This is the part I'm referencing:

> The unneeded dimensions don't learn anything meaningful and therefore remain a standard, multivariate, Gaussian distribution. This serves as a signal that such dimensions can safely be removed without significantly impacting the model's performance.

How do you explicitly measure and use this "signal"? I don't think you'd get far by just measuring "farness away from Gaussian", as you'd almost certainly end up throwing away certain useful dimensions that may simply appear "Gaussian enough".

> I didn’t get your point of looking at the decoder weights to figure out whether they are contributing? Do you compare them to their randomly initiated values to infer this?

If the model reaches this "optimal state" where certain dimensions aren't contributing to the decoder output, then you should be able to detect this with some form of sensitivity analysis - i.e. changing the values in those dimensions shouldn't affect the decoder output, if those dimensions aren't being used.

This assumes that the model would correctly learn to ignore unnecessary latent dimensions, but I'm not confident it would actually accomplish that.