# Explaination of coding of Back Propagation

Hi,
I am learning unit3 of “machine learning of robotic”. In topic 3.6 of back propagation, I can understand the theory and formular, but I can totally not understand the code which implementes it. The complete code is:

``````import numpy as np
import matplotlib.pyplot as plt

def create_data_set(points, classes):

X = np.zeros((points*classes, 2))
y = np.zeros(points*classes, dtype='uint8')
for class_number in range(classes):
ix = range(points*class_number, points*(class_number+1))
r = np.linspace(0.0, 1, points)
t = np.linspace(class_number*4, (class_number+1)*4, points) + np.random.randn(points)*0.5
X[ix] = np.c_[r*np.sin(t*1.0), r*np.cos(t*1.0)]
y[ix] = class_number
return X, y

X, y = create_data_set(400, 2)

N = 200 # number of points per class
D = 2 # dimensionality
K = 2 # number of classes
h = 1000 # size of hidden layer
W = 0.01 * np.random.randn(D,h)
b = np.zeros((1,h))
W2 = 0.01 * np.random.randn(h,K)
b2 = np.zeros((1,K))
step_size = 1e-0

num_examples = X.shape
ii = []
error = []

#here in for-loop we deply the back propagation alghorithm (gradient descent)

for i in range(3000):

# evaluate class scores, [N x K]
hidden_layer = np.maximum(0, np.dot(X, W) + b) # note, ReLU activation
scores = np.dot(hidden_layer, W2) + b2

# compute the Softmax class probabilities
exp_scores = np.exp(scores)
probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) # [N x K]

# compute the loss (cross-entropy loss)
corect_logprobs = -np.log(probs[range(num_examples),y])
data_loss = np.sum(corect_logprobs)/num_examples
#reg_loss = 0.5*reg*np.sum(W*W) + 0.5*reg*np.sum(W2*W2)
loss = data_loss # + reg_loss
if i % 100 == 0:
print "i:", i, "loss: ", loss
ii.append(i)
error.append(loss)

# compute the gradient on scores
dscores = probs
dscores[range(num_examples),y] -= 1
dscores /= num_examples

# apply the backpropate alghorithm(BP) the gradient

# first apply into parameters W2 and b2
dW2 = np.dot(hidden_layer.T, dscores)
db2 = np.sum(dscores, axis=0, keepdims=True)
# next BP into hidden layer
dhidden = np.dot(dscores, W2.T)
# backprop the ReLU non-linearity
dhidden[hidden_layer <= 0] = 0
# finally into W,b
dW = np.dot(X.T, dhidden)
db = np.sum(dhidden, axis=0, keepdims=True)

# perform a parameter update
W += -step_size * dW
b += -step_size * db
W2 += -step_size * dW2
b2 += -step_size * db2
``````

But I cannot understand what does this back propagation part function:

``````  # apply the backpropate alghorithm(BP) the gradient

# first apply into parameters W2 and b2
dW2 = np.dot(hidden_layer.T, dscores)
db2 = np.sum(dscores, axis=0, keepdims=True)
# next BP into hidden layer
dhidden = np.dot(dscores, W2.T)
# backprop the ReLU non-linearity
dhidden[hidden_layer <= 0] = 0
# finally into W,b
dW = np.dot(X.T, dhidden)
db = np.sum(dhidden, axis=0, keepdims=True)

# perform a parameter update
W += -step_size * dW
b += -step_size * db
W2 += -step_size * dW2
b2 += -step_size * db2
``````

Can anyone explain them in details? Or which code correspondes to which formular? I think there are too much skippings between them…

sorry, and this part:

``````  # compute the gradient on scores
dscores = probs
dscores[range(num_examples),y] -= 1
dscores /= num_examples
``````

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