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

Next: Update Function Previous: Next Layer

Example

If we use g(x) = x, g'(x) = 1, we let n = 1

                              ^
                              |
                              | y = 5        t = 10
                              |
                           +----------+
                           |          |
                           |  NODE 1  |
                           +----------+
                           ^     ^    ^
                          /      |     \
                        5/      2|      \5
                        /        |       \
                      +-+       +-+       +-+
                      |2|       |3|       |4|     (Output from these nodes is
                      +-+     > +-+ <     +-+      0, 0, 1)
                       ^     /   ^   \     ^
                       |    /    |    \    |
		       |1  /1    |1   0\   | 1
		       |  /      |      \  |
		       | /       |       \ |
		      +-+       +-+       +-+
		      |5|       |6|       |7|
		      +-+       +-+       +-+
		       ^         ^         ^
		       |         |         |
		       0         0         1

   delta_1 = (10 - 5) * 1 = 5

  w_21 = 5 + 1*0*5 = 5,  w_31 = 2 + 1*0*5 = 2,  w_41 = 5 + 1*1*5 = 5 + 5 = 10

  delta_2 = 1 * w_21 * delta_1 = 1 * 5 * 5 = 25
  delta_3 = 1 * w_31 * delta_1 = 1 * 2 * 5 = 10
  delta_4 = 1 * w_41 * delta_1 = 1 * 5 * 5 = 25

   Therefore

  w_52 = 1 + 1*0*25 = 1,   w_53 = 1 + 1*0*25 = 1
  w_63 = 1 + 1*0*10 = 1
  w_73 = 0 + 1*1*10 = 10,   w_74 = 1 + 1*1*25 = 26

Now for same values from input nodes (0, 0, and 1), output will be
10*2 + 26*5 = 150, which is a move in the right direction but too big a move.