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Re: Hi Ken. How do you feel about Analog Genetic Encoding (AGE)?

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  • JT
    Yes Ken. That s also what my question was referring, what advantage does it have. I can see AGE producing complex patterns via a intricate interaction map (or
    Message 1 of 7 , Feb 1, 2008
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      Yes Ken. That's also what my question was referring, what advantage
      does it have. I can see AGE producing complex patterns via a intricate
      interaction map (or matching scheme, are they just different terms for
      the same mechanism?) And I suppose you can evolve the interaction map
      too. But then how would that be any different than HyperNeat if you
      just consider a matching scheme as a general function with input and
      output. It seems to me HyperNeat take one more abstraction away and
      made it more focus on the end result with is patterns of organization.
      Or maybe I am just not understanding the essence of GRN and AGE?

      --- In neat@yahoogroups.com, "Kenneth Stanley" <kstanley@...> wrote:
      >
      > --- In neat@yahoogroups.com, "JT" <skybro77@> wrote:
      > >
      > > (This is my first post.)
      > >
      > > I recently came upon some literatures on Analog Genetic Encoding
      > > developed by Mattiussi and Floreano. It's interesting but certainly
      > > not revolutionary. After all it's just a simplified version of
      > > gene-regulation in real biological system. Some stats shows it is as
      > > robust as Neat. (Probably not tested against HyperNeat)
      > >
      > > Have you had any experience with it?
      > >
      >
      > I have no experience with Mattiussi's Analog Genetic Encoding aside
      > from reading about it myself.
      >
      > It is similar in a way to Joseph Reisinger's work with evolving a GRN-
      > based encoding with NEAT, as Joe mentions in his response to your
      > post.
      >
      > It is interesting as an abstraction of developmental encoding in
      > nature. In particular, it broadens our perspective on how such
      > abstractions can work and from which aspects of development they can
      > draw. The abstraction seems fairly high-level, i.e. it abstracts
      > away such details as chemical diffusion and growth from an embryo.
      > In that way, it has some similarities to HyperNEAT.
      >
      > The main question it brings to my mind is what exactly recommends
      > this particular abstraction over any other. Although the authors
      > note that it allows a large variety of genetic operations, aside from
      > that, it is unclear what the main principle is that supports the
      > approach, i.e. why we should prefer it to any other indirect
      > encoding.
      >
      > Of course, as a proponent of CPPNs and HyperNEAT, I think that one
      > important ingredient for a developmental encoding is the ability to
      > create patterns as a function of the domain geometry (as in the
      > substrate in HyperNEAT). AGE does not have such a capability. Its
      > interactions are detached from the geometry of the ultimate network
      > it encodes, which suggests to me that it may fare worse in domains
      > with a geometric basis, especially those with high
      > resolution/granularity.
      >
      > I also wonder why connection-centric parameters (such as weights)
      > should be derived through a matching scheme like sequence alignment
      > (which is one way AGE sets up its "device interaction map.") This
      > idea seems to be taken from biology simply for the sake of doing
      > something similarly to biology. Yet such matching schemes are ad hoc
      > because they do not relate to anything extrinsic to the genome.
      > HyperNEAT relates its connection weights to the outside world by
      > computing them as a function of the locations of nodes.
      >
      > As for comparisons with NEAT, I do believe that indirect encodings,
      > including AGE, should generally be superior to direct encodings in
      > tasks that involve moderate-sized patterns.
      >
      > ken
      >
    • Kenneth Stanley
      Yes, you make a good point. If you strip down the whole idea of an interaction map, all you really have left is a function that takes two nodes as input and
      Message 2 of 7 , Feb 1, 2008
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        Yes, you make a good point. If you strip down the whole idea of
        an "interaction map," all you really have left is a function that
        takes two nodes as input and outputs the parameters of the
        associated connection between them. In AGE, that function is based
        on a matching scheme. So the deeper question is, towards what kinds
        of patterns are matching schemes biased? It's all about bias when
        you're talking about indirect encoding. I do not see any argument
        that there is a beneficial bias for a matching scheme. The only
        thing the authors really say to recommend the matching scheme is
        that it allows a continuum of values. Yet so do many other types of
        functions.

        So yes, the crux of the issue is that any method for assigning
        values to compoments of a structure should ideally be based on some
        kind of principle that addresses how (i.e. in what kinds of
        patterns) we would like those values to relate to the underlying
        structure.

