def __init__(self, sess, x, logits, targeted_label, binary_search_steps,
max_iterations, initial_const, clip_min, clip_max, nb_classes,
batch_size):
self.sess = sess
self.x = x
self.logits = logits
assert logits.op.type != 'Softmax'
self.targeted_label = targeted_label
self.binary_search_steps = binary_search_steps
self.max_iterations = max_iterations
self.initial_const = initial_const
self.clip_min = clip_min
self.clip_max = clip_max
self.batch_size = batch_size
self.repeat = self.binary_search_steps >= 10
self.shape = tuple([self.batch_size] +
list(self.x.get_shape().as_list()[1:]))
self.ori_img = tf.Variable(np.zeros(self.shape),
dtype=tf_dtype,
name='ori_img')
self.const = tf.Variable(np.zeros(self.batch_size),
dtype=tf_dtype,
name='const')
self.score = softmax_cross_entropy_with_logits(
labels=self.targeted_label, logits=self.logits)
self.l2dist = reduce_sum(tf.square(self.x - self.ori_img))
# small self.const will result small adversarial perturbation
self.loss = reduce_sum(self.score * self.const) + self.l2dist
self.grad, = tf.gradients(self.loss, self.x)
def margin_logit_loss(model_logits, label, nb_classes=10, num_classes=None):
"""Computes difference between logit for `label` and next highest logit.
The loss is high when `label` is unlikely (targeted by default).
This follows the same interface as `loss_fn` for TensorOptimizer and
projected_optimization, i.e. it returns a batch of loss values.
"""
if num_classes is not None:
warnings.warn("`num_classes` is depreciated. Switch to `nb_classes`."
" `num_classes` may be removed on or after 2019-04-23.")
nb_classes = num_classes
del num_classes
if 'int' in str(label.dtype):
logit_mask = tf.one_hot(label, depth=nb_classes, axis=-1)
else:
logit_mask = label
if 'int' in str(logit_mask.dtype):
logit_mask = tf.to_float(logit_mask)
try:
label_logits = reduce_sum(logit_mask * model_logits, axis=-1)
except TypeError:
raise TypeError("Could not take row-wise dot product between "
"logit mask, of dtype " + str(logit_mask.dtype)
+ " and model_logits, of dtype "
+ str(model_logits.dtype))
logits_with_target_label_neg_inf = model_logits - logit_mask * 99999
highest_nonlabel_logits = reduce_max(
logits_with_target_label_neg_inf, axis=-1)
loss = highest_nonlabel_logits - label_logits
return loss
def spm(x, model, y=None, n_samples=None, dx_min=-0.1,
dx_max=0.1, n_dxs=5, dy_min=-0.1, dy_max=0.1, n_dys=5,
angle_min=-30, angle_max=30, n_angles=31, black_border_size=0):
"""
TensorFlow implementation of the Spatial Transformation Method.
:return: a tensor for the adversarial example
"""
if y is None:
preds = model.get_probs(x)
# Using model predictions as ground truth to avoid label leaking
preds_max = reduce_max(preds, 1, keepdims=True)
y = tf.to_float(tf.equal(preds, preds_max))
y = tf.stop_gradient(y)
del preds
y = y / reduce_sum(y, 1, keepdims=True)
# Define the range of transformations
dxs = np.linspace(dx_min, dx_max, n_dxs)
dys = np.linspace(dy_min, dy_max, n_dys)
angles = np.linspace(angle_min, angle_max, n_angles)
if n_samples is None:
import itertools
transforms = list(itertools.product(*[dxs, dys, angles]))
else:
sampled_dxs = np.random.choice(dxs, n_samples)
sampled_dys = np.random.choice(dys, n_samples)
sampled_angles = np.random.choice(angles, n_samples)
transforms = zip(sampled_dxs, sampled_dys, sampled_angles)
transformed_ims = parallel_apply_transformations(
x, transforms, black_border_size)
def _compute_xent(x):
preds = model.get_logits(x)
return tf.nn.softmax_cross_entropy_with_logits_v2(
labels=y, logits=preds)
all_xents = tf.map_fn(
_compute_xent,
transformed_ims,
parallel_iterations=1) # Must be 1 to avoid keras race conditions
# Return the adv_x with worst accuracy
# all_xents is n_total_samples x batch_size (SB)
all_xents = tf.stack(all_xents) # SB
# We want the worst case sample, with the largest xent_loss
worst_sample_idx = tf.argmax(all_xents, axis=0) # B
batch_size = tf.shape(x)[0]
keys = tf.stack([
tf.range(batch_size, dtype=tf.int32),
tf.cast(worst_sample_idx, tf.int32)
], axis=1)
transformed_ims_bshwc = tf.einsum('sbhwc->bshwc', transformed_ims)
after_lookup = tf.gather_nd(transformed_ims_bshwc, keys) # BHWC
return after_lookup
def kl_with_logits(p_logits,
q_logits,
scope=None,
loss_collection=tf.GraphKeys.REGULARIZATION_LOSSES):
"""Helper function to compute kl-divergence KL(p || q)
"""
with tf.name_scope(scope, "kl_divergence") as name:
p = tf.nn.softmax(p_logits)
p_log = tf.nn.log_softmax(p_logits)
q_log = tf.nn.log_softmax(q_logits)
loss = reduce_mean(reduce_sum(p * (p_log - q_log), axis=1), name=name)
tf.losses.add_loss(loss, loss_collection)
return loss
def clip_eta(eta, ord, eps):
"""
Helper function to clip the perturbation to epsilon norm ball.
