It's a pre-trained network on image classification dataset from 2014 called ImageNet. The network is called VGG, paper is here: http://arxiv.org/abs/1409.1556

There's no additional training apart from that. The neural network is used to extract patterns (grain/texture/style) and a separate optimization tries to reproduce them as appropriate.

Interesting. If A is the input image, and B is the style image, then from which of those two images is the NN extracting patterns? And how is the other image used to get the desired effect?

Just trying to get a birds-eye view of the algorithm :)

Both images have their patterns extracted by the NN, and the optimization then tries to match the best patches from one image with the other, performing gradient descent to adjust the pixel values from a random start image.