        Note that the AGE papers seem to imply that AGE could theoretically
        use methods other than matching schemes in the interaction map. But
        then, what other methods? It seems the most viable alternative
        assignment method is just to collapse into HyperNEAT. So the real
        core focus should be the matching scheme itself, i.e. not the gene
        alphabet and methods of recombination that AGE focuses on.

        ken

        --- In neat@yahoogroups.com, "JT" <skybro77@...> wrote:
        >
        > Yes Ken. That's also what my question was referring, what advantage
        > does it have. I can see AGE producing complex patterns via a
        intricate
        > interaction map (or matching scheme, are they just different terms
        for
        > the same mechanism?) And I suppose you can evolve the interaction
        map
        > too. But then how would that be any different than HyperNeat if you
        > just consider a matching scheme as a general function with input
        and
        > output. It seems to me HyperNeat take one more abstraction away and
        > made it more focus on the end result with is patterns of
        organization.
        > Or maybe I am just not understanding the essence of GRN and AGE?
        >
        > --- In neat@yahoogroups.com, "Kenneth Stanley" <kstanley@> wrote:
        > >
        > > --- In neat@yahoogroups.com, "JT" <skybro77@> wrote:
        > > >
        > > > (This is my first post.)
        > > >
        > > > I recently came upon some literatures on Analog Genetic
        Encoding
        > > > developed by Mattiussi and Floreano. It's interesting but
        certainly
        > > > not revolutionary. After all it's just a simplified version of
        > > > gene-regulation in real biological system. Some stats shows it
        is as
        > > > robust as Neat. (Probably not tested against HyperNeat)
        > > >
        > > > Have you had any experience with it?
        > > >
        > >
        > > I have no experience with Mattiussi's Analog Genetic Encoding
        aside
        > > from reading about it myself.
        > >
        > > It is similar in a way to Joseph Reisinger's work with evolving
        a GRN-
        > > based encoding with NEAT, as Joe mentions in his response to
        your
        > > post.
        > >
        > > It is interesting as an abstraction of developmental encoding
        in
        > > nature. In particular, it broadens our perspective on how such
        > > abstractions can work and from which aspects of development they
        can
        > > draw. The abstraction seems fairly high-level, i.e. it
        abstracts
        > > away such details as chemical diffusion and growth from an
        embryo.
        > > In that way, it has some similarities to HyperNEAT.
        > >
        > > The main question it brings to my mind is what exactly
        recommends
        > > this particular abstraction over any other. Although the
        authors
        > > note that it allows a large variety of genetic operations, aside
        from
        > > that, it is unclear what the main principle is that supports the
        > > approach, i.e. why we should prefer it to any other indirect
        > > encoding.
        > >
        > > Of course, as a proponent of CPPNs and HyperNEAT, I think that
        one
        > > important ingredient for a developmental encoding is the ability
        to
        > > create patterns as a function of the domain geometry (as in the
        > > substrate in HyperNEAT). AGE does not have such a capability.
        Its
        > > interactions are detached from the geometry of the ultimate
        network
        > > it encodes, which suggests to me that it may fare worse in
        domains
        > > with a geometric basis, especially those with high
        > > resolution/granularity.
        > >
        > > I also wonder why connection-centric parameters (such as
        weights)
        > > should be derived through a matching scheme like sequence
        alignment
        > > (which is one way AGE sets up its "device interaction map.")
        This
        > > idea seems to be taken from biology simply for the sake of doing
        > > something similarly to biology. Yet such matching schemes are
        ad hoc
        > > because they do not relate to anything extrinsic to the genome.
        > > HyperNEAT relates its connection weights to the outside world by
        > > computing them as a function of the locations of nodes.
        > >
        > > As for comparisons with NEAT, I do believe that indirect
        encodings,
        > > including AGE, should generally be superior to direct encodings
        in
        > > tasks that involve moderate-sized patterns.
        > >
        > > ken
        > >
        >
      • Jeff Clune
        Hello- I just read the AGE paper, thanks for posting it JT. Ken, I think you raise excellent issues in your analysis of their work. I agree that they do not do
        Message 3 of 7 , Feb 19, 2008
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          Hello-

          I just read the AGE paper, thanks for posting it JT.

