标题： 神经网络求解反问题的渐近行为 显示英文标题

标题： Neural Networks Asymptotic Behaviours for the Resolution of Inverse Problems

摘要： 本文研究了神经网络（NN）技术在量子场论相关反卷积逆问题中的有效性，同时也适用于更广泛的上下文。 我们考虑了神经网络的渐近极限，即对应的高斯过程（GP），在此情况下可以忽略神经网络参数中的非线性。 利用这些得到的高斯过程，我们解决了通过格点上的蒙特卡洛技术模拟的量子谐振子的反卷积逆问题。 在这个简单的玩具模型中，可以将反转的结果与已知的解析解进行比较。 我们的发现表明，使用神经网络解决逆问题的结果不如从神经网络渐近极限得出的高斯过程获得的结果表现好。 此外，我们观察到随着层数宽度增加，训练后的神经网络的准确性接近于高斯过程。 值得注意的是，其中一个高斯过程无法被解释为概率模型，这提供了与文献中现有方法不同的新颖视角。 我们的结果表明需要对更现实的设置中的训练动态进行详细研究。 显示英文摘要

摘要： 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.