Forward propagation Notation Input Output n : number of features Z1 Z2 x1 Notation Input n : number of features P : number of data Output m : number of features x2 xn Zm

Matrix multiplication (2 X 3) (3X 2)  (2 X 2) 일반적으로 (A X B) (B X C)  (A X C)

Z1 w11 x1 w12 Number of input feature : 2 Number of output feature : 3 Number of parameters : 2 X 3 Number of input feature : n Number of output feature : m Number of parameters : n X m w13 Z2 w21 w22 x2 w23 Z3

Z1 = x1*w11 + x2*w21 Number of input feature : 2 Number of output feature : 3 Number of parameters : 2 X 3 w11 x1 w12 w13 Z2 = x1*w12+x2*w22 w21 w11 w12 w13 w21 w22 w23 w22 [x1, x2] X x2 = [X1*w11 + x2*w21, x1*w12+x2*w22, x1*w13+x2*w23] w23 Z3 = X1*w13+x2*w23 (1 X 2) (2 X 3)  (1 X 3)

Number of input feature : 2 Number of output feature : 3 Number of parameters : 2 X 3 Number of input feature : n Number of output feature : m Number of parameters : n X m (1 X 2) (2 X 3)  (1 X 3) (1 X n) (n X m)  (1 X m) [x1, x2] X w11 w12 w13 w21 w22 w23 = [X1*w11 + x2*w21, x1*w12+x2*w22, x1*w13+x2*w23]

17 Z1 x1 23 x2 4 Z2 10 1 11 x5 Z3

Forward propation Notation Input Output n : number of features 1st data: Notation Input n : number of features p : number of data Output m : number of features 2nd data : [1 1 1 1 1] [65 65 65 ]

1st data: 2nd data : [1 1 1 1 1] [65 65 65 ] 12 19 65 65 65 0 0 0 1 0 1 1 1 1 1

12 19 65 65 65 0 0 0 1 0 1 1 1 1 1 2 X 5 5 X 3 2 X 3 n : number of input feature p : number of data p : number of data m : number of output feature

12 19 65 65 65 0 0 0 1 0 1 1 1 1 1

Forward propagation Apply activation Sigmoid. ….. sigmoid Z1 Z2 x1 x2 xn Zm

parameter input sigmoid output 12 19 65 65 65 0 0 0 1 0 1 1 1 1 1

W1 W2 W3 W4 input hidden1 hidden2 hidden3 output n features m features o features p features q features n X m m X o o X p p X q Z1 = np.dot(input, W1) O1 = sigmoid(Z1) Z2 = np.dot(O1, W2) O2 = sigmoid(Z2) Z3 = np.dot(O2, W3) O3 = sigmoid(Z3) Z4 = np.dot(O3, W4) O4 = sigmoid(Z4)