ANN architectures that perform faster/efficient prediction over time?
The machine learning term for this is dimensionality reduction (see here for a survey), which is used in a more general context than just neural networks. 

Dimensionality reduction can be both supervised and unsupervised. An example for unsupervised dim. reduction is PCA, in which a projection onto a lower-dimension space is found, in a way that preserves distances / structure as much as possible. In the case of supervised dimensionality reduction, the labels of the training set are also used in order to reduce the dimension. This is, however, a more advanced research area. This paper and references therein would be a good starting point.

Hope this helps.