          Ken, I think you raise excellent issues in your analysis of their work. I
          agree that they do not do a good job of motivating their choice of the
          function used in their interaction map (the local alignment of sequences).
          Partly because of that, I am inclined to think it unlikely that they
          stumbled onto a good one by accident. However, we do know that (at least in
          their 4 example problems) AGE seems to do well in comparison to GP and NEAT.
          Why is it that it does well?

          As you emphasize more in your first reply in this thread, it seems that the
          reason AGE does well is because it can take advantage of powerful genetic
          operators such as genome and gene duplication. I get the gist from their
          paper that they think this is the main advantage of AGE as well.

          It would be really interesting to see them experiment with AGE by
          systematically turning off some of these genetic operators and see how
          performance is affected. Has anyone here read the two other AGE works they
          cite (reference numbers 35 and 37 in the paper)? They might perform such
          experiments there.

          As far as comparing AGE to HyperNEAT, if it is the case that the genetic
          operators are what is driving AGE's success, how do you feel HyperNEAT
          allows (or substitutes) for such operators? I can think of HyperNEAT analogs
          to things like gene duplication, but I would be interested in hearing your
          take on it.


          Cheers,
          Jeff Clune

          Digital Evolution Lab, Michigan State University

          jclune@...
          517.214.1060




          > From: Kenneth Stanley <kstanley@...>
          > Reply-To: "neat@yahoogroups.com" <neat@yahoogroups.com>
          > Date: Fri, 01 Feb 2008 23:40:19 -0000
          > To: "neat@yahoogroups.com" <neat@yahoogroups.com>
          > Subject: [neat] Re: Hi Ken. How do you feel about Analog Genetic Encoding
          > (AGE)?
          >
          > Yes, you make a good point. If you strip down the whole idea of
          > an "interaction map," all you really have left is a function that
          > takes two nodes as input and outputs the parameters of the
          > associated connection between them. In AGE, that function is based
          > on a matching scheme. So the deeper question is, towards what kinds
          > of patterns are matching schemes biased? It's all about bias when
          > you're talking about indirect encoding. I do not see any argument
          > that there is a beneficial bias for a matching scheme. The only
          > thing the authors really say to recommend the matching scheme is
          > that it allows a continuum of values. Yet so do many other types of
          > functions.
          >
          > So yes, the crux of the issue is that any method for assigning
          > values to compoments of a structure should ideally be based on some
          > kind of principle that addresses how (i.e. in what kinds of
          > patterns) we would like those values to relate to the underlying
          > structure.
          >
          > Note that the AGE papers seem to imply that AGE could theoretically
          > use methods other than matching schemes in the interaction map. But
          > then, what other methods? It seems the most viable alternative
          > assignment method is just to collapse into HyperNEAT. So the real
          > core focus should be the matching scheme itself, i.e. not the gene
          > alphabet and methods of recombination that AGE focuses on.
          >
          > ken
          >
          > --- In neat@yahoogroups.com, "JT" <skybro77@...> wrote:
          >>
          >> Yes Ken. That's also what my question was referring, what advantage
          >> does it have. I can see AGE producing complex patterns via a
          > intricate
          >> interaction map (or matching scheme, are they just different terms
          > for
          >> the same mechanism?) And I suppose you can evolve the interaction
          > map
          >> too. But then how would that be any different than HyperNeat if you
          >> just consider a matching scheme as a general function with input
          > and
          >> output. It seems to me HyperNeat take one more abstraction away and
          >> made it more focus on the end result with is patterns of
          > organization.
          >> Or maybe I am just not understanding the essence of GRN and AGE?
          >>
          >> --- In neat@yahoogroups.com, "Kenneth Stanley" <kstanley@> wrote:
          >>>
          >>> --- In neat@yahoogroups.com, "JT" <skybro77@> wrote:
          >>>>
          >>>> (This is my first post.)
          >>>>
          >>>> I recently came upon some literatures on Analog Genetic
          > Encoding
          >>>> developed by Mattiussi and Floreano. It's interesting but
          > certainly
          >>>> not revolutionary. After all it's just a simplified version of
          >>>> gene-regulation in real biological system. Some stats shows it
          > is as
          >>>> robust as Neat. (Probably not tested against HyperNeat)
          >>>>
          >>>> Have you had any experience with it?
          >>>>
          >>>
          >>> I have no experience with Mattiussi's Analog Genetic Encoding
          > aside
          >>> from reading about it myself.
          >>>
          >>> It is similar in a way to Joseph Reisinger's work with evolving
          > a GRN-
          >>> based encoding with NEAT, as Joe mentions in his response to
          > your
          >>> post.
          >>>
          >>> It is interesting as an abstraction of developmental encoding
          > in
          >>> nature. In particular, it broadens our perspective on how such
          >>> abstractions can work and from which aspects of development they
          > can
          >>> draw. The abstraction seems fairly high-level, i.e. it
          > abstracts
          >>> away such details as chemical diffusion and growth from an
          > embryo.
          >>> In that way, it has some similarities to HyperNEAT.
          >>>
          >>> The main question it brings to my mind is what exactly
          > recommends
          >>> this particular abstraction over any other. Although the
          > authors
          >>> note that it allows a large variety of genetic operations, aside
          > from
          >>> that, it is unclear what the main principle is that supports the
          >>> approach, i.e. why we should prefer it to any other indirect
          >>> encoding.
          >>>
          >>> Of course, as a proponent of CPPNs and HyperNEAT, I think that
          > one
          >>> important ingredient for a developmental encoding is the ability
          > to
          >>> create patterns as a function of the domain geometry (as in the
          >>> substrate in HyperNEAT). AGE does not have such a capability.
          > Its
          >>> interactions are detached from the geometry of the ultimate
          > network
          >>> it encodes, which suggests to me that it may fare worse in
          > domains
          >>> with a geometric basis, especially those with high
          >>> resolution/granularity.
          >>>
          >>> I also wonder why connection-centric parameters (such as
          > weights)
          >>> should be derived through a matching scheme like sequence
          > alignment
          >>> (which is one way AGE sets up its "device interaction map.")
          > This
          >>> idea seems to be taken from biology simply for the sake of doing
          >>> something similarly to biology. Yet such matching schemes are
          > ad hoc
          >>> because they do not relate to anything extrinsic to the genome.
          >>> HyperNEAT relates its connection weights to the outside world by
          >>> computing them as a function of the locations of nodes.
          >>>
          >>> As for comparisons with NEAT, I do believe that indirect
          > encodings,
          >>> including AGE, should generally be superior to direct encodings
          > in
          >>> tasks that involve moderate-sized patterns.
          >>>
          >>> ken
          >>>
          >>
          >
          >
        • Kenneth Stanley
          Jeff, I am skeptical that the genetic operators are really that novel compared to any other indirect encoding. Note that the meaning of things like gene
          Message 4 of 7 , Feb 20, 2008
          • 0 Attachment
            Jeff,

