(Familiarity with SDRs , or space distributed representation will probably help for this question).
Problem explication :
Let's say that, at every milliseconds, a sensor measures the 3D coordinates [X,Y,Z] of an ever bouncing ball in a closed room.
At every timestep (1 millisecond), the sensor encodes all 3 coordinate [X,Y,Z] into a single binary SDR of size [1000], with 20 "ON bits".
Using only the resulting SDR of the current timestep, there is no way of knowing what were the initial 3 coordinates.
However, our SDRs are guaranteed to have "semantic" meaning :in other word, we can take for granted that similar SDRs from different timesteps had similar coordinates. If we stack these SDRs for a while, we arrive with an SDR vector.
The problem to solve is the following :
How, from analysing different "ON BIT" changes or variations in the vector's SDRs, can we get to know which "change / variation" belong to which coordinate ?
In other word, is there a math principle or algorithm that could we re-create 3 SDRs vectors:
One that would only have "ON bits" for X
One that would only have "ON bits" for Y
One that would only have "ON bits" for Z