makes sense, yep... i guess my intuition is that there are obviously a huge number of assemblies, so that the number of assemblies is not the hard part, the hard part lies in the weights...
On Tue, Oct 21, 2008 at 11:18 AM, Ed Porter <[EMAIL PROTECTED]> wrote: > Ben, > > > > In my email starting this thread on 10/15/08 7:41pm I pointed out that a > more sophisticated version of the algorithm would have to take connection > weights into account in determining cross talk, as you have suggested > below. But I asked for the answer to a more simple version of the problem, > since that might prove difficult enough, and since I was just trying to get > some rough feeling for whether or not node assemblies might offer > substantial gains in possible representational capability, before delving > more deeply into the subject. > > > > Ed Porter > > > > > > -----Original Message----- > *From:* Ben Goertzel [mailto:[EMAIL PROTECTED] > *Sent:* Monday, October 20, 2008 10:52 PM > *To:* [email protected] > *Subject:* Re: [agi] Who is smart enough to answer this question? > > > > > But, suppose you have two assemblies A and B, which have nA and nB neurons > respectively, and which overlap in O neurons... > > It seems that the system's capability to distinguish A from B is going to > depend on the specific **weight matrix** of the synapses inside the > assemblies A and B, not just on the numbers nA, nB and O. > > And this weight matrix depends on the statistical properties of the > memories being remembered. > > So, these counting arguments you're trying to do are only going to give you > a very crude indication, anyway, right? > > ben > > > On Mon, Oct 20, 2008 at 5:09 PM, Ed Porter <[EMAIL PROTECTED]> wrote: > > Ben, > > > > I am interested in exactly the case where individual nodes partake in > multiple attractors, > > > > I use the notation A(N,O,S) which is similar to the A(n,d,w) formula of > constant weight codes, except as Vlad says you would plug my varaiables into > the constant weight formula buy using A(N, 2*(S-0+1),S). > > > > I have asked my question assuming each node assembly has the same size S > for to make the math easier. Each such assembly is an autoassociative > attractor. I want to keep the overlap O low to reduce the cross talk > between attractors. So the question is how many node assemblies A, can you > make having a size S, and no more than an overlap O, given N nodes. > > > > Actually the cross talk between auto associative patterns becomes an even > bigger problem if there are many attractors being activated at once (such as > hundreds of them), but if the signaling driving different the population of > different attractors could have different timing or timing patterns, and if > the auto associatively was sensitive to such timing, this problem could be > greatly reduced. > > > > Ed Porter > > > > -----Original Message----- > *From:* Ben Goertzel [mailto:[EMAIL PROTECTED] > > *Sent:* Monday, October 20, 2008 4:16 PM > *To:* [email protected] > *Subject:* Re: [agi] Who is smart enough to answer this question? > > > > > Wait, now I'm confused. > > I think I misunderstood your question. > > Bounded-weight codes correspond to the case where the assemblies themselves > can have n or fewer neurons, rather than exactly n. > > Constant-weight codes correspond to assemblies with exactly n neurons. > > A complication btw is that an assembly can hold multiple memories in > multiple attractors. For instance using Storkey's palimpsest model a > completely connected assembly with n neurons can hold about .25n attractors, > where each attractor has around .5n neurons switched on. > > In a constant-weight code, I believe the numbers estimated tell you the > number of sets where the Hamming distance is greater than or equal to d. > The idea in coding is that the code strings denoting distinct messages > should not be closer to each other than d. > > But I'm not sure I'm following your notation exactly. > > ben g > > On Mon, Oct 20, 2008 at 3:19 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote: > > > > I also don't understand whether A(n,d,w) is the number of sets where the > hamming distance is exactly d (as it would seem from the text of > http://en.wikipedia.org/wiki/Constant-weight_code ), or whether it is the > number of set where the hamming distance is d or less. If the former case > is true then the lower bounds given in the tables would actually be lower > than the actual lower bounds for the question I asked, which would > correspond to all cases where the hamming distance is d or less. > > > > The case where the Hamming distance is d or less corresponds to a > bounded-weight code rather than a constant-weight code. > > I already forwarded you a link to a paper on bounded-weight codes, which > are also combinatorially intractable and have been studied only via > computational analysis. > > -- Ben G > > > > > > > -- > 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> > <https://www.listbox.com/member/archive/rss/303/>| > Modify<https://www.listbox.com/member/?&;>Your Subscription > > <http://www.listbox.com> > > > ------------------------------ > > *agi* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/>| > Modify<https://www.listbox.com/member/?&;>Your Subscription > > <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> > <https://www.listbox.com/member/archive/rss/303/>| > Modify<https://www.listbox.com/member/?&;>Your Subscription > > <http://www.listbox.com> > > > ------------------------------ > *agi* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <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