            I am skeptical that the genetic operators are really that novel
            compared to any other indirect encoding. Note that the meaning of
            things like "gene duplication" or "whole genome duplication" is
            different for CPPNs because the genome in CPPNs is a network. The
            genome in DNA or something like AGE is implicitly a network as well,
            but because it is not explicitly encoded as a network, copying a
            gene actually has an indirect effect on the implicit network
            structure. In other words, duplicating a gene in a linear genome is
            similar to adding a new node to a CPPN that connects two nodes that
            were already connected, even though that new node is not really
            a "duplicate" in the usual sense. In any case, therefore there
            isn't much difference in the operator effects.

            I think AGE is doing better than GP and NEAT for a number of
            reasons. One big reason should be that it still has the advantage
            of being an indirect encoding, even if it could be improved. An
            indirect encoding should do better than NEAT in tasks that require
            discovering nontrivial patterns.

            Yet probably in reality it has to do mostly with the test domains.
            Pole balancing is starting to become a meaningless benchmark. The
            paper where they compare NEAT to AGE in pole balancing shows a
            performance level for AGE that is actually lower than the NEAT
            performance that I reported in my dissertation. However, they
            reported an older result for NEAT from 2002.

            Here is their paper making this comparison:

            http://infoscience.epfl.ch/record/87949/files/DuerrMattiussiFloreano2
            006_PPSNIX_NeuroAGE.pdf

            The point is not that NEAT is therefore better after all. I think
            the real point is that pole balancing is a bad benchmark because now
            that it is understood, it is easy to rig a method to be excellent at
            it. In particular, NEAT showed that it can be solved with zero
            hidden nodes! So you barely need any structure at all to solve it.
            So if you in effect reduce the probability of creating structure
            (through any means), you give yourelf a large advantage. At that
            point, small factors like weight mutation strength start to make a
            difference. Yet such minutia are not the point of such experiments,
            which shows that they are starting to lose their import. In a way,
            I think NEAT kind of broke the utility of the pole balancing
            benchmark by showing that pole balancing requires almost no
            structure to solve.

