Critique

Overall a good read! I was very uncertain whether it was too dense but it turned out to be quite an interesting read and it was easy to digest.

I like the motivation of the first paper but I feel like Sphere Geometry and von Mises-Fisher Distribution from the background section are better suited to being part of Paper 1.

• The Objective Function is a reiteration, need to make this clear, or just remove the background section.

• There should be references to other sections if it is going to be elaborated. such as "Rejection Sampling"

• I would love to see some results from the Hyperspherical VAES :)

In the second paper "Thus, the use of a S-VAE is proposed instead" seems out of place as S-VAE is already introduced from the reader's perspective.

• The Visualisation should be elaborated, snippets of their results would be really interesting here, as well as a short description of the images/evaluation metrics. Or else the claims seem a bit baseless.

• Batch Effect Correction, Batch Invariance, Clustering Cells, and Inferring Spatial Locations all could've used some tables/images if they were provided as the reader can easily get lost. Right now they just seem a bit irrelevant to the main contributions of the paper. There needs to be a logical sequence that ties these experiments together.

Other than that, I think this is a very interesting application of VAEs, but paper 2 needs some pictures and images or the readers who aren't familiar with the background can be lost (maybe this section is the one that needs a background section?).