Knight's Tour As a Neural Network I read this article about how Knight's Tours in Chess could be found with a neural network, so as a programming exercise I tried implementing it.  What I found, however, is that it diverges and fails to find a solution much more than it converges, and I can't see how what I've done is any different than what's shown.
As a simple example, imagine a 3x3 chess board.  There are 8 possible squares a knight could move to, and 8 neurons, each of which have exactly two neighbors.  All eight neurons are part of the final solution.  However, imagine that one neuron is generated initially with an output of 0, and two neighbors each with outputs of 1.  Even though all neurons should be part of the final solution and should eventually have an output of 1, this one has already reached a stable state by having two active neighbors, even though it is inactive.  As a result, the graph as a whole never reaches a stable state and diverges.  
Testing my current program over 10,000 trials on the easiest possible board (3x3), yields a convergence rate of only 8.3%.  An 8x8 board diverges 99.9925% over 40,000 trials.  Contrast that with the screenshot in the link showing divergence rates of only 3% for an 8x8 board.
What am I missing here?
EDIT: I discovered the problem.  The wikipedia summary (which I originally read first) was incorrect.  It says that every neuron should update its state each turn, but there's a short passage in the blog article that says only neurons which are active change their states.  Upon making that change, my failure rates have crashed down to just 13% for an 8x8 board.  Thanks for the help.
 A: The article you link to admits that the algorithm is not guaranteed to find a knight's tour:

However, there are many other solutions that would satisfy the network
  that are not knight's tours. For example, the network could discover
  two or more small independent circuits within the knight's graph. In
  addition, there are certain cases that will cause the network to
  diverge (never become stable)....
In fact, the probability of obtaining a knight's tour on an n x n
  board virtually vanishes as n grows larger. Takefuji, at the time of
  his publication, only obtained solutions for n <= 20. Parberry was
  able to obtain a single knight's tour out of 40,000 trials for n = 26.
  I obtained one knight's tour out of about 200,000 trials for n = 28
  (three days' worth of calculation on my Pentium IV). Parberry wisely
  asserts that attempting to find a knight's tour for n >= 30 using this
  method would be futile.

EDIT:  Others have tried to implement this algorithm.  One reports that he had to change the algorithm to get valid solutions.  See https://stackoverflow.com/questions/1551157/knights-tour-using-a-neural-network and http://www.yacoby.net/programming/knights-tour.html for one programmer's experience. 
