The generator

The generator (counterfeiter)  is a function , where  is a noise vector in  and  is some data produced by the generator. Note that the dimensionality of the noise vector does not necessarily match the dimensionality of the data produced by the generator. When using GANs to produce images, for example, represents an image. We use ~ to differentiate between data that comes from the real distribution  ,and data that comes from the generators distribution, .