mse o out e n y e n 2 mse o out 1 1 y 1 1 2 o out 2
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MSE = (O out e,n Y e,n ) 2 MSE = [ + (o - PowerPoint PPT Presentation

Dec 28, 2022 •43 likes •783 views

Feedforward Backpropagation Y [[ 1 0 0] MSE = 0.138 [[ 0 1 0] [[ 0 0 1]] O in O out O delta O error H out T [[ 0.62 0.38 0.64] [[ 0.49 -0.49 0.57] [[-0.38 0.38 0.64] [[-0.09 0.09 0.15] [[ 0.81 0.97 0.97] [[ 0.43 -0.45

  1. Feedforward Backpropagation Y [[ 1 0 0] MSE = 0.138 [[ 0 1 0] [[ 0 0 1]] O in O out O delta O error H out T [[ 0.62 0.38 0.64] [[ 0.49 -0.49 0.57] [[-0.38 0.38 0.64] [[-0.09 0.09 0.15] [[ 0.81 0.97 0.97] [[ 0.43 -0.45 0.55] [[ 0.61 0.39 0.63] [[ 0.61 -0.61 0.63] [[ 0.15 -0.15 0.15] [[ 0.81 0.71 0.62]] [[ 0.59 0.40 0.62]] [[ 0.37 -0.41 0.50]] [[ 0.14 0.10 -0.09]] [[ 0.59 0.40 -0.38]] W 2-update W 2 ∂MSE(W 2 ) : O error = O out – Y [[0.023 0.003 0.020] [[ 0.0 -0.1 0.2] ∂W 2 [[0.013 0.003 0.019]] [[ 0.6 -0.5 0.5]] O delta = O error O out ( 1 – O out ) ⊙ ⊙ H in H out 1 W 2-update = (H out O delta ) T N [[ 1.47 1.42] [[ 0.81 0.81] [[ 3.42 0.91] [[ 0.97 0.71] ∂MSE(W 1 ) : [[ 3.62 0.47]] [[ 0.97 0.62]] ∂W 1 W 1 [[ 0.7 0.4] [[-0.8 0.0] [[ 0.3 -0.4] [[ 0.1 0.1]] X [[ 4.9 3.0 1.4 0.2] x 1 x 2 x 3 x 4 [ 6.4 3.2 4.5 1.5] [ 5.8 2.7 5.1 1.9]] 1

  2. Feedforward Backpropagation Y [[ 1 0 0] ∂ O out ∂ O in ∂ H out ∂ H in MSE = 0.138 ∂ MSE ∂ MSE [[ 0 1 0] (W 1 ) = ∂ O out ∂ O in ∂ H out ∂ W 1 [[ 0 0 1]] ∂ H in ∂ W 1 O in O out O delta O error H out T [[ 0.62 0.38 0.64] [[ 0.49 -0.49 0.57] [[-0.38 0.38 0.64] [[-0.09 0.09 0.15] ∂ O out ∂ O in ∂ MSE ∂ MSE [[ 0.81 0.97 0.97] [[ 0.43 -0.45 0.55] [[ 0.61 0.39 0.63] (W 2 ) = [[ 0.61 -0.61 0.63] [[ 0.15 -0.15 0.15] ∂ O out ∂ O in ∂ W 2 [[ 0.81 0.71 0.62]] ∂ W 2 [[ 0.59 0.40 0.62]] [[ 0.37 -0.41 0.50]] [[ 0.14 0.10 -0.09]] [[ 0.59 0.40 -0.38]] W 2-update W 2 ∂MSE(W 2 ) : O error = O out – Y [[0.023 0.003 0.020] [[ 0.0 -0.1 0.2] ∂W 2 [[0.013 0.003 0.019]] [[ 0.6 -0.5 0.5]] O delta = O error O out ( 1 – O out ) ⊙ ⊙ H in H out 1 W 2-update = (H out O delta ) T N [[ 1.47 1.42] [[ 0.81 0.81] [[ 3.42 0.91] [[ 0.97 0.71] ∂MSE(W 1 ) : [[ 3.62 0.47]] [[ 0.97 0.62]] ∂W 1 W 1 [[ 0.7 0.4] [[-0.8 0.0] [[ 0.3 -0.4] [[ 0.1 0.1]] X [[ 4.9 3.0 1.4 0.2] x 1 x 2 x 3 x 4 [ 6.4 3.2 4.5 1.5] [ 5.8 2.7 5.1 1.9]] 2

