Viability of perturbative expansion for quantum field theories on neurons
This work addresses the challenge of efficiently simulating quantum field theories using neural networks, which is incremental as it builds on prior proposals by analyzing finite-size effects and proposing improvements.
The paper tackled the problem of using neural networks with non-independent parameters to simulate quantum field theories for finite neuron numbers, finding that perturbative corrections are sensitive to ultraviolet cut-offs and converge weakly. It proposed a modified architecture to improve convergence and identified constraints for accurate results.
Neural Network (NN) architectures that break statistical independence of parameters have been proposed as a new approach for simulating local quantum field theories (QFTs). In the infinite neuron number limit, single-layer NNs can exactly reproduce QFT results. This paper examines the viability of this architecture for perturbative calculations of local QFTs for finite neuron number $N$ using scalar $φ^4$ theory in $d$ Euclidean dimensions as an example. We find that the renormalized $O(1/N)$ corrections to two- and four-point correlators yield perturbative series which are sensitive to the ultraviolet cut-off and therefore have a weak convergence. We propose a modification to the architecture to improve this convergence and discuss constraints on the parameters of the theory and the scaling of N which allow us to extract accurate field theory results.