6.034 Artificial Intelligence - Recitations, fall 2004 online slides on learning

Next: The AND Function Previous: Example

Example

Learn AND of two inputs, x1 and x2.

Initially, let w1 = 0, w2 = 0, T = 0, eta = 1

If (x1w2 + x2w2) $>$ T then y=1 else y=0

   x1 x2 | y^d
   ------|----
    0  0 |  0
    0  1 |  0
    1  0 |  0
    1  1 |  1

x1      x2      w1^old  w2^old  T^old    y      y^d  |  w1^new  w2^new  T^new
-----------------------------------------------------|------------------------
 0       0       0       0       0       0       0   |    0       0      0
 0       1       0       0       0       0       0   |    0       0      0
 1       0       0       0       0       0       0   |    0       0      0
 1       1       0       0       0       0       1   |    1       1     -1
                                                     |
-----------------------------------------------------|------------------------
                                                     |
 0       0       1       1      -1       1       0   |    1       1      0
 0       1       1       1       0       1       0   |    1       0      1
 1       0       1       0       1       0       0   |    1       0      1
 1       1       1       0       1       0       1   |    2       1      0
                                                     |
-----------------------------------------------------|------------------------
                                                     |
 0       0       1       1       0       0       0   |    2       1      0
 0       1       1       1       0       1       0   |    2       0      1
 1       0       2       0       1       1       0   |    1       0      2
 1       1       1       0       2       0       1   |    2       1      1
                                                     |
-----------------------------------------------------|------------------------
                                                     |
 0       0       2       1       1       0       0   |    2       1      1
 0       1       2       1       1       0       0   |    2       1      1
 1       0       2       1       1       1       0   |    1       1      2
 1       1       1       0       2       0       1   |    2       2      1
                                                     |
-----------------------------------------------------|------------------------
                                                     |
 0       0       2       2       1       0       0   |    2       2      1
 0       1       2       2       1       1       0   |    2       1      2
 1       0       2       1       2       0       0   |    2       1      2
 1       1       2       1       2       1       1   |    2       1      2
                                                     |
-----------------------------------------------------|------------------------
                                                     |
 0       0       2       1       2       0       0   |    2       1      2
 0       1       2       1       2       0       0   |    2       1      2
 1       0       2       1       2       0       0   |    2       1      2
 1       1       2       1       2       1       1   |    2       1      2
                                                     |
-----------------------------------------------------|------------------------

CONVERGENCE!