  3. Feedforward Backpropagation Y [[ 1 0 0] ∂ O out ∂ O in ∂ H out ∂ H in MSE = 0.138 ∂ MSE ∂ MSE [[ 0 1 0] (W 1 ) = ∂ O out ∂ O in ∂ H out ∂ W 1 [[ 0 0 1]] ∂ H in ∂ W 1 O in O out O delta O error H out T [[ 0.62 0.38 0.64] [[ 0.49 -0.49 0.57] [[-0.38 0.38 0.64] [[-0.09 0.09 0.15] ∂ O out ∂ O in ∂ MSE ∂ MSE [[ 0.81 0.97 0.97] [[ 0.43 -0.45 0.55] [[ 0.61 0.39 0.63] (W 2 ) = [[ 0.61 -0.61 0.63] [[ 0.15 -0.15 0.15] ∂ O out ∂ O in ∂ W 2 [[ 0.81 0.71 0.62]] ∂ W 2 [[ 0.59 0.40 0.62]] [[ 0.37 -0.41 0.50]] [[ 0.14 0.10 -0.09]] [[ 0.59 0.40 -0.38]] W 2-update W 2 ∂MSE(W 2 ) : O error = O out – Y [[0.023 0.003 0.020] [[ 0.0 -0.1 0.2] ∂W 2 [[0.013 0.003 0.019]] [[ 0.6 -0.5 0.5]] O delta = O error ⊙ O out ( 1 – O out ) ⊙ H in H out 1 W 2-update = N (H out O delta ) T [[ 1.47 1.42] [[ 0.81 0.81] [[ 3.42 0.91] [[ 0.97 0.71] ∂MSE(W 1 ) : [[ 3.62 0.47]] [[ 0.97 0.62]] ∂W 1 W 1 [[ 0.7 0.4] [[-0.8 0.0] [[ 0.3 -0.4] [[ 0.1 0.1]] X [[ 4.9 3.0 1.4 0.2] x 1 x 2 x 3 x 4 [ 6.4 3.2 4.5 1.5] [ 5.8 2.7 5.1 1.9]] 3

  4. Feedforward Backpropagation Y [[ 1 0 0] ∂ O out ∂ O in ∂ H out ∂ H in MSE = 0.138 ∂ MSE ∂ MSE [[ 0 1 0] (W 1 ) = ∂ O out ∂ O in ∂ H out ∂ W 1 [[ 0 0 1]] ∂ H in ∂ W 1 O in O out O delta O error H out T [[ 0.62 0.38 0.64] [[ 0.49 -0.49 0.57] [[-0.38 0.38 0.64] [[-0.09 0.09 0.15] ∂ O out ∂ O in ∂ MSE ∂ MSE [[ 0.81 0.97 0.97] [[ 0.43 -0.45 0.55] [[ 0.61 0.39 0.63] (W 2 ) = [[ 0.61 -0.61 0.63] [[ 0.15 -0.15 0.15] ∂ O out ∂ O in ∂ W 2 [[ 0.81 0.71 0.62]] ∂ W 2 [[ 0.59 0.40 0.62]] [[ 0.37 -0.41 0.50]] [[ 0.14 0.10 -0.09]] [[ 0.59 0.40 -0.38]] W 2-update W 2 ∂MSE(W 2 ) : O error = O out – Y [[0.023 0.003 0.020] [[ 0.0 -0.1 0.2] ∂W 2 [[0.013 0.003 0.019]] [[ 0.6 -0.5 0.5]] O delta = O error ⊙ O out ( 1 – O out ) ⊙ H in H out 1 W 2-update = N (H out O delta ) T [[ 1.47 1.42] [[ 0.81 0.81] [[ 3.42 0.91] [[ 0.97 0.71] ∂MSE(W 1 ) : [[ 3.62 0.47]] [[ 0.97 0.62]] ∂W 1 W 1 [[ 0.7 0.4] [[-0.8 0.0] [[ 0.3 -0.4] [[ 0.1 0.1]] X [[ 4.9 3.0 1.4 0.2] x 1 x 2 x 3 x 4 [ 6.4 3.2 4.5 1.5] [ 5.8 2.7 5.1 1.9]] 4

