There exist neural network structures that can solve the image processing problems shown when weights are randomly applied. This means that for these problems

There exist neural network structures that can solve the image processing problems shown when weights are randomly applied. This means that for these problems the solution is encoded entirely in the network structure and not the weights. We could use linear regression as an analogy: y = b f(x). This is akin to saying that for some class of problems, it's the case that you can get as good of a solution from the function you pick alone (x^2, log(x)) as you could from picking a function and then computing the best coefficient. Note this isn't true for linear regression for any meaningful problems, but I feel like it's a decent analogy.