:param eta: A tensor with the current perturbation.
:param ord: Order of the norm (mimics Numpy).
Possible values: np.inf, 1 or 2.
:param eps: Epsilon, bound of the perturbation.
"""
# Clipping perturbation eta to self.ord norm ball
if ord not in [np.inf, 1, 2]:
raise ValueError('ord must be np.inf, 1, or 2.')
reduc_ind = list(xrange(1, len(eta.get_shape())))
avoid_zero_div = 1e-12
if ord == np.inf:
eta = clip_by_value(eta, -eps, eps)
else:
if ord == 1:
raise NotImplementedError(
"The expression below is not the correct way"
" to project onto the L1 norm ball.")
norm = tf.maximum(
avoid_zero_div,
reduce_sum(tf.abs(eta), reduc_ind, keepdims=True))
elif ord == 2:
# avoid_zero_div must go inside sqrt to avoid a divide by zero
# in the gradient through this operation
norm = tf.sqrt(
tf.maximum(
avoid_zero_div,
reduce_sum(tf.square(eta), reduc_ind, keepdims=True)))
# We must *clip* to within the norm ball, not *normalize* onto the
# surface of the ball
factor = tf.minimum(1., div(eps, norm))
eta = eta * factor
return eta
def l2_batch_normalize(x, epsilon=1e-12, scope=None):
"""
Helper function to normalize a batch of vectors.
:param x: the input placeholder
:param epsilon: stabilizes division
:return: the batch of l2 normalized vector
"""
with tf.name_scope(scope, "l2_batch_normalize") as name_scope:
x_shape = tf.shape(x)
x = tf.contrib.layers.flatten(x)
x /= (epsilon + reduce_max(tf.abs(x), 1, keepdims=True))
square_sum = reduce_sum(tf.square(x), 1, keepdims=True)
x_inv_norm = tf.rsqrt(np.sqrt(epsilon) + square_sum)
x_norm = tf.multiply(x, x_inv_norm)
return tf.reshape(x_norm, x_shape, name_scope)
def optimize_linear(grad, eps, ord=np.inf):
"""
Solves for the optimal input to a linear function under a norm constraint.
Optimal_perturbation = argmax_{eta, ||eta||_{ord} < eps} dot(eta, grad)
:param grad: tf tensor containing a batch of gradients
:param eps: float scalar specifying size of constraint region
:param ord: int specifying order of norm
:returns:
tf tensor containing optimal perturbation
"""
# In Python 2, the `list` call in the following line is redundant / harmless.
# In Python 3, the `list` call is needed to convert the iterator returned by `range` into a list.
red_ind = list(range(1, len(grad.get_shape())))
avoid_zero_div = 1e-12
if ord == np.inf:
# Take sign of gradient
optimal_perturbation = tf.sign(grad)
# The following line should not change the numerical results.
# It applies only because `optimal_perturbation` is the output of
# a `sign` op, which has zero derivative anyway.
# It should not be applied for the other norms, where the
# perturbation has a non-zero derivative.
optimal_perturbation = tf.stop_gradient(optimal_perturbation)
elif ord == 1:
abs_grad = tf.abs(grad)
sign = tf.sign(grad)
max_abs_grad = tf.reduce_max(abs_grad, red_ind, keepdims=True)
tied_for_max = tf.to_float(tf.equal(abs_grad, max_abs_grad))
num_ties = tf.reduce_sum(tied_for_max, red_ind, keepdims=True)
optimal_perturbation = sign * tied_for_max / num_ties
elif ord == 2:
square = tf.maximum(
avoid_zero_div,
reduce_sum(tf.square(grad),
reduction_indices=red_ind,
keepdims=True))
optimal_perturbation = grad / tf.sqrt(square)
else:
raise NotImplementedError("Only L-inf, L1 and L2 norms are "
"currently implemented.")
