# Operator theory, kernels, and Feedforward Neural Networks

arXiv: https://arxiv.org/abs/2301.01327 · HTML: https://mlsanity.com/paper/2301.01327/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 53 references that are in the map.
- First posted on arXiv 3 Jan 2023.

## Builds on (most cited first, 10 of 10)

- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Tighter risk certificates for neural networks](https://mlsanity.com/paper/2007.12911/) (2020)
- [Error bounds for approximations with deep ReLU neural networks in Ws,p norms](https://mlsanity.com/paper/1902.07896/) (2019)
- [Approximation spaces of deep neural networks](https://mlsanity.com/paper/1905.01208/) (2019)
- [Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks](https://mlsanity.com/paper/2004.12131/) (2020)
- [Learning Deep ReLU Networks Is Fixed-Parameter Tractable](https://mlsanity.com/paper/2009.13512/) (2020)
- [Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation](https://mlsanity.com/paper/2107.04479/) (2021)
- [A proof of convergence for stochastic gradient descent in the training of artificial neural networks with ReLU activation for constant target functions](https://mlsanity.com/paper/2104.00277/) (2021)
- [Stochastic Feedforward Neural Networks: Universal Approximation](https://mlsanity.com/paper/1910.09763/) (2019)
- [Learning in Feedforward Neural Networks Accelerated by Transfer Entropy](https://mlsanity.com/paper/2104.14616/) (2021)

## Built on by (most cited first, 2 of 2)

- [Use of operator defect identities in multi-channel signal plus residual-analysis via iterated products and telescoping energy-residuals: Applications to kernels in machine learning](https://mlsanity.com/paper/2601.18080/) (2026)
- [The role of parameter Jacobians in the stability of network outputs](https://mlsanity.com/paper/2608.27748/) (2026)

## Abstract (arXiv)

In this paper we show how specific families of positive definite kernels serve as powerful tools in analyses of iteration algorithms for multiple layer feedforward Neural Network models. Our focus is on particular kernels that adapt well to learning algorithms for data-sets/features which display intrinsic self-similarities at feedforward iterations of scaling.