Renormalization in the neural network-quantum field theory correspondence

Harold Erbin (1) , Vincent Lahoche (1) , Dine Ousmane Samary (2)

1 DIASI (CEA, LIST) - Département Intelligence Ambiante et Systèmes Interactifs
2 ICMPA-UNESCO Chair

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.

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Harold Erbin, Vincent Lahoche, Dine Ousmane Samary. Renormalization in the neural network-quantum field theory correspondence. NeurIPS 2022 - Machine Learning and the Physical Sciences - the 36th conference on Neural Information Processing Systems, Dec 2022, New Orléans, United States. , 2022. ⟨cea-04082366⟩