLOHD hopes to advance both theory and real-world AI.

Objective

"This project aims at tackling problems in statistical mechanics, with a primary focus on spin glasses, followed by an exploration of machine learning related questions. Spin glasses, initially studied in the 1980s using non-rigorous methods by theoretical physicists, revealed complex behaviours which were previously unknown: They conjectured that the phenomenon they depicted should be present in many more models such as neuronal networks. From a mathematical perspective, spin glasses are disordered systems where each ""spin"" can be seen as a random variable, interacting with others through a network of complex, often conflicting, interactions. Recent recognition in the field, with Giorgio Parisi winning the Nobel Prize in 2021 and Michel Talagrand receiving the Abel Prize in 2024, highlights the importance of spin glass studies. However, many questions remain unanswered, particularly regarding the mixed SherringtonKirkpatrick model: the phase transition between the high and the low-temperature regime is not known rigorously. One key objective of the fellowship is to explore this phase transition mainly through a dynamical approach by viewing the disorder in the Hamiltonian as different Brownian motions, with temperature playing the role of time. Beyond spin glasses, the project will also investigate neural networks (specifically, one-hidden-layer models with a large but finite number of neurons): the algorithms underlying their training are still not fully understood, and we aim to elucidate why, despite the non-convexity of their objective, do they converge to a desirable solution?
Although spin glasses and machine learning may seem unrelated at first glance, it is believed that many probabilistic techniques from spin glass theory can be applied to understanding machine learning algorithms, especially in high-dimensional settings. By bridging these two areas, the fellowship aims to deepen our theoretical understanding of both domains.


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Programme(s)

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Topic(s)

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HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships

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Call for proposal

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(opens in new window) HORIZON-MSCA-2024-PF-01

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Coordinator

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Net EU contribution

Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.

€ 242 260,56
Total cost

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