Renormalization in the neural network-quantum field theory correspondence
This work provides a theoretical framework for understanding neural network ensembles through quantum field theory, which is incremental in applying renormalization concepts to machine learning.
The paper tackles the problem of describing statistical ensembles of neural networks using quantum field theory, showing that changing the weight distribution's standard deviation corresponds to renormalization flow in network space, with preliminary numerical results for translation-invariant kernels.
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.