def test_natural_gradient(self):
"""
Test random natural gradient cases.
"""
with tf.Graph().as_default():
with tf.Session() as sess:
for size in range(3, 9):
dist = NaturalSoftmax(size, epsilon=0)
softmax = CategoricalSoftmax(size)
param_row = tf.constant(np.random.normal(size=(size, )),
dtype=tf.float64)
params = tf.stack([param_row])
one_hot = np.zeros((1, size))
one_hot[0, 1] = 1
samples = tf.constant(one_hot, dtype=tf.float64)
kl_div = softmax.kl_divergence(tf.stop_gradient(params),
params)
hessian = sess.run(tf.hessians(kl_div, param_row)[0])
gradient = sess.run(
tf.gradients(softmax.log_prob(params, samples),
params)[0][0])
expected = np.matmul(np.array([gradient]),
np.linalg.pinv(hessian))[0]
actual = sess.run(
tf.gradients(dist.log_prob(params, samples),
params)[0][0])
self.assertTrue(np.allclose(actual, expected))
def test_nat_softmax_log_prob():
"""
Test log probabilities of NaturalSoftmax.
"""
with tf.Graph().as_default():
with tf.Session() as sess:
dist = NaturalSoftmax(7)
params = tf.constant(np.random.normal(size=(15, 7)), dtype=tf.float64)
sampled = tf.one_hot([random.randrange(7) for _ in range(15)], 7,
dtype=tf.float64)
actual = sess.run(dist.log_prob(params, sampled))
expected = sess.run(CategoricalSoftmax(7).log_prob(params, sampled))
assert np.allclose(actual, expected)
def test_nat_softmax_determinism():
"""
Make sure that the gradient of NaturalSoftmax doesn't
change from run to run.
"""
with tf.Graph().as_default():
with tf.Session() as sess:
dist = NaturalSoftmax(7)
params = tf.constant(np.random.normal(size=(15, 7)), dtype=tf.float64)
sampled = tf.one_hot([random.randrange(7) for _ in range(15)], 7,
dtype=tf.float64)
batched_grad = tf.gradients(dist.log_prob(params, sampled), params)[0]
first = sess.run(batched_grad)
for _ in range(10):
assert np.allclose(first, sess.run(batched_grad))
def test_nat_softmax_batched():
"""
Test that batched gradients from NaturalSoftmax
give the same results as single gradients.
"""
with tf.Graph().as_default():
with tf.Session() as sess:
dist = NaturalSoftmax(7)
params = tf.constant(np.random.normal(size=(15, 7)), dtype=tf.float64)
sampled = tf.one_hot([random.randrange(7) for _ in range(15)], 7,
dtype=tf.float64)
batched_grad = tf.gradients(dist.log_prob(params, sampled), params)[0]
single_grads = []
for i in range(15):
sub_params = params[i:i+1]
prob = dist.log_prob(sub_params, sampled[i:i+1])
single_grads.append(tf.gradients(prob, sub_params)[0])
single_grad = tf.concat(single_grads, axis=0)
batched, single = sess.run((batched_grad, single_grad))
assert batched.shape == single.shape
assert np.allclose(batched, single)