multimodal distributions with neural networks
Circle
The goal is to make a network that maps x to y where for every x there can be multiple y's, as in this case x,y forms a circle.
This is done by learning multiple normalized gaussian's and combining them into a joint probability distribution.
Sampling from this distribution will then give the model the ability to represent multiple values for one input.
bimodal distribution
Goal is to directly learn a bimodal distribution for a fixed input.
This is done by first predefining a fixed input, and then sampling target points around 5 and -5.