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/?member_id=8660244&id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
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