f(x) and NN

[Weimin Xiao <ranxiao@xxxxxxxxxxxx>]

Hi, there,

I would think P.J. Leonard's position = f(situation) function goes a little
bit too far. A simpler expression can be
    value = f(board)
which is what we know as an 'influence function'. Current influence
functions as oriented from Zoborist's diamond are simple minded. The effort
of using simple minded influence functions makes GO NP hard (such as min-max
search). The effort of reducing NP calculation at somewhat fraction yields
knowledge representation, pattern match, and all the AI and code twisting.

The point: we only need a good evaluation function. "Mathematical Go
Endgames", Benson's rule, etc. are not easy to use but have limited ability.
How to write the evaluation function? I would suggest the neural network is
a simple way to approach the function if we do not expect the mathematical
beauty.

Why existing NN approaches does not work well? My guess is people either
used
too few hidden nodes or too many layers. A three-layer BP NN without last
threshold should be fine to start the first level approximation. Since the
three-layer NN is actually a combined step function - each hidden node with
its threshold forms a step function, we would be able to
get the evaluation function by using enough nodes.

How many hidden nodes are needed? Roughly, one pattern one hidden node if
the
neural network has not been 'generalized' - if we guess it will be
generalized, then I do not know how few nodes will be used.

Any sign of possible success? Yes. I tested my NN using stock market data,
which is much smaller on problem space than GO, by using about 4000 weights
for one stock price (a stock has four prices: open, high, low, close). My
program said today's Microsoft's stock price (May 6, 1999) should be
    Open        High        Low         Close
    79.1875    80.125    76.6875   79
and actual the prices are
    Open        High        Low         Close
    80.6875    81.125    77.5        77.9375
My program also suggests that tomorrow (May 7, 1999), Microsoft's price will
be
    Open        High        Low         Close
    77.75       78.75       75.6875     77.9375
The program might guess that Bill is still selling his stocks. If the
program should wrong, I would suggest that the stock game is not so
determinate.

Weimin