# Scale perturbation to be the solution for the norm=eps rather than
# norm=1 problem
scaled_perturbation = utils_tf.mul(eps, optimal_perturbation)
return scaled_perturbation
def attack_single_step(self, x, eta, g_feat):
"""
TensorFlow implementation of the Fast Feature Gradient. This is a
single step attack similar to Fast Gradient Method that attacks an
internal representation.
:param x: the input placeholder
:param eta: A tensor the same shape as x that holds the perturbation.
:param g_feat: model's internal tensor for guide
:return: a tensor for the adversarial example
"""
adv_x = x + eta
a_feat = self.model.fprop(adv_x)[self.layer]
# feat.shape = (batch, c) or (batch, w, h, c)
axis = list(range(1, len(a_feat.shape)))
# Compute loss
# This is a targeted attack, hence the negative sign
loss = -reduce_sum(tf.square(a_feat - g_feat), axis)
# Define gradient of loss wrt input
grad, = tf.gradients(loss, adv_x)
# Multiply by constant epsilon
scaled_signed_grad = self.eps_iter * tf.sign(grad)
# Add perturbation to original example to obtain adversarial example
adv_x = adv_x + scaled_signed_grad
# If clipping is needed,
# reset all values outside of [clip_min, clip_max]
if (self.clip_min is not None) and (self.clip_max is not None):
adv_x = tf.clip_by_value(adv_x, self.clip_min, self.clip_max)
adv_x = tf.stop_gradient(adv_x)
eta = adv_x - x
eta = clip_eta(eta, self.ord, self.eps)
return eta
def _compute_gradients(self, loss_fn, x, unused_optim_state):
"""Compute gradient estimates using SPSA."""
# Assumes `x` is a list, containing a [1, H, W, C] image
# If static batch dimension is None, tf.reshape to batch size 1
# so that static shape can be inferred
assert len(x) == 1
static_x_shape = x[0].get_shape().as_list()
if static_x_shape[0] is None:
x[0] = tf.reshape(x[0], [1] + static_x_shape[1:])
assert x[0].get_shape().as_list()[0] == 1
x = x[0]
x_shape = x.get_shape().as_list()
def body(i, grad_array):
delta = self._delta
delta_x = self._get_delta(x, delta)
delta_x = tf.concat([delta_x, -delta_x], axis=0)
loss_vals = tf.reshape(
loss_fn(x + delta_x),
[2 * self._num_samples] + [1] * (len(x_shape) - 1))
avg_grad = reduce_mean(loss_vals * delta_x, axis=0) / delta
avg_grad = tf.expand_dims(avg_grad, axis=0)
new_grad_array = grad_array.write(i, avg_grad)
return i + 1, new_grad_array
def cond(i, _):
return i < self._num_iters
_, all_grads = tf.while_loop(
cond,
body,
loop_vars=[
0, tf.TensorArray(size=self._num_iters, dtype=tf_dtype)
],
back_prop=False,
parallel_iterations=1)
avg_grad = reduce_sum(all_grads.stack(), axis=0)
return [avg_grad]
def body(x_in, y_in, domain_in, i_in, cond_in):
# Create graph for model logits and predictions
logits = model.get_logits(x_in)
preds = tf.nn.softmax(logits)
preds_onehot = tf.one_hot(tf.argmax(preds, axis=1), depth=nb_classes)
# create the Jacobian graph
list_derivatives = []
for class_ind in xrange(nb_classes):
derivatives = tf.gradients(logits[:, class_ind], x_in)
list_derivatives.append(derivatives[0])
grads = tf.reshape(tf.stack(list_derivatives),
shape=[nb_classes, -1, nb_features])
