# Efficient Deep Learning of GMMs

arXiv: https://arxiv.org/abs/1902.05707 · HTML: https://mlsanity.com/paper/1902.05707/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2019.

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

- [Depth separation beyond radial functions](https://mlsanity.com/paper/2102.01621/) (2021)

## Abstract (arXiv)

We show that a collection of Gaussian mixture models (GMMs) in Rn can be optimally classified using O(n) neurons in a neural network with two hidden layers (deep neural network), whereas in contrast, a neural network with a single hidden layer (shallow neural network) would require at least O(exp(n)) neurons or possibly exponentially large coefficients. Given the universality of the Gaussian distribution in the feature spaces of data, e.g., in speech, image and text, our result sheds light on the observed efficiency of deep neural networks in practical classification problems.