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convolutional.py
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import numpy as np
def conv_single_step(a_slice_prev, W, b):
s = np.multiply(a_slice_prev,W)
Z = np.sum(s)
Z = Z+b
return Z
def conv_forward(A_prev, W, b, hparameters):
(m, n_H_prev, n_W_prev, n_C_prev) = A_prev.shape
(f, f, n_C_prev, n_C) = W.shape
stride = hparameters["stride"]
pad = hparameters["pad"]
n_H = int((n_H_prev - f + 2 * pad)/stride) + 1
n_W = int((n_W_prev - f + 2 * pad)/stride) + 1
Z = np.zeros((m, n_H, n_W, n_C))
A_prev_pad = zero_pad(A_prev, pad)
for i in range(m):
a_prev_pad = A_prev_pad[i,:,:,:]
for h in range(n_H):
for w in range(n_W):
for c in range(n_C):
vert_start = stride * h
vert_end = vert_start + f
horiz_start = stride * w
horiz_end = horiz_start + f
a_slice_prev = a_prev_pad[vert_start:vert_end,horiz_start:horiz_end,:]
Z[i, h, w, c] = conv_single_step(a_slice_prev,W[:,:,:,c], b[:,:,:,c])
assert(Z.shape == (m, n_H, n_W, n_C))
cache = (A_prev, W, b, hparameters)
return Z, cache
def fully_connected(A_prev, W, b):
A_new = np.reshape(A_prev, (A_prev.shape[0], -1))
Z = A_new.dot(W) + b
return Z
def relu(A_prev):
return np.maximum(0, A_prev)
def conv_backward(dZ, cache):
(A_prev, W, b, hparameters) = cache
(m, n_H_prev, n_W_prev, n_C_prev) = A_prev.shape
(f, f, n_C_prev, n_C) = W.shape
stride = hparameters["stride"]
pad = hparameters["pad"]
(m, n_H, n_W, n_C) = dZ.shape
dA_prev = np.zeros((m, n_H_prev, n_W_prev, n_C_prev))
dW = np.zeros((f, f, n_C_prev, n_C))
db = np.zeros((1, 1, 1, n_C))
A_prev_pad = zero_pad(A_prev, pad)
dA_prev_pad = zero_pad(dA_prev, pad)
for i in range(m):
a_prev_pad = A_prev_pad[i,:,:,:]
da_prev_pad = dA_prev_pad[i,:,:,:]
for h in range(n_H):
for w in range(n_W):
for c in range(n_C):
vert_start = stride * h
vert_end = vert_start + f
horiz_start = stride * w
horiz_end = horiz_start + f
a_slice = A_prev_pad[i, vert_start:vert_end, horiz_start:horiz_end, :]
da_prev_pad[vert_start:vert_end, horiz_start:horiz_end, :] += W[:,:,:,c] * dZ[i, h, w, c]
dW[:,:,:,c] += a_slice * dZ[i, h, w, c]
db[:,:,:,c] += dZ[i, h, w, c]
dA_prev[i, :, :, :] = da_prev_pad[pad:-pad, pad:-pad, :]
assert(dA_prev.shape == (m, n_H_prev, n_W_prev, n_C_prev))
return dA_prev, dW, db
def relu_backward(A_next):
return 1. * ( x > 0)
def mse(X, Y):
return (1. / 2. * X.shape[0]) * ((X - Y) ** 2.)
def mse_deriv(result, expected):
return (X - Y)/ X.shape[0]
np.random.seed(1)
#A_prev = 32*32 image
W = np.random.randn(1,3,3,4)
b = np.random.randn(1,1,1,4)
hparameters = {"pad":0, "stride":2}
Z, cache_conv = conv_forward(A_prev, W, b, hparameters)
Y = relu(Z)
W1 = np.random.randn(1064,10)
b1 = np.random.randn(1,10)
K = fully_connected(Y, W1, b1)
final_loss = mse_deriv(K, expected_result) # expected result of size 1 X 10
# for fcl
grad1 = K.T.dot(final_loss)
W1 -= grad1
# for relu
grad2 = relu_backward(Y) * grad1
grad3, grad4, grad5 = conv_backward(grad1, cache)
W -= grad3/grad4
b -= grad3/grad5