# The Neural Tangent Link Between CNN Denoisers and Non-Local Filters

arXiv: https://arxiv.org/abs/2006.02379 · HTML: https://mlsanity.com/paper/2006.02379/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2020.

## Built on by (most cited first, 9 of 9)

- [Spectral Analysis of the Neural Tangent Kernel for Deep Residual Networks](https://mlsanity.com/paper/2104.03093/) (2021)
- [Simple, Fast, and Flexible Framework for Matrix Completion with Infinite Width Neural Networks](https://mlsanity.com/paper/2108.00131/) (2021)
- [On the Spectral Bias of Convolutional Neural Tangent and Gaussian Process Kernels](https://mlsanity.com/paper/2203.09255/) (2022)
- [Analysis of Deep Image Prior and Exploiting Self-Guidance for Image Reconstruction](https://mlsanity.com/paper/2402.04097/) (2024)
- [Unsupervised Shape Completion via Deep Prior in the Neural Tangent Kernel Perspective](https://mlsanity.com/paper/2104.09023/) (2021)
- [Self-Supervised Learning from Noisy and Incomplete Data](https://mlsanity.com/paper/2601.03244/) (2026)
- [RINS-T: Robust Implicit Neural Solvers for Time Series Linear Inverse Problems](https://mlsanity.com/paper/2510.17396/) (2025)
- [Fast Gradient Methods for Data-Consistent Local Super-Resolution of Medical Images](https://mlsanity.com/paper/2202.10875/) (2022)
- [Equivariant Test-Time Training with Operator Sketching for Imaging Inverse Problems](https://mlsanity.com/paper/2411.05771/) (2024)

## Abstract (arXiv)

Convolutional Neural Networks (CNNs) are now a well-established tool for solving computational imaging problems. Modern CNN-based algorithms obtain state-of-the-art performance in diverse image restoration problems. Furthermore, it has been recently shown that, despite being highly overparameterized, networks trained with a single corrupted image can still perform as well as fully trained networks. We introduce a formal link between such networks through their neural tangent kernel (NTK), and well-known non-local filtering techniques, such as non-local means or BM3D. The filtering function associated with a given network architecture can be obtained in closed form without need to train the network, being fully characterized by the random initialization of the network weights. While the NTK theory accurately predicts the filter associated with networks trained using standard gradient descent, our analysis shows that it falls short to explain the behaviour of networks trained using the popular Adam optimizer. The latter achieves a larger change of weights in hidden layers, adapting the non-local filtering function during training. We evaluate our findings via extensive image denoising experiments.