How are positions and counts of higher concepts encoded in sparse representations? I understand that levels in the sensorimotor hierarchy of the brain learn recurring features of their input streams. The results are activation patterns with single neurons firing for the existence of specific higher level patterns. Those sparse representations are passed upward to the next higher layer.

For example, there is a neuron firing whenever there is a face in the scene. On this higher level, neurons are not restricted to a small window of our field of view anymore. My question is how those high level sparse representations still retain information about positions and counts of objects.

One bad explanation would be that there are neurons representing counts in general. If "three" and "face" are both active, there are three faces in the scene. But this doesn't hold for two kinds of objects at the same time since it's not clear which count is for which object. And what if both have the same count.
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.