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​A two session lecture on Februarry 6, 2026 (10:00–10:50 and 11:10-12:00) at P3.10@Técnico and Online (password:m4ai) withPaulo Mourão

Paulo Mourão, Sapienza Università di Roma
The Statistical Mechanics of Associative Memories

The Hopfield Neural Network has played, ever since its introduction in 1982 by John Hopfield, a fundamental role in the inter-disciplinary study of storage and retrieval capabilities of neural networks, further highlighted by the recent 2024 Physics Nobel Prize.

From its strong link with biological pattern retrieval mechanisms to its high-capacity Dense Associative Memory variants and connections to generative models, the Hopfield Neural Network has found relevance both in Neuroscience, as well as the most modern of AI systems.

Much of our theoretical knowledge of these systems however, comes from a surprising and powerful link with Statistical Mechanics, first established and explored in seminal works of Amit, Gutfreund and Sompolinsky in the second half of the 1980s: the interpretation of associative memories as spin-glass systems.

In this talk, we will present this duality, as well as the mathematical techniques from spin-glass systems that allow us to accurately and rigorously predict the behavior of different types of associative memories, capable of undertaking various different tasks.

 

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Mathematics for Artificial Intelligence is a series of seminars and lectures aimed primarily at mathematicians willing to contribute to mathematical challenges in the area of Artificial Intelligence.