I think A = floor((N-O)/(S-O)) * C(N,O) / (O+1). Charles Griffiths
--- On Wed, 10/15/08, Ed Porter <[EMAIL PROTECTED]> wrote: > From: Ed Porter <[EMAIL PROTECTED]> > Subject: [agi] Who is smart enough to answer this question? > To: [email protected] > Date: Wednesday, October 15, 2008, 4:40 PM > 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. > > 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 ------------------------------------------- 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
