How are positions and counts of higher concepts encoded in sparse representations?
Two ideas on this so far:


I think we have neurons representing multiple occurrences of a given feature, for example one neuron for "one face", one for "two faces", etc. At some number it doesn't really make a big difference anymore, so there is just a neuron for "group of faces". This would explain why we can recognize small number of objects in a glimpse but have to count for larger amount. Corrections and suggestions are welcome.
In his 2014 talk at MIT, Prof. Hinton explains how the brain might find equivariant features instead of invariant features. Basically, in addition to existence of a feature, neurons in the same cortical cell might output the properties of this feature. In vision, those properties would be position and rotation, for example.