I have 3 layer NN. 3 neurons in input, then 3 with RELU activation, then 3 with Sigmoig activation, then 3 with Softmax activation(its output). And there are weights:
W = np.array([[[0.1, 0.2, 0.3],
[0.3, 0.2, 0.7],
[0.1, 0.2, 0.3]],
[[0.2, 0.3, 0.5],
[0.3, 0.5, 0.7],
[0.6, 0.4, 0.8]],
[[0.1, 0.4, 0.8],
[0.3, 0.7, 0.2],
[0.5, 0.2, 0.9]]])
Input and result:
X = np.array([0.1, 0.2, 0.7])
Y = np.array([1.0, 0.0, 0.0])
Feed forward:
Z1 = W[0] @ X
H1 = RELU(Z1)
Z2 = W[1] @ H1
H2 = Sigmoid(Z2)
Z3 = W[2] @ H2
H3 = Softmax(Z3)
Loss = CrossEntropy(Ypred,Y)
Back propagation:
dLoss = dCrossEntropy(Ypred, Y)
o_error = dLoss
o_delta = dLoss*(dSoftmax(o_error))
z2_error = o_delta*(W[2].T)
z2_delta = z2_error * dSigmoid(Z2)
z1_error = z2_error*(W[1].T)
z1_delta = z1_error * dRELU(Z1)
W[0] += X.T.dot(z1_delta)
W[1] += (Z1.T).dot(z1_delta)
W[2] += (Z2.T).dot(o_delta)
Am I correct in backpropagation?