def __init__(self, *args):
self.n_unit = len(args)
super().__init__()
for i in range(self.n_unit - 1):
self.parameter["w_encode{i}"] = nn.Parameter(
np.random.randn(args[i], args[i + 1]))
self.parameter["b_encode{i}"] = nn.Parameter(np.zeros(args[i + 1]))
self.parameter["w_decode{i}"] = nn.Parameter(
np.random.randn(args[i + 1], args[i]))
self.parameter["b_decode{i}"] = nn.Parameter(np.zeros(args[i]))
def test_power(self):
x = nn.Parameter(2.)
y = 2**x
self.assertEqual(y.value, 4)
y.backward()
self.assertEqual(x.grad, 4 * np.log(2))
x = np.random.rand(10, 2)
xp = nn.Parameter(x)
y = xp**3
self.assertTrue((y.value == x**3).all())
y.backward(np.ones((10, 2)))
self.assertTrue(np.allclose(xp.grad, 3 * x**2))
def test_exp(self):
x = nn.Parameter(2.)
y = nn.exp(x)
self.assertEqual(y.value, np.exp(2))
y.backward()
self.assertEqual(x.grad, np.exp(2))
x = np.random.rand(5, 3)
p = nn.Parameter(x)
y = nn.exp(p)
self.assertTrue((y.value == np.exp(x)).all())
y.backward(np.ones((5, 3)))
self.assertTrue((p.grad == np.exp(x)).all())
def test_log(self):
x = nn.Parameter(2.)
y = nn.log(x)
self.assertEqual(y.value, np.log(2))
y.backward()
self.assertEqual(x.grad, 0.5)
x = np.random.rand(4, 6)
p = nn.Parameter(x)
y = nn.log(p)
self.assertTrue((y.value == np.log(x)).all())
y.backward(np.ones((4, 6)))
self.assertTrue((p.grad == 1 / x).all())
def test_negative(self):
x = nn.Parameter(2.)
y = -x
self.assertEqual(y.value, -2)
y.backward()
self.assertEqual(x.grad, -1)
x = np.random.rand(2, 3)
xp = nn.Parameter(x)
y = -xp
self.assertTrue((y.value == -x).all())
y.backward(np.ones((2, 3)))
self.assertTrue((xp.grad == -np.ones((2, 3))).all())
def test_multiply(self):
x = nn.Parameter(2)
y = x * 5
self.assertEqual(y.value, 10)
y.backward()
self.assertEqual(x.grad, 5)
x = np.random.rand(5, 4)
y = np.random.rand(4)
yp = nn.Parameter(y)
z = x * yp
self.assertTrue((z.value == x * y).all())
z.backward(np.ones((5, 4)))
self.assertTrue((yp.grad == x.sum(axis=0)).all())
def test_forward_backward(self):
x = nn.Parameter(2)
z = x - 5
self.assertEqual(z.value, -3)
z.backward()
self.assertEqual(x.grad, 1)
x = np.random.rand(5, 4)
y = np.random.rand(4)
p = nn.Parameter(y)
z = x - p
self.assertTrue((z.value == x - y).all())
z.backward(np.ones((5, 4)))
self.assertTrue((p.grad == -np.ones(4) * 5).all())
def test_add(self):
x = nn.Parameter(2)
z = x + 5
self.assertEqual(z.value, 7)
z.backward()
self.assertEqual(x.grad, 1)
x = np.random.rand(5, 4)
y = np.random.rand(4)
p = nn.Parameter(y)
z = x + p
self.assertTrue((z.value == x + y).all())
z.backward(np.ones((5, 4)))
self.assertTrue((p.grad == np.ones(4) * 5).all())
def test_matmul(self):
x = np.random.rand(10, 3)
y = np.random.rand(3, 5)
g = np.random.rand(10, 5)
xp = nn.Parameter(x)
z = xp @ y
self.assertTrue((z.value == x @ y).all())
z.backward(g)
self.assertTrue((xp.grad == g @ y.T).all())
yp = nn.Parameter(y)
z = x @ yp
self.assertTrue((z.value == x @ y).all())
z.backward(g)
self.assertTrue((yp.grad == x.T @ g).all())
def test_divide(self):
x = nn.Parameter(10.)
