I was just about to ask why not use a sphere? since it could be thought of as a nn, it will be into NN someday. guess the splitting and merge can be compared with dropout then.
I'm no expert, but my immediate thoughts are that evaluating a gaussian blob is very simple, it's just an exponential of a distance. The edge of a sphere makes it more complicated to compute, hence slower.
For backpropagation, the differentials of a gaussian is smooth while it's not for a sphere, again because of the edge.
Now, if you want to use a sphere you probably will do something like using an opacity falloff similar to ReLU[1], making it transparent at the edge.
This should make smooth enough as such I guess, but I imagine you still have the more complicated rendering. Though I may be mistaken.
For backpropagation, the differentials of a gaussian is smooth while it's not for a sphere, again because of the edge.
Now, if you want to use a sphere you probably will do something like using an opacity falloff similar to ReLU[1], making it transparent at the edge.
This should make smooth enough as such I guess, but I imagine you still have the more complicated rendering. Though I may be mistaken.
[1]: https://en.wikipedia.org/wiki/Rectifier_(neural_networks)