# Is the range of inception score flexible or bounded based on number of classes?

Inception score is used to evaluate the generative models. It is a score given based on quality and diversity of images generated.

I have doubt about the range of inception score because of the reason that an article mentions about the possibility of range $$[0, \infty]$$ and still talks about upper bound in practical setting

The lowest score possible is zero. Mathematically the highest possible score is infinity, although in practice there will probably emerge a non-infinite ceiling. For a ceiling to the IS, imagine that our generators produce perfectly uniform marginal label distributions and a single label delta distribution for each image — then the score would be bounded by the number of labels.

Suppose I have 1000 classes/labels in my task, then is it possible to get an inception score of 2000? Or is it mandatory that the inception score must lie in $$[1, 1000]$$?

To be concise: Is bounding inception score to a particular range $$[1, \text{number of classes}]$$ optional or mandatory?