In this work we prove a high dimensional analogue of the beloved Goldreich-Levin theorem (STOC 1989). We consider the following algorithmic problem: given oracle access to a function $f:\mathbb{Z}_q^m\rightarrow\mathbb{Z}_q^n$ such that ${\rm Prob}_{{\bf x}\sim\mathbb{Z}_q^m}\bigl[f({\bf x})={\bf Ax}\bigr]\geq\varepsilon$ for some ${\bf A}\in\mathbb{Z}_q^{n\times m}$ and $\varepsilon>0$, recover ${\bf A}$ (or a list of ... more >>>