Calculate Properties of random-uniform SDRs?

Science Tangential Theories
1

hi,

I’m trying to answer several questions about properties of randomly uniform generated SDR with sparsesness of “s”.
Let me know if I’m correct !

First question : given TWO SDRs of lengths “n” bits.

  • what is the probability that they don’t overlap at all ?
  • what is the probability that they match 100% ?
  • what is the probability that they overlap by “q” percent of “s” ?

Here is my thinking : the probability that bit at any position is 1 for both vectors is “s*s” i.e. s^2

From this it follows that the probability of full match is : (s^2)^(s*n)

Then the probability of partial match of q% is of s%*nbits is : (s^2)^(q*s*n)

For example if we have : n=100, s=0.02 , q=0.50
the probability of partial match is :

 -> (0.02^2)^(0.5*0.02*100)
 = 0.0004

from this it follows that : the probability of no overlap is : 1 - x => 0.9996

m’I correct ?

Next very important question how do I calculate those for “M” SDRs, not just TWO ?

Experimentally I’m getting max 8-9bits overlap when : n=2000, sparsity=0.02 and up 5000 random-samples full comparison i.e. 9/40= max 22.5% overlap

2

I think I should refer you to the existing literature on the subject. I do believe you will find answers to many of your questions in our SDR Research Papers, this one in particular.

3

they are not assuming randomly generated SDRs ! I think !

4

When I made this video I got the exact formulas for my code from those papers. I think what you are looking to define is something I called the “overlap set cardinality” in the video. Search the papers for cardinality.

1 Like
5

do you have the visualization you use in the videos running somewhere ?

6

Not running somewhere, but there is How to Run HTM School Visualizations and Building HTM Systems (both open source).

7

hmm… tried HTM several months ago, but it downgrades numpy and breaks other packages ;(

8

You don’t need NuPIC or HTM to run the client and see the SDR math visuals.