In this paper, we perform a study on the effectiveness of Neural Network (NN) techniques for deconvolution inverse problems. We consider NN's asymptotic limits, corresponding to Gaussian Processes (GPs), where parameter non-linearities are lost. 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. A scenario with a known analytical solution. Our findings indicate that solving the deconvolution inverse problem with a fully connected 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. Additionally, the NNs, in their asymptotic limit, provide cost-effective analytical solutions.

翻译：本文研究了神经网络技术在解卷积反问题中的有效性。我们考虑神经网络的渐近极限，即对应高斯过程的情形，其中参数非线性特征消失。利用这些高斯过程，我们求解了通过蒙特卡洛格子点阵技术模拟的量子谐振子的解卷积反问题——这是一个具有已知解析解的场景。研究结果表明，采用全连接神经网络求解解卷积反问题的效果，不及通过神经网络渐近极限衍生的高斯过程所得结果。此外，我们观察到随着网络层宽增加，训练后的神经网络精度逐渐趋近于高斯过程。值得注意的是，其中一类高斯过程无法被解释为概率模型，这为既有文献方法提供了全新视角。同时，处于渐近极限的神经网络还能提供成本效益较优的解析解。