Two different meanings of “multiplicative”
	• If we take two density models and multiply together their probability distributions at each point in data-space, we get a “product of experts”. – The product of  two Gaussian experts is a Gaussian. • If we take two variables and we multiply them together to provide input to a third variable we get a “multiplicative interaction”. – The distribution of the product of two Gaussian- distributed variables is NOT Gaussian distributed. It is a heavy-tailed distribution. One Gaussian determines the standard deviation of the other Gaussian. – Heavy-tailed distributions are the signatures of multiplicative interactions between latent variables.