On Wed, Oct 15, 2008 at 7:40 PM, Ed Porter <[EMAIL PROTECTED]> wrote:
> Is anybody on this list smart and/or knowledgeable enough to come up with a > formula for the following (I am not): > > Given N neural net nodes, what is the number A of unique node assemblies > (i.e., separate subsets of N) of size S that can have less than O > overlapping nodes, with the population of any other such node assembly > similarly selected from the N nodes to have the same size S and less than > the same O overlapping nodes with any other such node assembly. > > For example, if you have 1 billion nodes (N = 1G), how many cell assemblies > (A) of size 10,000 (S=10K) will have less than 5,000 nodes (0 = 5K) in > common with the population of any other node assembly. > > Its easy to figure out how many unique cell assemblies drawn from a > population of N nodes that can have a size S, but I haven't a clue, other > than by computational exploration to figure out how many will each have > less > than a given level of overlap with any other unique cell assemblies. Is the "other node assembly" B fixed? So you're asking how many assemblies of size S will have less than O nodes overlap with some specific node assembly B with size S? The way to do the calculation is as a sum. For each k between 0 and O, calculate the number of assemblies of size S that overlap with B in exactly k places. Then sum over k. To calculate the number of assemblies of size S that overlap with B in exactly k places, multiply -- the number of size=k subsets of B -- the number of size=(O-S) subsets of N-O I don't feel like doing the combinatorics, but that's how I'd do it ;-p The answer will be a very large number! ben > > > And for anyone who knows how to solve the above, if possible, could you > also > please also tell me, once you have close to A node assemblies selected that > have less than O overlap, how can you rapidly determine the population of a > new node assembly that has less than O overlap? > > > This is not just an meaningless math problem. > > A lot of people believe the human brain uses cell assemblies to represent > nodes in a representation of semantic knowledge. Such cell assemblies > create problems with current computer hardware because they tend to require > very high internal bandwidth, but in future architectures this problem may > not exist, and if the number of cell assemblies that can be created with a > sufficiently low cross-talk is large relative to the number of nodes, the > use of cell assemblies can allow for redundancy, high representational > capacity, and gradual degrading of memories over time to make room for more > memories. > > Actually any system using cell assemblies properly for semantic > representation is likely to include more sophistication than the above > model > by: > -(a) when determining the degree of allowable overlap, taking into account > not only the number of nodes that overlap the population of another node, > but also the strength of the interconnection between the nodes of the other > population it overlaps (i.e., basing overlap on the strength of the cross > talk); > -(b) being able to recruit new nodes for a cell assembly if cross talk with > other cell assemblies grows, and both cell assemblies have been found to > have enough importance to remain separately recollectable; and > -(c) the cell assemblies are likely to have not just relatively uniform > auto-associative properties within a given cell assembly, but also > auto-associative properties from elements of pattern represented by the > cell > assembly and/or from patterns in which the pattern represented by the cell > assembly is, itself, an element. > > But these additions represent levels of complication to be dealt with after > I get an idea how much simple representation capacity cell assemblies give > you with a given number of neural net nodes > > Anyway I would appreciate any thoughts on this topic. I would just like to > beable to get a rough idea to what extent the use of cell assemblies > increase or decrease the number of semantic nodes a set of neural net nodes > can represent. > > Ed Porter > > > > > > ------------------------------------------- > agi > Archives: https://www.listbox.com/member/archive/303/=now > RSS Feed: https://www.listbox.com/member/archive/rss/303/ > Modify Your Subscription: > https://www.listbox.com/member/?&; > Powered by Listbox: http://www.listbox.com > -- Ben Goertzel, PhD CEO, Novamente LLC and Biomind LLC Director of Research, SIAI [EMAIL PROTECTED] "Nothing will ever be attempted if all possible objections must be first overcome " - Dr Samuel Johnson ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