# Compute the Jacobian components
# To help with the computation later, reshape the target_class
# and other_class to [nb_classes, -1, 1].
# The last dimention is added to allow broadcasting later.
target_class = tf.reshape(tf.transpose(y_in, perm=[1, 0]),
shape=[nb_classes, -1, 1])
other_classes = tf.cast(tf.not_equal(target_class, 1), tf_dtype)
grads_target = reduce_sum(grads * target_class, axis=0)
grads_other = reduce_sum(grads * other_classes, axis=0)
# Remove the already-used input features from the search space
# Subtract 2 times the maximum value from those value so that
# they won't be picked later
increase_coef = (4 * int(increase) - 2) \
* tf.cast(tf.equal(domain_in, 0), tf_dtype)
target_tmp = grads_target
target_tmp -= increase_coef \
* reduce_max(tf.abs(grads_target), axis=1, keepdims=True)
target_sum = tf.reshape(target_tmp, shape=[-1, nb_features, 1]) \
+ tf.reshape(target_tmp, shape=[-1, 1, nb_features])
other_tmp = grads_other
other_tmp += increase_coef \
* reduce_max(tf.abs(grads_other), axis=1, keepdims=True)
other_sum = tf.reshape(other_tmp, shape=[-1, nb_features, 1]) \
+ tf.reshape(other_tmp, shape=[-1, 1, nb_features])
# Create a mask to only keep features that match conditions
if increase:
scores_mask = ((target_sum > 0) & (other_sum < 0))
else:
scores_mask = ((target_sum < 0) & (other_sum > 0))
# Create a 2D numpy array of scores for each pair of candidate features
scores = tf.cast(scores_mask, tf_dtype) \
* (-target_sum * other_sum) * zero_diagonal
# Extract the best two pixels
best = tf.argmax(tf.reshape(scores,
shape=[-1, nb_features * nb_features]),
axis=1)
p1 = tf.mod(best, nb_features)
p2 = tf.floordiv(best, nb_features)
p1_one_hot = tf.one_hot(p1, depth=nb_features)
p2_one_hot = tf.one_hot(p2, depth=nb_features)
# Check if more modification is needed for each sample
mod_not_done = tf.equal(reduce_sum(y_in * preds_onehot, axis=1), 0)
cond = mod_not_done & (reduce_sum(domain_in, axis=1) >= 2)
# Update the search domain
cond_float = tf.reshape(tf.cast(cond, tf_dtype), shape=[-1, 1])
to_mod = (p1_one_hot + p2_one_hot) * cond_float
domain_out = domain_in - to_mod
# Apply the modification to the images
to_mod_reshape = tf.reshape(to_mod,
shape=([-1] + x_in.shape[1:].as_list()))
if increase:
x_out = tf.minimum(clip_max, x_in + to_mod_reshape * theta)
else:
x_out = tf.maximum(clip_min, x_in - to_mod_reshape * theta)
# Increase the iterator, and check if all misclassifications are done
i_out = tf.add(i_in, 1)
cond_out = reduce_any(cond)
return x_out, y_in, domain_out, i_out, cond_out
def __init__(self, sess, model, beta, decision_rule, batch_size,
confidence, targeted, learning_rate, binary_search_steps,
max_iterations, abort_early, initial_const, clip_min,
clip_max, num_labels, shape):
"""
EAD Attack
Return a tensor that constructs adversarial examples for the given
input. Generate uses tf.py_func in order to operate over tensors.
:param sess: a TF session.
:param model: a cleverhans.model.Model object.
:param beta: Trades off L2 distortion with L1 distortion: higher
produces examples with lower L1 distortion, at the
cost of higher L2 (and typically Linf) distortion
:param decision_rule: EN or L1. Select final adversarial example from
all successful examples based on the least
elastic-net or L1 distortion criterion.
:param batch_size: Number of attacks to run simultaneously.
:param confidence: Confidence of adversarial examples: higher produces
examples with larger l2 distortion, but more
strongly classified as adversarial.
:param targeted: boolean controlling the behavior of the adversarial
examples produced. If set to False, they will be
misclassified in any wrong class. If set to True,
they will be misclassified in a chosen target class.
:param learning_rate: The learning rate for the attack algorithm.
Smaller values produce better results but are
slower to converge.
:param binary_search_steps: The number of times we perform binary
search to find the optimal tradeoff-
constant between norm of the perturbation
and confidence of the classification. Set
'initial_const' to a large value and fix
this param to 1 for speed.
