def test_grad_of_grad():
x2 = ad.Variable(name="x2")
x3 = ad.Variable(name="x3")
y = x2 * x2 + x2 * x3
grad_x2, grad_x3 = ad.gradients(y, [x2, x3])
grad_x2_x2, grad_x2_x3 = ad.gradients(grad_x2, [x2, x3])
executor = ad.Executor([y, grad_x2, grad_x3, grad_x2_x2, grad_x2_x3])
x2_val = 2 * np.ones(3)
x3_val = 3 * np.ones(3)
y_val, grad_x2_val, grad_x3_val, grad_x2_x2_val, grad_x2_x3_val = executor.run(feed_dict={x2: x2_val, x3: x3_val})
expected_yval = x2_val * x2_val + x2_val * x3_val
expected_grad_x2_val = 2 * x2_val + x3_val
expected_grad_x3_val = x2_val
expected_grad_x2_x2_val = 2 * np.ones_like(x2_val)
expected_grad_x2_x3_val = 1 * np.ones_like(x2_val)
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, expected_yval)
assert np.array_equal(grad_x2_val, expected_grad_x2_val)
assert np.array_equal(grad_x3_val, expected_grad_x3_val)
assert np.array_equal(grad_x2_x2_val, expected_grad_x2_x2_val)
assert np.array_equal(grad_x2_x3_val, expected_grad_x2_x3_val)
def test_logistic_loss():
x = ad.Variable(name='x')
w = ad.Variable(name='w')
y = ad.Variable(name='y')
h = 1 / (1 + ad.exp(-ad.reduce_sum(w * x)))
L = y * ad.log(h) + (1 - y) * ad.log(1 - h)
w_grad, = ad.gradients(L, [w])
executor = ad.Executor([L, w_grad])
y_val = 0
x_val = np.array([2, 3, 4])
w_val = np.random.random(3)
L_val, w_grad_val = executor.run(feed_dict={x: x_val, y: y_val, w: w_val})
logistic = 1 / (1 + np.exp(-np.sum(w_val * x_val)))
expected_L_val = y_val * np.log(logistic) + (1 - y_val) * np.log(1 - logistic)
expected_w_grad = (y_val - logistic) * x_val
print(L_val)
print(expected_L_val)
print(expected_w_grad)
print(w_grad_val)
assert expected_L_val == L_val
assert np.sum(np.abs(expected_w_grad - w_grad_val)) < 1E-9
def test_sub_by_const():
x2 = ad.Variable(name='x2')
y = 3 - x2
grad_x2, = ad.gradients(y, [x2])
executor = ad.Executor([y, grad_x2])
x2_val = 2 * np.ones(3)
y_val, grad_x2_val = executor.run(feed_dict={x2: x2_val})
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, 3 - x2_val)
assert np.array_equal(grad_x2_val, -np.ones_like(x2_val))
def test_reduce_sum_mix():
x1 = ad.Variable(name="x1")
y = ad.exp(ad.reduce_sum(x1))
grad_x1, = ad.gradients(y, [x1])
executor = ad.Executor([y, grad_x1])
x1_val = 2 * np.ones(3)
y_val, grad_x1_val = executor.run(feed_dict={x1: x1_val})
expected_y_val = np.exp(np.sum(x1_val))
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, expected_y_val)
assert np.array_equal(grad_x1_val, expected_y_val * np.ones_like(x1_val))
y2 = ad.log(ad.reduce_sum(x1))
grad_x2, = ad.gradients(y2, [x1])
executor2 = ad.Executor([y2, grad_x2])
y2_val, grad_x2_val = executor2.run(feed_dict={x1: x1_val})
expected_y2_val = np.log(np.sum(x1_val))
assert isinstance(y2, ad.Node)
assert np.array_equal(y2_val, expected_y2_val)
assert np.array_equal(grad_x2_val, (1 / np.sum(x1_val)) * np.ones_like(x1_val))
def test_mul_by_const():
x2 = ad.Variable(name="x2")
y = 5 * x2
grad_x2, = ad.gradients(y, [x2])
executor = ad.Executor([y, grad_x2])
x2_val = 2 * np.ones(3)
y_val, grad_x2_val = executor.run(feed_dict={x2: x2_val})
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, x2_val * 5)
assert np.array_equal(grad_x2_val, np.ones_like(x2_val) * 5)
def test_reduce_sum():
x1 = ad.Variable(name="x1")
y = ad.reduce_sum(x1)
grad_x1, = ad.gradients(y, [x1])
executor = ad.Executor([y, grad_x1])
x1_val = 2 * np.ones(3)
y_val, grad_x1_val = executor.run(feed_dict={x1: x1_val})
