MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint

Universal Approximation of Markov Kernels by Shallow Stochastic Feedforward Networks

Guido Montúfar


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 $k\geq1$ input units, can be approximated arbitrarily well by a network with $2^{k-1}(2^{n-1}-1)$ hidden units.

Mar 24, 2015
Mar 26, 2015
stochastic feedforward network, universal approximation, sufficiency bounds

Related publications

2015 Repository Open Access
Guido Montúfar

Universal approximation of Markov kernels by shallow stochastic feedforward networks