# Universal Approximation of Markov Kernels by Shallow Stochastic Feedforward Networks

arXiv: https://arxiv.org/abs/1503.07211 · HTML: https://mlsanity.com/paper/1503.07211/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2015.

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

- [Quantitative Universal Approximation Bounds for Deep Belief Networks](https://mlsanity.com/paper/2208.09033/) (2022)

## Abstract (arXiv)

We establish upper bounds for the minimal number of hidden units for which a binary stochastic feedforward network with sigmoid activation probabilities and a single hidden layer is a universal approximator of Markov kernels. We show that each possible probabilistic assignment of the states of n output units, given the states of k≥1 input units, can be approximated arbitrarily well by a network with 2k-1(2n-1-1) hidden units.