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, np.sum(x1_val))
assert np.array_equal(grad_x1_val, np.ones_like(x1_val))
def test_div_by_const():
x2 = ad.Variable(name="x2")
y = 5 / x2
grad_x2, = ad.gradients(y, [x2])
executor = ad.Executor([y, grad_x2])
x2_val = 2 * np.ones(3)
y_val, grad_x2_val = executor.run(feed_dict={x2: x2_val})
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, 5 / x2_val)
print(grad_x2_val)
print(-5 / (x2_val * x2_val))
assert np.array_equal(grad_x2_val, -5 / (x2_val * x2_val))
def test_mul_two_vars():
x2 = ad.Variable(name="x2")
x3 = ad.Variable(name="x3")
y = x2 * x3
grad_x2, grad_x3 = ad.gradients(y, [x2, x3])
executor = ad.Executor([y, grad_x2, grad_x3])
x2_val = 2 * np.ones(3)
x3_val = 3 * np.ones(3)
y_val, grad_x2_val, grad_x3_val = executor.run(feed_dict={x2: x2_val, x3: x3_val})
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, x2_val * x3_val)
assert np.array_equal(grad_x2_val, x3_val)
assert np.array_equal(grad_x3_val, x2_val)
def test_neg():
x1 = ad.Variable(name='x1')
x2 = ad.Variable(name='x2')
y = -x2 + x1
grad_x1, grad_x2 = ad.gradients(y, [x1, x2])
executor = ad.Executor([y, grad_x1, grad_x2])
x2_val = 2 * np.ones(3)
x1_val = 3 * np.ones(3)
y_val, grad_x1_val, grad_x2_val = executor.run(feed_dict={x1: x1_val, x2: x2_val})
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, -x2_val + x1_val)
assert np.array_equal(grad_x2_val, -np.ones_like(x2_val))
assert np.array_equal(grad_x1_val, np.ones_like(x1_val))
def test_exp_mix_op():
x1 = ad.Variable(name="x1")
x2 = ad.Variable(name="x2")
y = ad.exp(ad.log(x1 * x2) + 1)
grad_x1, grad_x2 = ad.gradients(y, [x1, x2])
executor = ad.Executor([y, grad_x1, grad_x2])
x1_val = 2 * np.ones(3)
x2_val = 4 * np.ones(3)
y_val, grad_x1_val, grad_x2_val = executor.run(feed_dict={x1: x1_val, x2: x2_val})
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, np.exp(np.log(x1_val * x2_val) + 1))
assert np.array_equal(grad_x1_val, y_val * x2_val / (x1_val * x2_val))
assert np.array_equal(grad_x2_val, y_val * x1_val / (x1_val * x2_val))
def test_div_two_vars():
x1 = ad.Variable(name='x1')
x2 = ad.Variable(name='x2')
y = x1 / x2
grad_x1, grad_x2 = ad.gradients(y, [x1, x2])
executor = ad.Executor([y, grad_x1, grad_x2])
x1_val = 2 * np.ones(3)
x2_val = 5 * np.ones(3)
y_val, grad_x1_val, grad_x2_val = executor.run(feed_dict={x1: x1_val, x2: x2_val})
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, x1_val / x2_val)
assert np.array_equal(grad_x1_val, np.ones_like(x1_val) / x2_val)
assert np.array_equal(grad_x2_val, -x1_val / (x2_val * x2_val))
def test_mix_all():
x1 = ad.Variable(name="x1")
y = 1 / (1 + ad.exp(-ad.reduce_sum(x1)))
grad_x1, = ad.gradients(y, [x1])
executor = ad.Executor([y, grad_x1])
x1_val = 2 * np.ones(3)
y_val, grad_x1_val = executor.run(feed_dict={x1: x1_val})
expected_y_val = 1 / (1 + np.exp(-np.sum(x1_val)))
expected_y_grad = expected_y_val * (1 - expected_y_val) * np.ones_like(x1_val)
print(expected_y_grad)
print(grad_x1_val)
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, expected_y_val)
assert np.sum(np.abs(grad_x1_val - expected_y_grad)) < 1E-10
def test_add_mul_mix_1():
x1 = ad.Variable(name="x1")
x2 = ad.Variable(name="x2")
x3 = ad.Variable(name="x3")
y = x1 + x2 * x3 * x1
grad_x1, grad_x2, grad_x3 = ad.gradients(y, [x1, x2, x3])
executor = ad.Executor([y, grad_x1, grad_x2, grad_x3])
x1_val = 1 * np.ones(3)
x2_val = 2 * np.ones(3)
