# Asymptotic properties of one-layer artificial neural networks with sparse connectivity

arXiv: https://arxiv.org/abs/2112.00732 · HTML: https://mlsanity.com/paper/2112.00732/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 19 references that are in the map.
- First posted on arXiv 1 Dec 2021.

## Builds on (most cited first, 6 of 6)

- [A Mean Field View of the Landscape of Two-Layers Neural Networks](https://mlsanity.com/paper/1804.06561/) (2018)
- [On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport](https://mlsanity.com/paper/1805.09545/) (2018)
- [Scalable Training of Artificial Neural Networks with Adaptive Sparse Connectivity inspired by Network Science](https://mlsanity.com/paper/1707.04780/) (2017)
- [Mean Field Analysis of Neural Networks: A Central Limit Theorem](https://mlsanity.com/paper/1808.09372/) (2018)
- [Pre-Defined Sparse Neural Networks with Hardware Acceleration](https://mlsanity.com/paper/1812.01164/) (2018)
- [Understanding brain networks and brain organization](https://mlsanity.com/paper/1403.7151/) (2014)

## Abstract (arXiv)

A law of large numbers for the empirical distribution of parameters of a one-layer artificial neural networks with sparse connectivity is derived for a simultaneously increasing number of both, neurons and training iterations of the stochastic gradient descent.