With locality sensitive hashing better to forget the h word.
You get thousands of little geometry sensors that 50:50 tell you on which side of a random hyperplane your input data is.
Despite being 50:50 each bit is quite informative.
Several bits together narrow down which geometric region the input is in.
If the inputs have regularities, bits can be codependent while still showing 50:50 on off behavior. That's kind of a subtle point but a gift from random projections - locality sensitive hashing.
Starting from there you can build LSH context dependent neural networks where parameter selection (information routing) is determined using LSH bits.
I've a bunch of notes of say preliminary draft quality.