x3_val = 3 * np.ones(3)
y_val, grad_x1_val, grad_x2_val, grad_x3_val = executor.run(feed_dict={x1: x1_val, x2: x2_val, x3: x3_val})
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, x1_val + x2_val * x3_val)
assert np.array_equal(grad_x1_val, np.ones_like(x1_val) + x2_val * x3_val)
assert np.array_equal(grad_x2_val, x3_val * x1_val)
assert np.array_equal(grad_x3_val, x2_val * x1_val)
def test_logistic():
x1 = ad.Variable(name="x1")
w = ad.Variable(name='w')
y = 1 / (1 + ad.exp(-ad.reduce_sum(w * x1)))
grad_w, = ad.gradients(y, [w])
executor = ad.Executor([y, grad_w])
x1_val = 3 * np.ones(3)
w_val = 3 * np.zeros(3)
y_val, grad_w_val = executor.run(feed_dict={x1: x1_val, w: w_val})
expected_y_val = 1 / (1 + np.exp(-np.sum(w_val * x1_val)))
expected_y_grad = expected_y_val * (1 - expected_y_val) * x1_val
print(expected_y_grad)
print(grad_w_val)
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, expected_y_val)
assert np.sum(np.abs(grad_w_val - expected_y_grad)) < 1E-7
def test_add_mul_mix_3():
x2 = ad.Variable(name="x2")
x3 = ad.Variable(name="x3")
z = x2 * x2 + x2 + x3 + 3
y = z * z + x3
grad_x2, grad_x3 = ad.gradients(y, [x2, x3])
executor = ad.Executor([y, grad_x2, grad_x3])
x2_val = 2 * np.ones(3)
x3_val = 3 * np.ones(3)
y_val, grad_x2_val, grad_x3_val = executor.run(feed_dict={x2: x2_val, x3: x3_val})
z_val = x2_val * x2_val + x2_val + x3_val + 3
expected_yval = z_val * z_val + x3_val
expected_grad_x2_val = 2 * (x2_val * x2_val + x2_val + x3_val + 3) * (2 * x2_val + 1)
expected_grad_x3_val = 2 * (x2_val * x2_val + x2_val + x3_val + 3) + 1
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, expected_yval)
assert np.array_equal(grad_x2_val, expected_grad_x2_val)
assert np.array_equal(grad_x3_val, expected_grad_x3_val)
def test_matmul_two_vars():
x2 = ad.Variable(name="x2")
x3 = ad.Variable(name="x3")
y = ad.matmul_op(x2, x3)
grad_x2, grad_x3 = ad.gradients(y, [x2, x3])
executor = ad.Executor([y, grad_x2, grad_x3])
x2_val = np.array([[1, 2], [3, 4], [5, 6]]) # 3x2
x3_val = np.array([[7, 8, 9], [10, 11, 12]]) # 2x3
y_val, grad_x2_val, grad_x3_val = executor.run(feed_dict={x2: x2_val, x3: x3_val})
expected_yval = np.matmul(x2_val, x3_val)
expected_grad_x2_val = np.matmul(np.ones_like(expected_yval), np.transpose(x3_val))
expected_grad_x3_val = np.matmul(np.transpose(x2_val), np.ones_like(expected_yval))
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, expected_yval)
assert np.array_equal(grad_x2_val, expected_grad_x2_val)
assert np.array_equal(grad_x3_val, expected_grad_x3_val)
def auto_diff_lr():
x = ad.Variable(name='x')
w = ad.Variable(name='w')
y = ad.Variable(name='y')
# 注意，以下实现某些情况会有很大的数值误差，
# 所以一般真实系统实现会提供高阶算子，从而减少数值误差
h = 1 / (1 + ad.exp(-ad.reduce_sum(w * x)))
L = y * ad.log(h) + (1 - y) * ad.log(1 - h)
w_grad, = ad.gradients(L, [w])
executor = ad.Executor([L, w_grad])
N = 100
X_val, Y_val = gen_2d_data(N)
w_val = np.ones(3)
plot(N, X_val, Y_val, w_val)
executor = ad.Executor([L, w_grad])
test_accuracy(w_val, X_val, Y_val)
alpha = 0.01
max_iters = 300
for iteration in range(max_iters):
acc_L_val = 0
for i in range(N):
x_val = X_val[i]
y_val = np.array(Y_val[i])
L_val, w_grad_val = executor.run(feed_dict={
w: w_val,
x: x_val,
y: y_val
})
w_val += alpha * w_grad_val
acc_L_val += L_val
print("iter = %d, likelihood = %s, w = %s" %
(iteration, acc_L_val, w_val))
test_accuracy(w_val, X_val, Y_val)
plot(N, X_val, Y_val, w_val, True)
