It is well known that if $G$ is a countable amenable group and the action of $G$ on $(Y, \nu)$ factors onto the action of $G$ on $(X, \mu)$, then the entropy of the first action must be greater than or equal to the entropy of the second action. In particular, if the action of $G$ on $(X, \mu)$ has infinite entropy then the action of $G$ on $(Y, \nu)$ does not admit any finite generating partition. In this talk, I will show that this completely fails for actions of non-amenable groups. Specifically, if $G$ is a countable non-amenable group then there exists a finite integer $n$ with the following property: for every pmp action of $G$ on $(X, \mu)$ there is a $G$-invariant probability measure $\nu$ on $n^G$ such that the action of $G$ on $(n^G, \nu)$ factors onto the action of $G$ on $(X, \mu)$. For many non-amenable groups, $n$ can be chosen to be 4 or smaller. We also obtain a similar result for continuous actions on compact metric spaces and continuous factor maps.