z = x / 2
self.assertEqual(z.value, 5)
z.backward()
self.assertEqual(x.grad, 0.5)
x = np.random.rand(5, 10, 3)
y = np.random.rand(10, 1)
p = nn.Parameter(y)
z = x / p
self.assertTrue((z.value == x / y).all())
z.backward(np.ones((5, 10, 3)))
d = np.sum(-x / y**2, axis=0).sum(axis=1, keepdims=True)
self.assertTrue((p.grad == d).all())
def test_laplace(self):
obs = np.arange(3)
loc = nn.Parameter(0)
s = nn.Parameter(1)
for _ in range(1000):
loc.cleargrad()
s.cleargrad()
x = nn.random.Laplace(loc, nn.softplus(s), data=obs)
x.log_pdf().sum().backward()
loc.value += loc.grad * 0.01
s.value += s.grad * 0.01
self.assertAlmostEqual(x.loc.value, np.median(obs), places=1)
self.assertAlmostEqual(x.scale.value,
np.mean(np.abs(obs - x.loc.value)),
places=1)
def test_cauchy(self):
np.random.seed(1234)
obs = np.random.standard_cauchy(size=10000)
obs = 2 * obs + 1
loc = nn.Parameter(0)
s = nn.Parameter(1)
for _ in range(100):
loc.cleargrad()
s.cleargrad()
x = nn.random.Cauchy(loc, nn.softplus(s), data=obs)
x.log_pdf().sum().backward()
loc.value += loc.grad * 0.001
s.value += s.grad * 0.001
self.assertAlmostEqual(x.loc.value, 1, places=1)
self.assertAlmostEqual(x.scale.value, 2, places=1)
def test_trace(self):
arrays = [np.random.normal(size=(2, 2)), np.random.normal(size=(3, 4))]
for arr in arrays:
arr = nn.Parameter(arr)
tr_arr = nn.linalg.trace(arr)
self.assertEqual(tr_arr.value, np.trace(arr.value))
a = np.array([[1.5, 0], [-0.1, 1.1]])
a = nn.Parameter(a)
for _ in range(100):
a.cleargrad()
loss = nn.square(nn.linalg.trace(a) - 2)
loss.backward()
a.value -= 0.1 * a.grad
self.assertEqual(nn.linalg.trace(a).value, 2)
def test_broadcast(self):
x = nn.Parameter(np.ones((1, 1)))
shape = (5, 2, 3)
y = broadcast_to(x, shape)
self.assertEqual(y.shape, shape)
y.backward(np.ones(shape))
self.assertTrue((x.grad == np.ones((1, 1)) * 30).all())
def test_solve(self):
A = np.array([[2., 1.], [1., 3.]])
B = np.array([1., 2.])[:, None]
AinvB = np.linalg.solve(A, B)
self.assertTrue((AinvB == nn.linalg.solve(A, B).value).all())
A = nn.Parameter(A)
B = nn.Parameter(B)
for _ in range(100):
A.cleargrad()
B.cleargrad()
AinvB = nn.linalg.solve(A, B)
loss = nn.square(AinvB - 1).sum()
loss.backward()
A.value -= A.grad
B.value -= B.grad
self.assertTrue(np.allclose(AinvB.value, 1))
def test_gamma(self):
self.assertEqual(24, nn.gamma(5).value)
a = nn.Parameter(2.5)
eps = 1e-5
b = nn.gamma(a)
b.backward()
num_grad = ((nn.gamma(a + eps) - nn.gamma(a - eps)) / (2 * eps)).value
self.assertAlmostEqual(a.grad, num_grad)
def test_reshape(self):
self.assertRaises(ValueError, nn.reshape, 1, (2, 3))
x = np.random.rand(2, 6)
p = nn.Parameter(x)
y = p.reshape(3, 4)
self.assertTrue((x.reshape(3, 4) == y.value).all())
y.backward(np.ones((3, 4)))
self.assertTrue((p.grad == np.ones((2, 6))).all())
def test_split(self):
x = np.random.rand(10, 7)
a = nn.Parameter(x)
b, c = nn.split(a, (3, ), axis=-1)
self.assertTrue((b.value == x[:, :3]).all())
self.assertTrue((c.value == x[:, 3:]).all())
b.backward(np.ones((10, 3)))
self.assertIs(a.grad, None)
c.backward(np.ones((10, 4)))
self.assertTrue((a.grad == np.ones((10, 7))).all())
def test_bernoulli(self):
np.random.seed(1234)
obs = np.random.choice(2, 1000, p=[0.1, 0.9])
a = nn.Parameter(0)
for _ in range(100):
a.cleargrad()
x = nn.random.Bernoulli(logit=a, data=obs)
x.log_pdf().sum().backward()
a.value += a.grad * 0.01
self.assertAlmostEqual(x.mu.value, np.mean(obs))
def test_exponential(self):
np.random.seed(1234)
obs = np.random.gamma(1, 1 / 0.5, size=1000)
a = nn.Parameter(0)
for _ in range(100):
a.cleargrad()
x = nn.random.Exponential(nn.softplus(a), data=obs)
x.log_pdf().sum().backward()
a.value += a.grad * 0.001
self.assertAlmostEqual(x.rate.value, 0.475135117)
def test_flatten(self):
self.assertRaises(TypeError, nn.flatten, "abc")
self.assertRaises(ValueError, nn.flatten, np.ones(1))
x = np.random.rand(5, 4)
p = nn.Parameter(x)
y = p.flatten()
self.assertTrue((y.value == x.flatten()).all())
y.backward(np.ones(20))
self.assertTrue((p.grad == np.ones((5, 4))).all())
def test_categorical(self):
np.random.seed(1234)
obs = np.random.choice(3, 100, p=[0.2, 0.3, 0.5])
obs = np.eye(3)[obs]
a = nn.Parameter(np.zeros(3))
for _ in range(100):
a.cleargrad()
x = nn.random.Categorical(logit=a, data=obs)
x.log_pdf().sum().backward()
a.value += 0.01 * a.grad
self.assertTrue(np.allclose(np.mean(obs, 0), x.mu.value))
def test_abs(self):
np.random.seed(1234)
x = nn.Parameter(np.random.randn(5, 7))
sign = np.sign(x.value)
y = nn.abs(x)
self.assertTrue((y.value == np.abs(x.value)).all())
for _ in range(10000):
x.cleargrad()
y = nn.abs(x)
nn.square(y - 0.01).sum().backward()
x.value -= x.grad * 0.001
self.assertTrue(np.allclose(x.value, 0.01 * sign))
def test_determinant(self):
A = np.array([[2., 1.], [1., 3.]])
