XPost: comp.ai.genetic, comp.ai.neural-nets   
   From: joe@burgershack.net   
      
   Mick wrote:   
   > Newbie question here:   
   >   
   >  Does anyone know which systems/topology would be best to   
   >  implement a "square root" function, either using   
   >  neural networks, genetic algorithms, etc   
   >   
   >  Idea here is 1 input (source value),   
   >   
   >  two outputs:   
   >  1. square root value   
   >  2. Indicator - when set high, calculation has finished.   
   >   
   >  Idea here is that the training set will be a "simple" table   
   >  of inputs (original values) and outputs (square roots).   
   >  [with indicator output to say when calculation finished, or   
   >  1000 iterations, whichever comes first]   
   >   
   >  Id like to see which systems could automatically deduce   
   >  a newtonian solution (or other) to this problem.   
      
   When I see a prospective endeavor like this, I think I hear a Siren song   
   somewhere in the distance.  Since I've been lashed to the mast by my   
   experiences with traditional searched-based AI, I feel a sudden need to   
   sing along in disharmony.  (Geez.  Am I a geek, or what?)   
      
   1) Using a traditional implementation of an AI technique to *find* a   
   specific solution to an iterative math problem is not going to be   
   useful, except as an illustration of the limits of the technique you're   
   using.  If you use a proprietary third party software package to do   
   this, you will accomplish even less, except perhaps learning how to use   
   the tool.   
      
   2) Using a traditional implementation of an AI technique to *discover* a   
   general purpose method to solving iterative math problems like this is   
   not going to be practical.  It's been tried (AM, Eurisko, other   
   discovery systems, most of which are more than 20 years old now), and   
   the results were not encouraging.  They did not scale and they required   
   a great deal of contextual guidance to be at all useful (efficient).   
   And each system was a *boat load* of work to build.   
      
   In general, yes, you could use any kind of rule-generating technique to   
   deduce a symbolic system that will solve iterative math problems.  But   
   you're going to have to give it substantial guidance to finish building   
   the project in less than an epoch, which rather obviates the point of   
   the whole enterprise, IMHO.   
      
   I'm not as sure of the (de)value of using subsymbolic approaches, but   
   NNs are *not* the first method I would consider when you know that, for   
   the class of problem you're trying to solve, the use of iterative   
   reductive methods is inevitable.   
      
   Since you know that the type of problems that you're trying to solve   
   *is* amenable to Newtonian/Taylor series methods, I think that using AI   
   techniques to solve such problems, or even to discover that you can   
   solve them iteratively, will be misguided.  Unless you're just doing   
   something for school, of course.  Then it doesn't matter whether you're   
   wasting your time, as long as you're prepared to learn what *not* to do   
   with AI.   
      
   There.  I think I've shouted down the Sirens...   
      
        Randy   
      
   --   
   Randy Crawford   http://www.ruf.rice.edu/~rand   rand AT rice DOT edu   
      
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