The raw representations of porous organic cage molecules as g × g × g 3D porosity images lie in a very high-dimensional space (g 3 = 125, 000; flattening each image and viewing it as a vector). The main idea in this work is that the intrinsic cavities of porous cage molecules are not randomly distributed in this enormous space, but rather approximately lay in a much lower-dimensional subspace of R g 3 . As a revealing thought experiment, consider generating a random 3D porosity image by choosing each pixel as 0 or 1 randomly; it is extremely likely that this image will not resemble any known cage molecule. That is, the effective dimension of 3D porosity images is much lower than g 3 = 125, 000.