# Understanding How Over-Parametrization Leads to Acceleration: A case of learning a single teacher neuron

arXiv: https://arxiv.org/abs/2010.01637 · HTML: https://mlsanity.com/paper/2010.01637/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Oct 2020.

## Built on by (most cited first, 1 of 1)

- [Optimal Nonlinearities Improve Generalization Performance of Random Features](https://mlsanity.com/paper/2309.16846/) (2023)

## Abstract (arXiv)

Over-parametrization has become a popular technique in deep learning. It is observed that by over-parametrization, a larger neural network needs a fewer training iterations than a smaller one to achieve a certain level of performance -- namely, over-parametrization leads to acceleration in optimization. However, despite that over-parametrization is widely used nowadays, little theory is available to explain the acceleration due to over-parametrization. In this paper, we propose understanding it by studying a simple problem first. Specifically, we consider the setting that there is a single teacher neuron with quadratic activation, where over-parametrization is realized by having multiple student neurons learn the data generated from the teacher neuron. We provably show that over-parametrization helps the iterate generated by gradient descent to enter the neighborhood of a global optimal solution that achieves zero testing error faster. On the other hand, we also point out an issue regarding the necessity of over-parametrization and study how the scaling of the output neurons affects the convergence time.