  5. Feedforward Backpropagation Y [[ 1 0 0] ∂ O out ∂ O in ∂ H out ∂ H in MSE = 0.138 ∂ MSE ∂ MSE [[ 0 1 0] (W 1 ) = ∂ O out ∂ O in ∂ H out ∂ W 1 [[ 0 0 1]] ∂ H in ∂ W 1 O in O out O delta O error H out T [[ 0.62 0.38 0.64] [[ 0.49 -0.49 0.57] [[-0.38 0.38 0.64] [[-0.09 0.09 0.15] ∂ O out ∂ O in ∂ MSE ∂ MSE [[ 0.81 0.97 0.97] [[ 0.43 -0.45 0.55] [[ 0.61 0.39 0.63] (W 2 ) = [[ 0.61 -0.61 0.63] [[ 0.15 -0.15 0.15] ∂ O out ∂ O in ∂ W 2 [[ 0.81 0.71 0.62]] ∂ W 2 [[ 0.59 0.40 0.62]] [[ 0.37 -0.41 0.50]] [[ 0.14 0.10 -0.09]] [[ 0.59 0.40 -0.38]] W 2-update W 2 ∂MSE(W 2 ) : O error = O out – Y [[0.023 0.003 0.020] [[ 0.0 -0.1 0.2] ∂W 2 [[0.013 0.003 0.019]] [[ 0.6 -0.5 0.5]] O delta = O error ⊙ O out ( 1 – O out ) ⊙ H in H out 1 W 2-update = N (H out O delta ) T [[ 1.47 1.42] [[ 0.81 0.81] [[ 3.42 0.91] [[ 0.97 0.71] ∂MSE(W 1 ) : [[ 3.62 0.47]] [[ 0.97 0.62]] ∂W 1 W 1 [[ 0.7 0.4] [[-0.8 0.0] [[ 0.3 -0.4] [[ 0.1 0.1]] X [[ 4.9 3.0 1.4 0.2] x 1 x 2 x 3 x 4 [ 6.4 3.2 4.5 1.5] [ 5.8 2.7 5.1 1.9]] 5

  6. Feedforward Backpropagation Y [[ 1 0 0] ∂ O out ∂ O in ∂ H out ∂ H in MSE = 0.138 ∂ MSE ∂ MSE [[ 0 1 0] (W 1 ) = ∂ O out ∂ O in ∂ H out ∂ W 1 [[ 0 0 1]] ∂ H in ∂ W 1 O in O out O delta O error H out T [[ 0.62 0.38 0.64] [[ 0.49 -0.49 0.57] [[-0.38 0.38 0.64] [[-0.09 0.09 0.15] ∂ O out ∂ O in ∂ MSE ∂ MSE [[ 0.81 0.97 0.97] [[ 0.43 -0.45 0.55] [[ 0.61 0.39 0.63] (W 2 ) = [[ 0.61 -0.61 0.63] [[ 0.15 -0.15 0.15] ∂ O out ∂ O in ∂ W 2 [[ 0.81 0.71 0.62]] ∂ W 2 [[ 0.59 0.40 0.62]] [[ 0.37 -0.41 0.50]] [[ 0.14 0.10 -0.09]] [[ 0.59 0.40 -0.38]] W 2-update W 2 ∂MSE(W 2 ) : O error = O out – Y [[0.023 0.003 0.020] [[ 0.0 -0.1 0.2] ∂W 2 [[0.013 0.003 0.019]] [[ 0.6 -0.5 0.5]] O delta = O error ⊙ O out ( 1 – O out ) ⊙ H in H out 1 W 2-update = N (H out O delta ) T [[ 1.47 1.42] [[ 0.81 0.81] [[ 3.42 0.91] [[ 0.97 0.71] ∂MSE(W 1 ) : [[ 3.62 0.47]] [[ 0.97 0.62]] ∂W 1 W 1 [[ 0.7 0.4] [[-0.8 0.0] [[ 0.3 -0.4] [[ 0.1 0.1]] X [[ 4.9 3.0 1.4 0.2] x 1 x 2 x 3 x 4 [ 6.4 3.2 4.5 1.5] [ 5.8 2.7 5.1 1.9]] 6

