Typical set of arbitrary distributions

In general, the typical set, $\mathcal T_{p(x)}^{\epsilon}$, is intractable to compute for arbitrary continuous distributions. However, we can approximate the typical set, using a rectified flow that maps from a target data distribution to a Gaussian source distribution.

We back up this claim in two parts:

a derivation showing that;
- for linear transformations the image of the typical set equals the typical set of the image.
- for general flows they are not generally equal.
experimental evidence showing that;
- (WIP) the closer to flow is to being linear, the more accurate the typical set approximation.