def l2(tt):
"""Applies l2 regularization to TensorTrain object."""
with tf.name_scope(scope, 'l2_regularizer', [tt]) as name:
my_scale = tf.convert_to_tensor(scale,
dtype=tt.dtype.base_dtype,
name='scale')
return tf.mul(my_scale, ops.frobenius_norm_squared(tt), name=name)
def testFrobeniusNormDifferentiableBatch(self):
with self.test_session() as sess:
tt = initializers.random_tensor_batch((3, 3, 3), tt_rank=2, batch_size=5,
dtype=self.dtype)
norm_sq_diff = ops.frobenius_norm_squared(tt, differentiable=True)
variables = [norm_sq_diff, ops.full(tt)]
norm_sq_diff_val, tt_full = sess.run(variables)
desired_norm = np.linalg.norm(tt_full.reshape((5, -1)), axis=1)**2
self.assertAllClose(norm_sq_diff_val, desired_norm, atol=1e-5, rtol=1e-5)
def testFrobeniusNormTens(self):
# Frobenius norm of a batch of TT-tensors.
with self.test_session() as sess:
tt = initializers.tensor_batch_with_random_cores((2, 1, 3), batch_size=3,
dtype=self.dtype)
norm_sq_actual = ops.frobenius_norm_squared(tt)
norm_actual = ops.frobenius_norm(tt)
vars = [norm_sq_actual, norm_actual, ops.full(tt)]
norm_sq_actual_val, norm_actual_val, tt_val = sess.run(vars)
tt_val = tt_val.reshape((3, -1))
norm_sq_desired_val = np.sum(tt_val * tt_val, axis=1)
norm_desired_val = np.sqrt(norm_sq_desired_val)
self.assertAllClose(norm_sq_actual_val, norm_sq_desired_val)
self.assertAllClose(norm_actual_val, norm_desired_val, atol=1e-5,
rtol=1e-5)
def testToAndFromDeltas(self):
# Test converting to and from deltas representation of the tangent space
# element.
what = initializers.random_tensor((2, 3, 4), 4, dtype=self.dtype)
where = initializers.random_tensor((2, 3, 4), 3, dtype=self.dtype)
projected = riemannian.project(what, where)
deltas = riemannian.tangent_space_to_deltas(projected)
reconstructed_projected = riemannian.deltas_to_tangent_space(deltas, where)
# Tangent space element norm can be computed from deltas norm.
projected_normsq_desired = ops.frobenius_norm_squared(projected)
projected_normsq_actual = tf.add_n([tf.reduce_sum(c * c) for c in deltas])
desired_val, actual_val = self.evaluate((ops.full(projected),
ops.full(reconstructed_projected)))
self.assertAllClose(desired_val, actual_val)
desired_val, actual_val = self.evaluate((projected_normsq_desired,
projected_normsq_actual))
self.assertAllClose(desired_val, actual_val)
def testFrobeniusNormMatrix(self):
# Frobenius norm of a TT-matrix.
shape_list = (((2, 2), (3, 4)),
((2, 3, 4), (2, 2, 2)))
rank_list = (1, 2)
with self.test_session() as sess:
for tensor_shape in shape_list:
for rank in rank_list:
tt = initializers.random_matrix(tensor_shape, tt_rank=rank,
dtype=self.dtype)
norm_sq_actual = ops.frobenius_norm_squared(tt)
norm_actual = ops.frobenius_norm(tt)
vars = [norm_sq_actual, norm_actual, ops.full(tt)]
norm_sq_actual_val, norm_actual_val, tt_val = sess.run(vars)
tt_val = tt_val.flatten()
norm_sq_desired_val = tt_val.dot(tt_val)
norm_desired_val = np.linalg.norm(tt_val)
self.assertAllClose(norm_sq_actual_val, norm_sq_desired_val)
self.assertAllClose(norm_actual_val, norm_desired_val, atol=1e-5,
rtol=1e-5)
def testToAndFromDeltasBatch(self):
# Test converting to and from deltas representation of the tangent space
# element in the batch case.
what = initializers.random_matrix_batch(((2, 3, 4), (3, 3, 3)), 4,
batch_size=3, dtype=self.dtype)
where = initializers.random_matrix(((2, 3, 4), (3, 3, 3)), 3,
dtype=self.dtype)
projected = riemannian.project(what, where)
deltas = riemannian.tangent_space_to_deltas(projected)
reconstructed_projected = riemannian.deltas_to_tangent_space(deltas, where)
# Tangent space element norm can be computed from deltas norm.
projected_normsq_desired = ops.frobenius_norm_squared(projected)
d_normssq = [tf.reduce_sum(tf.reshape(c, (3, -1)) ** 2, 1) for c in deltas]
projected_normsq_actual = tf.add_n(d_normssq)
desired_val, actual_val = self.evaluate((ops.full(projected),
ops.full(reconstructed_projected)))
self.assertAllClose(desired_val, actual_val)
desired_val, actual_val = self.evaluate((projected_normsq_desired,
projected_normsq_actual))
self.assertAllClose(desired_val, actual_val)
def testFrobeniusNormTens(self):
# Frobenius norm of a TT-tensor.
shape_list = ((2, 2), (2, 3, 4), (4, 2, 5, 2))
rank_list = (1, 2)
for shape in shape_list:
for rank in rank_list:
tt = initializers.random_tensor(shape,
tt_rank=rank,
dtype=self.dtype)
norm_sq_actual = ops.frobenius_norm_squared(tt)
norm_actual = ops.frobenius_norm(tt, epsilon=0.0)
vars = [norm_sq_actual, norm_actual, ops.full(tt)]
norm_sq_actual_val, norm_actual_val, tt_val = self.evaluate(
vars)
tt_val = tt_val.flatten()
norm_sq_desired_val = tt_val.dot(tt_val)
norm_desired_val = np.linalg.norm(tt_val)
self.assertAllClose(norm_sq_actual_val, norm_sq_desired_val)
self.assertAllClose(norm_actual_val,
norm_desired_val,
atol=1e-5,
rtol=1e-5)
