# Towards an Understanding of Residual Networks Using Neural Tangent Hierarchy (NTH)

arXiv: https://arxiv.org/abs/2007.03714 · HTML: https://mlsanity.com/paper/2007.03714/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2020.

## Built on by (most cited first, 4 of 4)

- [Phase Diagram of Initial Condensation for Two-layer Neural Networks](https://mlsanity.com/paper/2303.06561/) (2023)
- [Neural Circuit Diagrams: Robust Diagrams for the Communication, Implementation, and Analysis of Deep Learning Architectures](https://mlsanity.com/paper/2402.05424/) (2024)
- [Learn Singularly Perturbed Solutions via Homotopy Dynamics](https://mlsanity.com/paper/2502.00488/) (2025)
- [There is a Singularity in the Loss Landscape](https://mlsanity.com/paper/2201.06964/) (2022)

## Abstract (arXiv)

Gradient descent yields zero training loss in polynomial time for deep neural networks despite non-convex nature of the objective function. The behavior of network in the infinite width limit trained by gradient descent can be described by the Neural Tangent Kernel (NTK) introduced in citeJacot2018Neural. In this paper, we study dynamics of the NTK for finite width Deep Residual Network (ResNet) using the neural tangent hierarchy (NTH) proposed in citeHuang2019Dynamics. For a ResNet with smooth and Lipschitz activation function, we reduce the requirement on the layer width m with respect to the number of training samples n from quartic to cubic. Our analysis suggests strongly that the particular skip-connection structure of ResNet is the main reason for its triumph over fully-connected network.