Local learning rules like Contrastive Hebbian Learning, XCAL, etc. are based on the idea of strengthening edges when the neurons they connect fire simultaneously. This causes frequent patterns in the input stream to be encoded in the layers.
I understand how this attracts similar input patterns into learned activation states. However, I fail to see how this memory can be used to predict the future input. How is it possible for neurons to predict future input streams under local learning rules?