If an auto-regressive network has been trained on predicting values when given input in an arbitrary order, there is a simple technique that can be used to improve the accuracy of a prediction. Given $n$ input vectors, there are $n!$ many ways to arrange those vectors in order to predict the next output. Let $n! \geq k$ and let $o^{(i)}$ be a unique input permutation for $i$ ranging from 1 to $k$. $p_{ensemble}(x) = \frac{1}{k}\sum_{i=1}^{k} p(x | o^{(i)})$