  7. Feedforward Backpropagation Y [[ 1 0 0] ∂ O out ∂ O in ∂ H out ∂ H in MSE = 0.138 ∂ MSE ∂ MSE [[ 0 1 0] (W 1 ) = ∂ O out ∂ O in ∂ H out ∂ W 1 [[ 0 0 1]] ∂ H in ∂ W 1 O in O out O delta O error H out T [[ 0.62 0.38 0.64] [[ 0.49 -0.49 0.57] [[-0.38 0.38 0.64] [[-0.09 0.09 0.15] ∂ O out ∂ O in ∂ MSE ∂ MSE [[ 0.81 0.97 0.97] [[ 0.43 -0.45 0.55] [[ 0.61 0.39 0.63] (W 2 ) = [[ 0.61 -0.61 0.63] [[ 0.15 -0.15 0.15] ∂ O out ∂ O in ∂ W 2 [[ 0.81 0.71 0.62]] ∂ W 2 [[ 0.59 0.40 0.62]] [[ 0.37 -0.41 0.50]] [[ 0.14 0.10 -0.09]] [[ 0.59 0.40 -0.38]] W 2-update W 2 ∂MSE(W 2 ) : O error = O out – Y [[0.023 0.003 0.020] [[ 0.0 -0.1 0.2] ∂W 2 [[0.013 0.003 0.019]] [[ 0.6 -0.5 0.5]] O delta = O error ⊙ O out ( 1 – O out ) ⊙ H in H out 1 W 2-update = N (H out O delta ) T [[ 1.47 1.42] [[ 0.81 0.81] [[ 3.42 0.91] [[ 0.97 0.71] ∂MSE(W 1 ) : [[ 3.62 0.47]] [[ 0.97 0.62]] ∂W 1 W 1 [[ 0.7 0.4] [[-0.8 0.0] [[ 0.3 -0.4] [[ 0.1 0.1]] X [[ 4.9 3.0 1.4 0.2] x 1 x 2 x 3 x 4 [ 6.4 3.2 4.5 1.5] [ 5.8 2.7 5.1 1.9]] 7

  8. Feedforward Backpropagation Y [[ 1 0 0] ∂ O out ∂ O in ∂ H out ∂ H in MSE = 0.138 ∂ MSE ∂ MSE [[ 0 1 0] (W 1 ) = O out = sigmoid(O in ) ∂ O out ∂ O in ∂ H out ∂ W 1 [[ 0 0 1]] ∂ H in ∂ W 1 O in O out O delta O error O in = H out W 2 H out T [[ 0.62 0.38 0.64] [[ 0.49 -0.49 0.57] [[-0.38 0.38 0.64] [[-0.09 0.09 0.15] ∂ O out ∂ O in ∂ MSE ∂ MSE [[ 0.81 0.97 0.97] [[ 0.43 -0.45 0.55] [[ 0.61 0.39 0.63] (W 2 ) = H out = sigmoid(H in ) [[ 0.61 -0.61 0.63] [[ 0.15 -0.15 0.15] ∂ O out ∂ O in ∂ W 2 [[ 0.81 0.71 0.62]] ∂ W 2 [[ 0.59 0.40 0.62]] [[ 0.37 -0.41 0.50]] [[ 0.14 0.10 -0.09]] [[ 0.59 0.40 -0.38]] H in = XW 1 W 2-update W 2 ∂MSE(W 2 ) : O error = O out – Y [[0.023 0.003 0.020] [[ 0.0 -0.1 0.2] ∂W 2 [[0.013 0.003 0.019]] [[ 0.6 -0.5 0.5]] O delta = O error ⊙ O out ( 1 – O out ) ⊙ H in H out 1 W 2-update = N (H out O delta ) T [[ 1.47 1.42] [[ 0.81 0.81] [[ 3.42 0.91] [[ 0.97 0.71] ∂MSE(W 1 ) : [[ 3.62 0.47]] [[ 0.97 0.62]] ∂W 1 W 1 [[ 0.7 0.4] [[-0.8 0.0] [[ 0.3 -0.4] [[ 0.1 0.1]] X [[ 4.9 3.0 1.4 0.2] x 1 x 2 x 3 x 4 [ 6.4 3.2 4.5 1.5] [ 5.8 2.7 5.1 1.9]] 8

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