What is meant by "function on the unit cube"?
From these slides (emphasis mine):
We proved that any continuous function on the unit cube can be uniformly approximated by a one layer network with an arbitrary continuous sigmoidal nonlinearity.
What does the author mean by "function on the unit cube"?
Solution 1:
Look at slide 8: $I_n=[0,1]^n$ is the n-dimensional unit cube.
Functions on the unit cube means functions with $I_n$ as its domain.
Solution 2:
The domain of the function is the unit cube, $[0,1]^n$.