Here is a low computational cost way of doing random projections:https://drive.google.com/open?id=0BwsgMLjV0BnhOGNxOTVITHY1U28
You can then go and do <vector,vector> or <vector,scalar> single layer networks using that:
https://drive.google.com/open?id=0BwsgMLjV0BnhRFNoTTh3UEhwZlk
Or if you are willing to use evolution you can do deep networks with it. For example this algorithm works well:
https://pdfs.semanticscholar.org/c980/dc8942b4d058be301d463dc3177e8aab850e.pdf