The Royal Society Milner Award Lecture 2023 given by Professor Stéphane Mallat.

The remarkable performances of deep neural network remains a mathematical mystery. How come similar network architectures can capture properties of data as different as languages, natural images or physical fields? Physics provides a rich framework to understand this mystery. This presentation bridges neural network and physics, by showing in what sense they rely on similar mathematical principles. It introduces models of deep neural networks and complex physical fields, by separating phenomena appearing at different scales. Interactions of structures across scales are learned with random weights and wavelets. These models are applied to image classification, as well as generation of fluid turbulence and cosmological fields.

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