:param max_iterations: The maximum number of iterations. Setting this
to a larger value will produce lower distortion
results. Using only a few iterations requires
a larger learning rate, and will produce larger
distortion results.
:param abort_early: If true, allows early abort when the total
loss starts to increase (greatly speeds up attack,
but hurts performance, particularly on ImageNet)
:param initial_const: The initial tradeoff-constant to use to tune the
relative importance of size of the perturbation
and confidence of classification.
If binary_search_steps is large, the initial
constant is not important. A smaller value of
this constant gives lower distortion results.
For computational efficiency, fix
binary_search_steps to 1 and set this param
to a large value.
:param clip_min: (optional float) Minimum input component value.
:param clip_max: (optional float) Maximum input component value.
:param num_labels: the number of classes in the model's output.
:param shape: the shape of the model's input tensor.
"""
self.sess = sess
self.TARGETED = targeted
self.LEARNING_RATE = learning_rate
self.MAX_ITERATIONS = max_iterations
self.BINARY_SEARCH_STEPS = binary_search_steps
self.ABORT_EARLY = abort_early
self.CONFIDENCE = confidence
self.initial_const = initial_const
self.batch_size = batch_size
self.clip_min = clip_min
self.clip_max = clip_max
self.model = model
self.decision_rule = decision_rule
self.beta = beta
self.beta_t = tf.cast(self.beta, tf_dtype)
self.repeat = binary_search_steps >= 10
self.shape = shape = tuple([batch_size] + list(shape))
# these are variables to be more efficient in sending data to tf
self.timg = tf.Variable(np.zeros(shape), dtype=tf_dtype, name='timg')
self.newimg = tf.Variable(np.zeros(shape),
dtype=tf_dtype,
name='newimg')
self.slack = tf.Variable(np.zeros(shape), dtype=tf_dtype, name='slack')
self.tlab = tf.Variable(np.zeros((batch_size, num_labels)),
dtype=tf_dtype,
name='tlab')
self.const = tf.Variable(np.zeros(batch_size),
dtype=tf_dtype,
name='const')
# and here's what we use to assign them
self.assign_timg = tf.placeholder(tf_dtype, shape, name='assign_timg')
self.assign_newimg = tf.placeholder(tf_dtype,
shape,
name='assign_newimg')
self.assign_slack = tf.placeholder(tf_dtype,
shape,
name='assign_slack')
self.assign_tlab = tf.placeholder(tf_dtype, (batch_size, num_labels),
name='assign_tlab')
self.assign_const = tf.placeholder(tf_dtype, [batch_size],
name='assign_const')
self.global_step = tf.Variable(0, trainable=False)
self.global_step_t = tf.cast(self.global_step, tf_dtype)
# Fast Iterative Shrinkage Thresholding
self.zt = tf.divide(self.global_step_t,
self.global_step_t + tf.cast(3, tf_dtype))
cond1 = tf.cast(
tf.greater(tf.subtract(self.slack, self.timg), self.beta_t),
tf_dtype)
cond2 = tf.cast(
tf.less_equal(tf.abs(tf.subtract(self.slack, self.timg)),
self.beta_t), tf_dtype)
cond3 = tf.cast(
tf.less(tf.subtract(self.slack, self.timg),
tf.negative(self.beta_t)), tf_dtype)
upper = tf.minimum(tf.subtract(self.slack, self.beta_t),
tf.cast(self.clip_max, tf_dtype))
lower = tf.maximum(tf.add(self.slack, self.beta_t),
tf.cast(self.clip_min, tf_dtype))
self.assign_newimg = tf.multiply(cond1, upper)
self.assign_newimg += tf.multiply(cond2, self.timg)
self.assign_newimg += tf.multiply(cond3, lower)
self.assign_slack = self.assign_newimg
self.assign_slack += tf.multiply(self.zt,
self.assign_newimg - self.newimg)
# --------------------------------
self.setter = tf.assign(self.newimg, self.assign_newimg)
self.setter_y = tf.assign(self.slack, self.assign_slack)
# prediction BEFORE-SOFTMAX of the model
self.output = model.get_logits(self.newimg)
self.output_y = model.get_logits(self.slack)
# distance to the input data
self.l2dist = reduce_sum(tf.square(self.newimg - self.timg),
list(range(1, len(shape))))
self.l2dist_y = reduce_sum(tf.square(self.slack - self.timg),
list(range(1, len(shape))))
self.l1dist = reduce_sum(tf.abs(self.newimg - self.timg),
list(range(1, len(shape))))
self.l1dist_y = reduce_sum(tf.abs(self.slack - self.timg),
list(range(1, len(shape))))
self.elasticdist = self.l2dist + tf.multiply(self.l1dist, self.beta_t)
self.elasticdist_y = self.l2dist_y + tf.multiply(
self.l1dist_y, self.beta_t)
if self.decision_rule == 'EN':
self.crit = self.elasticdist
self.crit_p = 'Elastic'
else:
self.crit = self.l1dist
self.crit_p = 'L1'
# compute the probability of the label class versus the maximum other
real = reduce_sum((self.tlab) * self.output, 1)
real_y = reduce_sum((self.tlab) * self.output_y, 1)
other = reduce_max((1 - self.tlab) * self.output - (self.tlab * 10000),
1)
other_y = reduce_max(
(1 - self.tlab) * self.output_y - (self.tlab * 10000), 1)
if self.TARGETED:
# if targeted, optimize for making the other class most likely
loss1 = tf.maximum(ZERO(), other - real + self.CONFIDENCE)
loss1_y = tf.maximum(ZERO(), other_y - real_y + self.CONFIDENCE)
else:
# if untargeted, optimize for making this class least likely.
loss1 = tf.maximum(ZERO(), real - other + self.CONFIDENCE)
loss1_y = tf.maximum(ZERO(), real_y - other_y + self.CONFIDENCE)
# sum up the losses
self.loss21 = reduce_sum(self.l1dist)
self.loss21_y = reduce_sum(self.l1dist_y)
self.loss2 = reduce_sum(self.l2dist)
self.loss2_y = reduce_sum(self.l2dist_y)
self.loss1 = reduce_sum(self.const * loss1)
self.loss1_y = reduce_sum(self.const * loss1_y)
self.loss_opt = self.loss1_y + self.loss2_y
self.loss = self.loss1 + self.loss2 + tf.multiply(
self.beta_t, self.loss21)
self.learning_rate = tf.train.polynomial_decay(self.LEARNING_RATE,
self.global_step,
self.MAX_ITERATIONS,
0,
power=0.5)
# Setup the optimizer and keep track of variables we're creating
start_vars = set(x.name for x in tf.global_variables())
optimizer = tf.train.GradientDescentOptimizer(self.learning_rate)
self.train = optimizer.minimize(self.loss_opt,
var_list=[self.slack],
global_step=self.global_step)
end_vars = tf.global_variables()
new_vars = [x for x in end_vars if x.name not in start_vars]
# these are the variables to initialize when we run
self.setup = []
self.setup.append(self.timg.assign(self.assign_timg))
self.setup.append(self.tlab.assign(self.assign_tlab))
self.setup.append(self.const.assign(self.assign_const))
var_list = [self.global_step] + [self.slack] + [self.newimg] + new_vars
self.init = tf.variables_initializer(var_list=var_list)
def __init__(self, sess, model, batch_size, confidence, targeted,
learning_rate, binary_search_steps, max_iterations,
abort_early, initial_const, clip_min, clip_max, num_labels,
shape):
"""
Return a tensor that constructs adversarial examples for the given
input. Generate uses tf.py_func in order to operate over tensors.
:param sess: a TF session.
:param model: a cleverhans.model.Model object.
:param batch_size: Number of attacks to run simultaneously.
:param confidence: Confidence of adversarial examples: higher produces
examples with larger l2 distortion, but more
strongly classified as adversarial.
:param targeted: boolean controlling the behavior of the adversarial
examples produced. If set to False, they will be
misclassified in any wrong class. If set to True,
they will be misclassified in a chosen target class.
:param learning_rate: The learning rate for the attack algorithm.
Smaller values produce better results but are
slower to converge.
:param binary_search_steps: The number of times we perform binary
search to find the optimal tradeoff-
constant between norm of the purturbation
and confidence of the classification.
:param max_iterations: The maximum number of iterations. Setting this
to a larger value will produce lower distortion
results. Using only a few iterations requires
a larger learning rate, and will produce larger
distortion results.
:param abort_early: If true, allows early aborts if gradient descent
is unable to make progress (i.e., gets stuck in
a local minimum).
:param initial_const: The initial tradeoff-constant to use to tune the
relative importance of size of the pururbation
and confidence of classification.
If binary_search_steps is large, the initial
constant is not important. A smaller value of
this constant gives lower distortion results.
