def compute_gradients(dL_da2, da2_dz2, dz2_dW2, dz2_db2, dz2_da1, da1_dz1,
dz1_dW1, dz1_db1):
'''
Given the local gradients, compute the gradient of the loss function L w.r.t. model parameters: the weights W1, W2 and biases b1 and b2.
Input: see details in the above functions.
Output:
dL_dW2: the gradient of the loss function L w.r.t. the weight matrix W2
dL_db2: the gradient of the loss function L w.r.t. the biases b2
dL_dW1: the gradient of the loss function L w.r.t. the weight matrix W1
dL_db1: the gradient of the loss function L w.r.t. the biases b1
Hint: you could re-use the functions in problem1, such as sr.compute_dL_dz(...)
'''
#########################################
## INSERT YOUR CODE HERE
# the 2nd layer
dL_dz2 = sr.compute_dL_dz(dL_da2, da2_dz2)
dL_dW2 = sr.compute_dL_dW(dL_dz2, dz2_dW2)
dL_db2 = sr.compute_dL_db(dL_dz2, dz2_db2)
# the 1st layer
dL_da1 = compute_dL_da1(dL_dz2, dz2_da1)
dL_dz1 = np.multiply(dL_da1, da1_dz1)
dL_dW1 = sr.compute_dL_dW(dL_dz1, dz1_dW1)
dL_db1 = sr.compute_dL_db(dL_dz1, dz1_db1)
#########################################
return dL_dW2, dL_db2, dL_dW1, dL_db1
def compute_dL_dz1(dL_da1, da1_dz1):
'''
Compute local gradient of the loss function L w.r.t. the logits z1 using chain rule.
(2 points)
Input:
dL_da1: the gradient of the loss function L w.r.t. the activations a1
da1_dz1: the gradient of the activations z1 L w.r.t. the logits z1
Output:
dL_dz1: the partial gradient of the loss function w.r.t. the logits z1, a numpy float vector of shape h by 1.
Each element represents the partial gradient of the loss function L w.r.t. the i-th logit z1[i]: d_L / d_z1[i]
'''
#########################################
## INSERT YOUR CODE HERE
dL_dz1 = sr.compute_dL_dW(dL_da1, da1_dz1)
#########################################
return dL_dz1