# Neural Networks Asymptotic Behaviours for the Resolution of Inverse Problems

arXiv: https://arxiv.org/abs/2402.09338 · HTML: https://mlsanity.com/paper/2402.09338/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 14 Feb 2024.

## Builds on (most cited first, 14 of 14)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [Exponential expressivity in deep neural networks through transient chaos](https://mlsanity.com/paper/1606.05340/) (2016)
- [Deep Information Propagation](https://mlsanity.com/paper/1611.01232/) (2016)
- [Bayesian Deep Convolutional Networks with Many Channels are Gaussian Processes](https://mlsanity.com/paper/1810.05148/) (2018)
- [Mean Field Residual Networks: On the Edge of Chaos](https://mlsanity.com/paper/1712.08969/) (2017)
- [Applications of Machine Learning to Lattice Quantum Field Theory](https://mlsanity.com/paper/2202.05838/) (2022)
- [Machine learning spectral functions in lattice QCD](https://mlsanity.com/paper/2110.13521/) (2021)
- [Reconstructing spectral functions via automatic differentiation](https://mlsanity.com/paper/2111.14760/) (2021)
- [Exascale Deep Learning for Scientific Inverse Problems](https://mlsanity.com/paper/1909.11150/) (2019)
- [Automatic differentiation approach for reconstructing spectral functions with neural networks](https://mlsanity.com/paper/2112.06206/) (2021)
- [Neural network approach to reconstructing spectral functions and complex poles of confined particles](https://mlsanity.com/paper/2203.03293/) (2022)

## Abstract (arXiv)

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.