:param clip_min: (optional float) Minimum input component value.
:param clip_max: (optional float) Maximum input component value.
:param num_labels: the number of classes in the model's output.
:param shape: the shape of the model's input tensor.
"""
self.sess = sess
self.TARGETED = targeted
self.LEARNING_RATE = learning_rate
self.MAX_ITERATIONS = max_iterations
self.BINARY_SEARCH_STEPS = binary_search_steps
self.ABORT_EARLY = abort_early
self.CONFIDENCE = confidence
self.initial_const = initial_const
self.batch_size = batch_size
self.clip_min = clip_min
self.clip_max = clip_max
self.model = model
self.repeat = binary_search_steps >= 10
self.shape = shape = tuple([batch_size] + list(shape))
# the variable we're going to optimize over
modifier = tf.Variable(np.zeros(shape, dtype=np_dtype))
# these are variables to be more efficient in sending data to tf
self.timg = tf.Variable(np.zeros(shape), dtype=tf_dtype, name='timg')
self.tlab = tf.Variable(np.zeros((batch_size, num_labels)),
dtype=tf_dtype,
name='tlab')
self.const = tf.Variable(np.zeros(batch_size),
dtype=tf_dtype,
name='const')
# and here's what we use to assign them
self.assign_timg = tf.placeholder(tf_dtype, shape, name='assign_timg')
self.assign_tlab = tf.placeholder(tf_dtype, (batch_size, num_labels),
name='assign_tlab')
self.assign_const = tf.placeholder(tf_dtype, [batch_size],
name='assign_const')
# the resulting instance, tanh'd to keep bounded from clip_min
# to clip_max
self.newimg = (tf.tanh(modifier + self.timg) + 1) / 2
self.newimg = self.newimg * (clip_max - clip_min) + clip_min
# prediction BEFORE-SOFTMAX of the model
self.output = model.get_logits(self.newimg)
# distance to the input data
self.other = (tf.tanh(self.timg) + 1) / \
2 * (clip_max - clip_min) + clip_min
self.l2dist = reduce_sum(tf.square(self.newimg - self.other),
list(range(1, len(shape))))
# compute the probability of the label class versus the maximum other
real = reduce_sum((self.tlab) * self.output, 1)
other = reduce_max((1 - self.tlab) * self.output - self.tlab * 10000,
1)
if self.TARGETED:
# if targeted, optimize for making the other class most likely
loss1 = tf.maximum(ZERO(), other - real + self.CONFIDENCE)
else:
# if untargeted, optimize for making this class least likely.
loss1 = tf.maximum(ZERO(), real - other + self.CONFIDENCE)
# sum up the losses
self.loss2 = reduce_sum(self.l2dist)
self.loss1 = reduce_sum(self.const * loss1)
self.loss = self.loss1 + self.loss2
# Setup the adam optimizer and keep track of variables we're creating
start_vars = set(x.name for x in tf.global_variables())
optimizer = tf.train.AdamOptimizer(self.LEARNING_RATE)
self.train = optimizer.minimize(self.loss, var_list=[modifier])
end_vars = tf.global_variables()
new_vars = [x for x in end_vars if x.name not in start_vars]
# these are the variables to initialize when we run
self.setup = []
self.setup.append(self.timg.assign(self.assign_timg))
self.setup.append(self.tlab.assign(self.assign_tlab))
self.setup.append(self.const.assign(self.assign_const))
self.init = tf.variables_initializer(var_list=[modifier] + new_vars)
def generate(self, x, **kwargs):
"""
Generate symbolic graph for adversarial examples and return.
:param x: The model's symbolic inputs.
:param kwargs: Keyword arguments. See `parse_params` for documentation.
