# On the Equivalence between Implicit and Explicit Neural Networks: A High-dimensional Viewpoint

arXiv: https://arxiv.org/abs/2308.16425 · HTML: https://mlsanity.com/paper/2308.16425/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 11 references that are in the map.
- First posted on arXiv 31 Aug 2023.

## Builds on (most cited first, 7 of 7)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Multiscale Deep Equilibrium Models](https://mlsanity.com/paper/2006.08656/) (2020)
- [Spectra of the Conjugate Kernel and Neural Tangent Kernel for linear-width neural networks](https://mlsanity.com/paper/2005.11879/) (2020)
- [Global Convergence of Over-parameterized Deep Equilibrium Models](https://mlsanity.com/paper/2205.13814/) (2022)
- [Random matrices in service of ML footprint: ternary random features with no performance loss](https://mlsanity.com/paper/2110.01899/) (2021)
- [Global Convergence Rate of Deep Equilibrium Models with General Activations](https://mlsanity.com/paper/2302.05797/) (2023)

## Abstract (arXiv)

Implicit neural networks have demonstrated remarkable success in various tasks. However, there is a lack of theoretical analysis of the connections and differences between implicit and explicit networks. In this paper, we study high-dimensional implicit neural networks and provide the high dimensional equivalents for the corresponding conjugate kernels and neural tangent kernels. Built upon this, we establish the equivalence between implicit and explicit networks in high dimensions.