            More problematic for an indirect encoding like AGE is that it makes
            no sense to test it on pole balancing. Pole balancing networks have
            no regularity whatsoever and virtually no structure. So what could
            such a benchmark show us to be useful about an indirect encoding?
            If anything, one might argue an indirect encoding should be worse on
            such problems because indirect encodings should ideally be biased to
            searching for large-scale patterns. Anyway, it's hard to know what
            to conclude from a benchmark test on a task like that when the goal
            is to test the power of indirect encoding.

            It would be more intereting to see AGE tested on problems that
            require large networks such as those in our HyperNEAT papers.

            ken

            --- In neat@yahoogroups.com, Jeff Clune <jclune@...> wrote:
            >
            > Hello-
            >
            > I just read the AGE paper, thanks for posting it JT.
            >
            > Ken, I think you raise excellent issues in your analysis of their
            work. I
            > agree that they do not do a good job of motivating their choice of
            the
            > function used in their interaction map (the local alignment of
            sequences).
            > Partly because of that, I am inclined to think it unlikely that
            they
            > stumbled onto a good one by accident. However, we do know that (at
            least in
            > their 4 example problems) AGE seems to do well in comparison to GP
            and NEAT.
            > Why is it that it does well?
            >
            > As you emphasize more in your first reply in this thread, it seems
            that the
            > reason AGE does well is because it can take advantage of powerful
            genetic
            > operators such as genome and gene duplication. I get the gist from
            their
            > paper that they think this is the main advantage of AGE as well.
            >
            > It would be really interesting to see them experiment with AGE by
            > systematically turning off some of these genetic operators and see
            how
            > performance is affected. Has anyone here read the two other AGE
            works they
            > cite (reference numbers 35 and 37 in the paper)? They might
            perform such
            > experiments there.
            >
            > As far as comparing AGE to HyperNEAT, if it is the case that the
            genetic
            > operators are what is driving AGE's success, how do you feel
            HyperNEAT
            > allows (or substitutes) for such operators? I can think of
            HyperNEAT analogs
            > to things like gene duplication, but I would be interested in
            hearing your
            > take on it.
            >
            >
            > Cheers,
            > Jeff Clune
            >
            > Digital Evolution Lab, Michigan State University
            >
            > jclune@...
            > 517.214.1060
            >
            >
            >
            >
            > > From: Kenneth Stanley <kstanley@...>
            > > Reply-To: "neat@yahoogroups.com" <neat@yahoogroups.com>
            > > Date: Fri, 01 Feb 2008 23:40:19 -0000
            > > To: "neat@yahoogroups.com" <neat@yahoogroups.com>
            > > Subject: [neat] Re: Hi Ken. How do you feel about Analog Genetic
            Encoding
            > > (AGE)?
            > >
            > > Yes, you make a good point. If you strip down the whole idea of
            > > an "interaction map," all you really have left is a function that
            > > takes two nodes as input and outputs the parameters of the
            > > associated connection between them. In AGE, that function is
            based
            > > on a matching scheme. So the deeper question is, towards what
            kinds
            > > of patterns are matching schemes biased? It's all about bias when
            > > you're talking about indirect encoding. I do not see any
            argument
            > > that there is a beneficial bias for a matching scheme. The only
            > > thing the authors really say to recommend the matching scheme is
            > > that it allows a continuum of values. Yet so do many other
            types of
            > > functions.
            > >
            > > So yes, the crux of the issue is that any method for assigning
            > > values to compoments of a structure should ideally be based on
            some
            > > kind of principle that addresses how (i.e. in what kinds of
            > > patterns) we would like those values to relate to the underlying
            > > structure.
            > >
            > > Note that the AGE papers seem to imply that AGE could
            theoretically
            > > use methods other than matching schemes in the interaction map.
            But
            > > then, what other methods? It seems the most viable alternative
            > > assignment method is just to collapse into HyperNEAT. So the
            real
            > > core focus should be the matching scheme itself, i.e. not the
            gene
            > > alphabet and methods of recombination that AGE focuses on.
