44. Taking p = q = 1, use feed forward to determine the value of o:

w_pr*A_p + w_qr*A_q = (2.5)*(1) + (1.2)*(1) = 3.7, so A_r = 1.

w_ps*A_p + w_qs*A_q = (-1.4)*(1) + (2.1)*(1) = 0.7, so A_s = 1.

w_ro*A_r + w_so*A_s = (-1.6)*(1) + (1.4)*(1) = -0.2, so A_o = 0.

This is the wrong answer, so use backpropagation to adjust the weights: first, compute the errors at neurons o, r, and s.

e_o = target value - computed value = 1 - 0 = 1

e_r = e_o*w_ro = (1)*(-1.6) = -1.6

e_s = e_o*w_so = (1)*(1.4) = 1.4

Now compute the new weights.

neww_ro = oldw_ro + e_o*A_r = -1.6 + (1)*(1) = -0.6

neww_so = oldw_so + e_o*A_s = 1.4 + (1)*(1) = 2.4

neww_pr = oldw_pr + e_r*A_p = 2.5 + (-1.6)*(1) = 0.9

neww_ps = oldw_ps + e_s*A_p = -1.4 + (1.4)*(1) = 0

neww_qr = oldw_qr + e_r*A_q = 1.2 + (-1.6)*(1) = -0.4

neww_qs = oldw_qs + e_s*A_q = 2.1 + (1.4)*(1) = 3.5

To see if this backpropagation has succeeded in adjusting the weights, compute the output o by feed forward:

neww_pr*A_p + neww_qr*A_q = (0.9)*(1) + (-0.4)*(1) = 0.5, so A_r = 1.

neww_ps*A_p + neww_qs*A_q = (0)*(1) + (3.5)*(1) = 3.5, so A_s = 1.

neww_ro*A_r + neww_so*A_s = (-0.6)*(1) + (2.4)*(1) = 1.8,, so A_o = 1.

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