"""
# Parse and save attack-specific parameters
assert self.parse_params(**kwargs)
asserts = []
# If a data range was specified, check that the input was in that range
if self.clip_min is not None:
asserts.append(utils_tf.assert_greater_equal(x,
tf.cast(self.clip_min,
x.dtype)))
if self.clip_max is not None:
asserts.append(utils_tf.assert_less_equal(x,
tf.cast(self.clip_max,
x.dtype)))
# Initialize loop variables
momentum = tf.zeros_like(x)
adv_x = x
# Fix labels to the first model predictions for loss computation
y, _nb_classes = self.get_or_guess_labels(x, kwargs)
y = y / reduce_sum(y, 1, keepdims=True)
targeted = (self.y_target is not None)
def cond(i, _, __):
"""Iterate until number of iterations completed"""
return tf.less(i, self.nb_iter)
def body(i, ax, m):
"""Do a momentum step"""
logits = self.model.get_logits(ax)
loss = softmax_cross_entropy_with_logits(labels=y, logits=logits)
if targeted:
loss = -loss
# Define gradient of loss wrt input
grad, = tf.gradients(loss, ax)
# Normalize current gradient and add it to the accumulated gradient
red_ind = list(range(1, len(grad.get_shape())))
avoid_zero_div = tf.cast(1e-12, grad.dtype)
grad = grad / tf.maximum(
avoid_zero_div,
reduce_mean(tf.abs(grad), red_ind, keepdims=True))
m = self.decay_factor * m + grad
optimal_perturbation = optimize_linear(m, self.eps_iter, self.ord)
if self.ord == 1:
raise NotImplementedError("This attack hasn't been tested for ord=1."
"It's not clear that FGM makes a good inner "
"loop step for iterative optimization since "
"it updates just one coordinate at a time.")
# Update and clip adversarial example in current iteration
ax = ax + optimal_perturbation
ax = x + utils_tf.clip_eta(ax - x, self.ord, self.eps)
if self.clip_min is not None and self.clip_max is not None:
ax = utils_tf.clip_by_value(ax, self.clip_min, self.clip_max)
ax = tf.stop_gradient(ax)
return i + 1, ax, m
_, adv_x, _ = tf.while_loop(
cond, body, (tf.zeros([]), adv_x, momentum), back_prop=True,
maximum_iterations=self.nb_iter)
if self.sanity_checks:
with tf.control_dependencies(asserts):
adv_x = tf.identity(adv_x)
return adv_x
def fgm(x,
logits,
y=None,
eps=0.3,
ord=np.inf,
clip_min=None,
clip_max=None,
targeted=False,
sanity_checks=True):
"""
TensorFlow implementation of the Fast Gradient Method.
:param x: the input placeholder
:param logits: output of model.get_logits
:param y: (optional) A placeholder for the true labels. If targeted
is true, then provide the target label. Otherwise, only provide
this parameter if you'd like to use true labels when crafting
adversarial samples. Otherwise, model predictions are used as
labels to avoid the "label leaking" effect (explained in this
paper: https://arxiv.org/abs/1611.01236). Default is None.
Labels should be one-hot-encoded.
:param eps: the epsilon (input variation parameter)
:param ord: (optional) Order of the norm (mimics NumPy).
Possible values: np.inf, 1 or 2.
:param clip_min: Minimum float value for adversarial example components
:param clip_max: Maximum float value for adversarial example components
:param targeted: Is the attack targeted or untargeted? Untargeted, the
default, will try to make the label incorrect. Targeted
will instead try to move in the direction of being more
like y.
:return: a tensor for the adversarial example
"""
asserts = []
# If a data range was specified, check that the input was in that range
if clip_min is not None:
asserts.append(
utils_tf.assert_greater_equal(x, tf.cast(clip_min, x.dtype)))
if clip_max is not None:
asserts.append(
utils_tf.assert_less_equal(x, tf.cast(clip_max, x.dtype)))
# Make sure the caller has not passed probs by accident
assert logits.op.type != 'Softmax'
if y is None:
# Using model predictions as ground truth to avoid label leaking
preds_max = reduce_max(logits, 1, keepdims=True)
y = tf.to_float(tf.equal(logits, preds_max))
y = tf.stop_gradient(y)
y = y / reduce_sum(y, 1, keepdims=True)
# Compute loss
loss = softmax_cross_entropy_with_logits(labels=y, logits=logits)
if targeted:
loss = -loss
# Define gradient of loss wrt input
grad, = tf.gradients(loss, x)
optimal_perturbation = optimize_linear(grad, eps, ord)
# Add perturbation to original example to obtain adversarial example
adv_x = x + optimal_perturbation
# If clipping is needed, reset all values outside of [clip_min, clip_max]
if (clip_min is not None) or (clip_max is not None):
# We don't currently support one-sided clipping
assert clip_min is not None and clip_max is not None
adv_x = utils_tf.clip_by_value(adv_x, clip_min, clip_max)
if sanity_checks:
with tf.control_dependencies(asserts):
adv_x = tf.identity(adv_x)
return adv_x
