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Workshop: Machine Learning and the Physical Sciences

Renormalization in the neural network-quantum field theory correspondence

Harold Erbin · Vincent Lahoche · Dine Ousmane Samary


A statistical ensemble of neural networks can be described in terms of a quantum field theory (NN-QFT correspondence). The infinite-width limit is mapped to a free field theory, while finite N corrections are mapped to interactions. After reviewing the correspondence, we will describe how to implement renormalization in this context and discuss preliminary numerical results for translation-invariant kernels. A major outcome is that changing the standard deviation of the neural network weight distribution corresponds to a renormalization flow in the space of networks.

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