One can visulaize how embeddings transform using Alpha Complexes. https://www.preprints.org/manuscript/202505.0097/v1

As embeddings transfer through various layers, you can see what contribution each layer of transformer is making to classification. There are 3 types of holes that form 1-d, 2-d 3-d... each is telling the shape of data (embedding) as it traverses... It can help is reducing layers/reducing backprop. Some layers are more important than others...

You will see none of this using Vietoris Rips!