def test_model_backward():
np.random.seed(3)
al = np.random.randn(1, 2)
y = np.array([[1, 0]])
a1 = np.random.randn(4, 2)
w1 = np.random.randn(3, 4)
b1 = np.random.randn(3, 1)
z1 = np.random.randn(3, 2)
a2 = np.random.randn(3, 2)
w2 = np.random.randn(1, 3)
b2 = np.random.randn(1, 1)
z2 = np.random.randn(1, 2)
nn = NeuralNetwork(w=[w1, w2], b=[b1, b2], params_ok=True)
nn.cache = [(a1, z1), (a2, z2)]
nn.w = [w1, w2]
nn.b = [b1, b2]
grads = nn.model_backward(al, y)
assert_eq(grads[0][0], [
[0.41010002, 0.07807203, 0.1379844364, 0.1050216745],
[0., 0., 0., 0.],
[0.05283652, 0.0100586544, 0.017777656, 0.0135307956]
])
assert_eq(grads[1][0], [
[-0.2200706339], [0.], [-0.02835349]
])
def test_backward_propagation_dropout():
np.random.seed(1)
x = np.random.randn(3, 5)
y = np.array([[1, 1, 0, 1, 0]])
w1 = np.array([[-1.09989127, -0.17242821, -0.87785842],
[0.04221375, 0.58281521, -1.10061918]])
b1 = np.array([[1.14472371], [0.90159072]])
w2 = np.array([[0.50249434, 0.90085595], [-0.68372786, -0.12289023],
[-0.93576943, -0.26788808]])
b2 = np.array([[0.53035547], [-0.69166075], [-0.39675353]])
w3 = np.array([[-0.6871727, -0.84520564, -0.67124613]])
b3 = np.array([[-0.0126646]])
nn = NeuralNetwork(w=[w1, w2, w3], b=[b1, b2, b3], params_ok=True)
z1 = np.array(
[[-1.52855314, 3.32524635, 2.13994541, 2.60700654, -0.75942115],
[-1.98043538, 4.1600994, 0.79051021, 1.46493512, -0.45506242]])
d1 = np.array(
[[True, False, True, True, True], [True, True, True, True, False]],
dtype=bool)
a1 = np.array([[0., 0., 4.27989081, 5.21401307, 0.],
[0., 8.32019881, 1.58102041, 2.92987024, 0.]])
z2 = np.array(
[[0.53035547, 8.02565606, 4.10524802, 5.78975856, 0.53035547],
[-0.69166075, -1.71413186, -3.81223329, -4.61667916, -0.69166075],
[-0.39675353, -2.62563561, -4.82528105, -6.0607449, -0.39675353]])
d2 = np.array(
[[True, False, True, False, True], [False, True, False, True, True],
[False, False, True, False, False]],
dtype=bool)
a2 = np.array([
[1.06071093, 0., 8.21049603, 0., 1.06071093],
[0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0.],
])
z3 = np.array(
[[-0.7415562, -0.0126646, -5.65469333, -0.0126646, -0.7415562]])
a3 = np.array(
[[0.32266394, 0.49683389, 0.00348883, 0.49683389, 0.32266394]])
nn.cache = [(x, z1, d1), (a1, z2, d2), (a2, z3)]
gradw, _ = nn.model_backward(a3, y, keep_prop=0.8)
assert_eq(gradw[0], [[0.0001988393, 0.0002865694, 0.0001213795],
[0.0003564729, 0.0005137526, 0.0002176053]],
rtol=1e-5)
assert_eq(gradw[1], [[-0.0025651848, -0.0009475965], [0., 0.], [0., 0.]],
rtol=1e-5)
assert_eq(gradw[2], [[-0.0695119105, 0., 0.]])
def test_backward_propagation_regulation():
np.random.seed(1)
x = np.random.randn(3, 5)
y = np.array([[1, 1, 0, 1, 0]])
w1 = np.array([[-1.09989127, -0.17242821, -0.87785842],
[0.04221375, 0.58281521, -1.10061918]])
b1 = np.array([[1.14472371], [0.90159072]])
w2 = np.array([[0.50249434, 0.90085595], [-0.68372786, -0.12289023],
[-0.93576943, -0.26788808]])
b2 = np.array([[0.53035547], [-0.69166075], [-0.39675353]])
w3 = np.array([[-0.6871727, -0.84520564, -0.67124613]])
b3 = np.array([[-0.0126646]])
z1 = np.array(
[[-1.52855314, 3.32524635, 2.13994541, 2.60700654, -0.75942115],
[-1.98043538, 4.1600994, 0.79051021, 1.46493512, -0.45506242]])
a1 = np.array([[0., 3.32524635, 2.13994541, 2.60700654, 0.],
[0., 4.1600994, 0.79051021, 1.46493512, 0.]])
z2 = np.array(
[[0.53035547, 5.94892323, 2.31780174, 3.16005701, 0.53035547],
[-0.69166075, -3.47645987, -2.25194702, -2.65416996, -0.69166075],
[-0.39675353, -4.62285846, -2.61101729, -3.22874921, -0.39675353]])
a2 = np.array(
[[0.53035547, 5.94892323, 2.31780174, 3.16005701, 0.53035547],
[0., 0., 0., 0., 0.], [0., 0., 0., 0., 0.]])
z3 = np.array(
[[-0.3771104, -4.10060224, -1.60539468, -2.18416951, -0.3771104]])
a3 = np.array(
[[0.40682402, 0.01629284, 0.16722898, 0.10118111, 0.40682402]])
nn = NeuralNetwork(w=[w1, w2, w3],
b=[b1, b2, b3],
lambd=0.7,
params_ok=True)
nn.cache = [(x, z1), (a1, z2), (a2, z3)]
gradw, gradb = nn.model_backward(a3, y)
assert_eq(gradw[0], [[-0.256046467, 0.122988299, -0.28297132],
[-0.17706304, 0.34536100, -0.4410572]],
rtol=1e-5)
assert_eq(gradw[1], [[0.792764876, 0.85133918], [-0.0957219, -0.01720463],
[-0.13100772, -0.03750433]],
rtol=1e-5)
assert_eq(gradw[2], [[-1.77691347, -0.11832879, -0.09397446]], rtol=1e-5)