def make_loss(self, ll_constraint=True, ll_cutoff=0.004):
"""
Construct the update of the adjacency matrix based on the meta gradients.
Parameters
----------
ll_constraint: bool
Whether to enforce the unnoticeability constraint on the degree distribution.
ll_cutoff: float
Cutoff value for the unnoticeability constraint. Smaller means stricter constraint. 0.004 corresponds to a
p-value of 0.95 in the Chi-square distribution with one degree of freedom.
"""
with self.graph.as_default():
logits_attack = tf.gather(self.logits_final, self.idx_attack)
labels_atk = tf.gather(self.labels_onehot, self.idx_attack)
attack_loss_per_node = tf.nn.softmax_cross_entropy_with_logits_v2(
logits=logits_attack, labels=labels_atk)
attack_loss = tf.reduce_mean(attack_loss_per_node)
# Meta gradient computation.
self.adjacency_meta_grad = tf.multiply(
tf.gradients(attack_loss, self.adjacency_changes)[0],
tf.reshape(self.modified_adjacency, [-1]) * -2 + 1,
name="Meta_gradient")
# Make sure that the minimum entry is 0.
self.adjacency_meta_grad -= tf.reduce_min(self.adjacency_meta_grad)
# Set entries to 0 that could lead to singleton nodes.
singleton_mask = self.filter_potential_singletons()
self.adjacency_meta_grad = tf.multiply(self.adjacency_meta_grad,
singleton_mask)
if ll_constraint:
print("Enforcing likelihood ratio constraint with cutoff {}".
format(ll_cutoff))
allowed_mask, self.ll_ratio = self.log_likelihood_constraint(
ll_cutoff)
# Set entries to 0 that would violate the log likelihood constraint.
self.adjacency_meta_grad = tf.multiply(
self.adjacency_meta_grad, allowed_mask)
# Get argmax of the meta gradients.
adj_meta_grad_argmax = tf.argmax(self.adjacency_meta_grad)
# Compute the index corresponding to the reverse direction of the edge (i.e. in the other triangle of the
# matrix).
adj_argmax_transpose_ix = utils.ravel_index(
utils.unravel_index_tf(adj_meta_grad_argmax,
[self.N, self.N])[::-1],
[self.N, self.N])
# Stack both indices to make sure our matrix remains symmetric.
adj_argmax_combined = tf.stack(
[adj_meta_grad_argmax, adj_argmax_transpose_ix],
name="Meta_grad_argmax_combined")
# Add the change to the perturbations.
self.adjacency_meta_update = tf.scatter_add(
self.adjacency_changes,
indices=adj_argmax_combined,
updates=-2 *
tf.gather(tf.reshape(self.modified_adjacency, [-1]),
adj_argmax_combined) + 1)
if self.attack_features:
# Get meta gradients of the attributes.
self.attribute_meta_grad = tf.multiply(
tf.gradients(attack_loss, self.attribute_changes)[0],
tf.reshape(self.attributes, [-1]) * -2 + 1)
self.attribute_meta_grad -= tf.reduce_min(
self.attribute_meta_grad)
attribute_meta_grad_argmax = tf.argmax(
self.attribute_meta_grad)
self.attribute_meta_update = tf.scatter_add(
self.attribute_changes,
indices=attribute_meta_grad_argmax,
updates=-2 * tf.gather(tf.reshape(self.attributes, [-1]),
attribute_meta_grad_argmax) + 1),
adjacency_meta_grad_max = tf.reduce_max(
self.adjacency_meta_grad)
attribute_meta_grad_max = tf.reduce_max(
self.attribute_meta_grad)
# If the meta gradient of the structure meta gradient is larger, we perform a structure perturbation.
# Otherwise, we change an attribute.
cond = adjacency_meta_grad_max > attribute_meta_grad_max
self.combined_update = tf.cond(
cond, lambda: self.adjacency_meta_update,
lambda: self.attribute_meta_update)
def make_loss(self, ll_constraint=True, ll_cutoff=0.004):
"""
Construct the update of the adjacency matrix based on the (approximate) meta gradients.
Parameters
----------
ll_constraint: bool
Whether to enforce the unnoticeability constraint on the degree distribution.
ll_cutoff: float
Cutoff value for the unnoticeability constraint. Smaller means stricter constraint. 0.004 corresponds to a
p-value of 0.95 in the Chi-square distribution with one degree of freedom.
"""
with self.graph.as_default():
logits_labeled = tf.gather(self.logits, self.idx_labeled)
labels_train = tf.gather(self.labels_onehot, self.idx_labeled)
logits_attack = tf.gather(self.logits, self.idx_unlabeled)
labels_attack = tf.gather(self.labels_onehot, self.idx_attack)
loss_labeled = tf.reduce_mean(
tf.nn.softmax_cross_entropy_with_logits_v2(
logits=logits_labeled, labels=labels_train))
loss_attack = tf.reduce_mean(
tf.nn.softmax_cross_entropy_with_logits_v2(
logits=logits_attack, labels=labels_attack))
if self.lambda_ == 1:
attack_loss = loss_labeled
elif self.lambda_ == 0:
attack_loss = loss_attack
else:
attack_loss = self.lambda_ * loss_labeled + (
1 - self.lambda_) * loss_attack
# This variable "stores" the gradients of every inner training step.
self.grad_sum = tf.Variable(np.zeros(self.N * self.N),
dtype=self.dtype)
self.adjacency_grad = tf.multiply(
tf.gradients(attack_loss, self.adjacency_changes)[0],
tf.reshape(self.modified_adjacency, [-1]) * -2 + 1,
name="Adj_gradient")
# Add the current gradient to the sum.
self.grad_sum_add = tf.assign_add(self.grad_sum,
self.adjacency_grad)
# Make sure that the minimum entry is 0.
self.grad_sum_mod = self.grad_sum - tf.reduce_min(self.grad_sum)
# Set entries to 0 that could lead to singleton nodes.
singleton_mask = self.filter_potential_singletons()
self.grad_sum_mod = tf.multiply(self.grad_sum_mod, singleton_mask)
if ll_constraint:
print("Enforcing likelihood ratio constraint with cutoff {}".
format(ll_cutoff))
allowed_mask, self.ll_ratio = self.log_likelihood_constraint(
ll_cutoff)
# Set entries to 0 that would violate the log likelihood constraint.
self.grad_sum_mod = tf.multiply(self.grad_sum_mod,
allowed_mask)
# Get argmax of the approximate meta gradients.
adj_meta_approx_argmax = tf.argmax(self.grad_sum_mod)
# Compute the index corresponding to the reverse direction of the edge (i.e. in the other triangle of the
# matrix).
adj_argmax_transpose_ix = utils.ravel_index(
utils.unravel_index_tf(adj_meta_approx_argmax,
[self.N, self.N])[::-1],
[self.N, self.N])
# Stack both indices to make sure our matrix remains symmetric.
adj_argmax_combined = tf.stack(
[adj_meta_approx_argmax, adj_argmax_transpose_ix],
name="Meta_approx_argmax_combined")
# Add the change to the perturbations.
self.adjacency_update = tf.scatter_add(
self.adjacency_changes,
indices=adj_argmax_combined,
updates=-2 *
tf.gather(tf.reshape(self.modified_adjacency, [-1]),
adj_argmax_combined) + 1)