detA = np.linalg.det(A)
self.assertTrue((detA == nn.linalg.det(A).value).all())
A = nn.Parameter(A)
for _ in range(100):
A.cleargrad()
detA = nn.linalg.det(A)
loss = nn.square(detA - 1)
loss.backward()
A.value -= 0.1 * A.grad
self.assertAlmostEqual(detA.value, 1.)
def test_transpose(self):
arrays = [
np.random.normal(size=(2, 3)),
np.random.normal(size=(2, 3, 4))
]
axes = [None, (2, 0, 1)]
for arr, ax in zip(arrays, axes):
arr = nn.Parameter(arr)
arr_t = nn.transpose(arr, ax)
self.assertEqual(arr_t.shape, np.transpose(arr.value, ax).shape)
da = np.random.normal(size=arr_t.shape)
arr_t.backward(da)
self.assertEqual(arr.grad.shape, arr.shape)
def test_multivariate_gaussian(self):
self.assertRaises(ValueError, nn.random.MultivariateGaussian,
np.zeros(2), np.eye(3))
self.assertRaises(ValueError, nn.random.MultivariateGaussian,
np.zeros(2),
np.eye(2) * -1)
x_train = np.array([[1., 1.], [1., -1], [-1., 1.], [-1., -2.]])
mu = nn.Parameter(np.ones(2))
cov = nn.Parameter(np.eye(2) * 2)
for _ in range(1000):
mu.cleargrad()
cov.cleargrad()
x = nn.random.MultivariateGaussian(mu,
cov + cov.transpose(),
data=x_train)
log_likelihood = x.log_pdf().sum()
log_likelihood.backward()
mu.value += 0.1 * mu.grad
cov.value += 0.1 * cov.grad
self.assertTrue(np.allclose(mu.value, x_train.mean(axis=0)))
self.assertTrue(
np.allclose(np.cov(x_train, rowvar=False, bias=True), x.cov.value))
def test_mean(self):
x = np.random.rand(5, 1, 2)
xp = nn.Parameter(x)
z = xp.mean()
self.assertEqual(z.value, x.mean())
z.backward()
self.assertTrue((xp.grad == np.ones((5, 1, 2)) / 10).all())
xp.cleargrad()
z = xp.mean(axis=0, keepdims=True)
self.assertEqual(z.shape, (1, 1, 2))
self.assertTrue((z.value == x.mean(axis=0, keepdims=True)).all())
z.backward(np.ones((1, 1, 2)))
self.assertTrue((xp.grad == np.ones((5, 1, 2)) / 5).all())
def test_inverse(self):
A = np.array([[2., 1.], [1., 3.]])
Ainv = np.linalg.inv(A)
self.assertTrue((Ainv == nn.linalg.inv(A).value).all())
B = np.array([[-1., 1.], [1., 0.5]])
A = nn.Parameter(np.array([[-0.4, 0.7], [0.7, 0.7]]))
for _ in range(100):
A.cleargrad()
Ainv = nn.linalg.inv(A)
loss = nn.square(Ainv - B).sum()
loss.backward()
A.value -= 0.1 * A.grad
self.assertTrue(np.allclose(A.value, np.linalg.inv(B)))
def test_cholesky(self):
A = np.array([[2., -1], [-1., 5.]])
L = np.linalg.cholesky(A)
Ap = nn.Parameter(A)
L_test = nn.linalg.cholesky(Ap)
self.assertTrue((L == L_test.value).all())
T = np.array([[1., 0.], [-1., 2.]])
for _ in range(1000):
Ap.cleargrad()
L_ = nn.linalg.cholesky(Ap)
loss = nn.square(T - L_).sum()
loss.backward()
Ap.value -= 0.1 * Ap.grad
self.assertTrue(np.allclose(Ap.value, T @ T.T))
def test_dirichlet(self):
np.random.seed(1234)
obs = np.random.choice(3, 100, p=[0.2, 0.3, 0.5])
obs = np.eye(3)[obs]
a = nn.Parameter(np.zeros(3))
for _ in range(100):
a.cleargrad()
mu = nn.softmax(a)
d = nn.random.Dirichlet(np.ones(3) * 10, data=mu)
x = nn.random.Categorical(mu, data=obs)
log_posterior = x.log_pdf().sum() + d.log_pdf().sum()
log_posterior.backward()
a.value += 0.01 * a.grad
count = np.sum(obs, 0) + 10
p = count / count.sum(keepdims=True)
self.assertTrue(np.allclose(p, mu.value, 1e-2, 1e-2))
