  This paper presents a study of the effectiveness of Neural Network (NN)
techniques for deconvolution inverse problems relevant for applications in
Quantum Field Theory, but also in more general contexts. We consider NN's
asymptotic limits, corresponding to Gaussian Processes (GPs), where
non-linearities in the parameters of the NN can be neglected. Using these
resulting GPs, we address the deconvolution inverse problem in the case of a
quantum harmonic oscillator simulated through Monte Carlo techniques on a
lattice. In this simple toy model, the results of the inversion can be compared
with the known analytical solution. Our findings indicate that solving the
inverse problem with a NN yields less performing results than those obtained
using the GPs derived from NN's asymptotic limits. Furthermore, we observe the
trained NN's accuracy approaching that of GPs with increasing layer width.
Notably, one of these GPs defies interpretation as a probabilistic model,
offering a novel perspective compared to established methods in the literature.
Our results suggest the need for detailed studies of the training dynamics in
more realistic set-ups.