            > >
            > > ken
            > >
            > > --- In neat@yahoogroups.com, "JT" <skybro77@> wrote:
            > >>
            > >> Yes Ken. That's also what my question was referring, what
            advantage
            > >> does it have. I can see AGE producing complex patterns via a
            > > intricate
            > >> interaction map (or matching scheme, are they just different
            terms
            > > for
            > >> the same mechanism?) And I suppose you can evolve the
            interaction
            > > map
            > >> too. But then how would that be any different than HyperNeat if
            you
            > >> just consider a matching scheme as a general function with input
            > > and
            > >> output. It seems to me HyperNeat take one more abstraction away
            and
            > >> made it more focus on the end result with is patterns of
            > > organization.
            > >> Or maybe I am just not understanding the essence of GRN and AGE?
            > >>
            > >> --- In neat@yahoogroups.com, "Kenneth Stanley" <kstanley@>
            wrote:
            > >>>
            > >>> --- In neat@yahoogroups.com, "JT" <skybro77@> wrote:
            > >>>>
            > >>>> (This is my first post.)
            > >>>>
            > >>>> I recently came upon some literatures on Analog Genetic
            > > Encoding
            > >>>> developed by Mattiussi and Floreano. It's interesting but
            > > certainly
            > >>>> not revolutionary. After all it's just a simplified version of
            > >>>> gene-regulation in real biological system. Some stats shows it
            > > is as
            > >>>> robust as Neat. (Probably not tested against HyperNeat)
            > >>>>
            > >>>> Have you had any experience with it?
            > >>>>
            > >>>
            > >>> I have no experience with Mattiussi's Analog Genetic Encoding
            > > aside
            > >>> from reading about it myself.
            > >>>
            > >>> It is similar in a way to Joseph Reisinger's work with evolving
            > > a GRN-
            > >>> based encoding with NEAT, as Joe mentions in his response to
            > > your
            > >>> post.
            > >>>
            > >>> It is interesting as an abstraction of developmental encoding
            > > in
            > >>> nature. In particular, it broadens our perspective on how such
            > >>> abstractions can work and from which aspects of development
            they
            > > can
            > >>> draw. The abstraction seems fairly high-level, i.e. it
            > > abstracts
            > >>> away such details as chemical diffusion and growth from an
            > > embryo.
            > >>> In that way, it has some similarities to HyperNEAT.
            > >>>
            > >>> The main question it brings to my mind is what exactly
            > > recommends
            > >>> this particular abstraction over any other. Although the
            > > authors
            > >>> note that it allows a large variety of genetic operations,
            aside
            > > from
            > >>> that, it is unclear what the main principle is that supports
            the
            > >>> approach, i.e. why we should prefer it to any other indirect
            > >>> encoding.
            > >>>
            > >>> Of course, as a proponent of CPPNs and HyperNEAT, I think that
            > > one
            > >>> important ingredient for a developmental encoding is the
            ability
            > > to
            > >>> create patterns as a function of the domain geometry (as in the
            > >>> substrate in HyperNEAT). AGE does not have such a capability.
            > > Its
            > >>> interactions are detached from the geometry of the ultimate
            > > network
            > >>> it encodes, which suggests to me that it may fare worse in
            > > domains
            > >>> with a geometric basis, especially those with high
            > >>> resolution/granularity.
            > >>>
            > >>> I also wonder why connection-centric parameters (such as
            > > weights)
            > >>> should be derived through a matching scheme like sequence
            > > alignment
            > >>> (which is one way AGE sets up its "device interaction map.")
            > > This
            > >>> idea seems to be taken from biology simply for the sake of
            doing
            > >>> something similarly to biology. Yet such matching schemes are
            > > ad hoc
            > >>> because they do not relate to anything extrinsic to the genome.
            > >>> HyperNEAT relates its connection weights to the outside world
            by
            > >>> computing them as a function of the locations of nodes.
            > >>>
            > >>> As for comparisons with NEAT, I do believe that indirect
            > > encodings,
            > >>> including AGE, should generally be superior to direct encodings
            > > in
            > >>> tasks that involve moderate-sized patterns.
            > >>>
            > >>> ken
            > >>>
            > >>
            > >
            > >
            >
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