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.

翻译：本文研究了神经网络技术在反卷积反问题中的有效性，该问题与量子场论中的实际应用相关，同时也适用于更广泛的领域。我们分析了神经网络的渐近极限，即对应的高斯过程，在此极限下神经网络参数的非线性效应可忽略不计。基于这些高斯过程，我们通过蒙特卡罗方法在格点上模拟量子谐振子，解决了其反卷积反问题。在该简化玩具模型中，反演结果可与已知解析解进行对比。研究发现，直接使用神经网络求解反问题的性能低于采用神经网络渐近极限导出的高斯过程。此外，观察到随着网络层宽度增加，训练后神经网络的精度逐渐趋近于高斯过程。值得注意的是，其中一个高斯过程无法被解释为概率模型，为文献中已有方法提供了全新视角。我们的结果表明，需要在更真实的场景中对训练动力学进行详细研究。