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hsja.py
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hsja.py
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from __future__ import absolute_import, division, print_function
import numpy as np
def hsja(model,
sample,
clip_max = 1,
clip_min = 0,
constraint = 'l2',
num_iterations = 40,
gamma = 1.0,
target_label = None,
target_image = None,
stepsize_search = 'geometric_progression',
max_num_evals = 1e4,
init_num_evals = 100,
verbose = True):
"""
Main algorithm for HopSkipJumpAttack.
Inputs:
model: the object that has predict method.
predict outputs probability scores.
clip_max: upper bound of the image.
clip_min: lower bound of the image.
constraint: choose between [l2, linf].
num_iterations: number of iterations.
gamma: used to set binary search threshold theta. The binary search
threshold theta is gamma / d^{3/2} for l2 attack and gamma / d^2 for
linf attack.
target_label: integer or None for nontargeted attack.
target_image: an array with the same size as sample, or None.
stepsize_search: choose between 'geometric_progression', 'grid_search'.
max_num_evals: maximum number of evaluations for estimating gradient.
init_num_evals: initial number of evaluations for estimating gradient.
Output:
perturbed image.
"""
# Set parameters
original_label = np.argmax(model.predict(sample))
params = {'clip_max': clip_max, 'clip_min': clip_min,
'shape': sample.shape,
'original_label': original_label,
'target_label': target_label,
'target_image': target_image,
'constraint': constraint,
'num_iterations': num_iterations,
'gamma': gamma,
'd': int(np.prod(sample.shape)),
'stepsize_search': stepsize_search,
'max_num_evals': max_num_evals,
'init_num_evals': init_num_evals,
'verbose': verbose,
}
# Set binary search threshold.
if params['constraint'] == 'l2':
params['theta'] = params['gamma'] / (np.sqrt(params['d']) * params['d'])
else:
params['theta'] = params['gamma'] / (params['d'] ** 2)
# Initialize.
perturbed = initialize(model, sample, params)
# Project the initialization to the boundary.
perturbed, dist_post_update = binary_search_batch(sample,
np.expand_dims(perturbed, 0),
model,
params)
dist = compute_distance(perturbed, sample, constraint)
for j in np.arange(params['num_iterations']):
params['cur_iter'] = j + 1
# Choose delta.
delta = select_delta(params, dist_post_update)
# Choose number of evaluations.
num_evals = int(params['init_num_evals'] * np.sqrt(j+1))
num_evals = int(min([num_evals, params['max_num_evals']]))
# approximate gradient.
gradf = approximate_gradient(model, perturbed, num_evals,
delta, params)
if params['constraint'] == 'linf':
update = np.sign(gradf)
else:
update = gradf
# search step size.
if params['stepsize_search'] == 'geometric_progression':
# find step size.
epsilon = geometric_progression_for_stepsize(perturbed,
update, dist, model, params)
# Update the sample.
perturbed = clip_image(perturbed + epsilon * update,
clip_min, clip_max)
# Binary search to return to the boundary.
perturbed, dist_post_update = binary_search_batch(sample,
perturbed[None], model, params)
elif params['stepsize_search'] == 'grid_search':
# Grid search for stepsize.
epsilons = np.logspace(-4, 0, num=20, endpoint = True) * dist
epsilons_shape = [20] + len(params['shape']) * [1]
perturbeds = perturbed + epsilons.reshape(epsilons_shape) * update
perturbeds = clip_image(perturbeds, params['clip_min'], params['clip_max'])
idx_perturbed = decision_function(model, perturbeds, params)
if np.sum(idx_perturbed) > 0:
# Select the perturbation that yields the minimum distance # after binary search.
perturbed, dist_post_update = binary_search_batch(sample,
perturbeds[idx_perturbed], model, params)
# compute new distance.
dist = compute_distance(perturbed, sample, constraint)
if verbose:
print('iteration: {:d}, {:s} distance {:.4E}'.format(j+1, constraint, dist))
return perturbed
def decision_function(model, images, params):
"""
Decision function output 1 on the desired side of the boundary,
0 otherwise.
"""
images = clip_image(images, params['clip_min'], params['clip_max'])
prob = model.predict(images)
if params['target_label'] is None:
return np.argmax(prob, axis = 1) != params['original_label']
else:
return np.argmax(prob, axis = 1) == params['target_label']
def clip_image(image, clip_min, clip_max):
# Clip an image, or an image batch, with upper and lower threshold.
return np.minimum(np.maximum(clip_min, image), clip_max)
def compute_distance(x_ori, x_pert, constraint = 'l2'):
# Compute the distance between two images.
if constraint == 'l2':
return np.linalg.norm(x_ori - x_pert)
elif constraint == 'linf':
return np.max(abs(x_ori - x_pert))
def approximate_gradient(model, sample, num_evals, delta, params):
clip_max, clip_min = params['clip_max'], params['clip_min']
# Generate random vectors.
noise_shape = [num_evals] + list(params['shape'])
if params['constraint'] == 'l2':
rv = np.random.randn(*noise_shape)
elif params['constraint'] == 'linf':
rv = np.random.uniform(low = -1, high = 1, size = noise_shape)
rv = rv / np.sqrt(np.sum(rv ** 2, axis = (1,2,3), keepdims = True))
perturbed = sample + delta * rv
perturbed = clip_image(perturbed, clip_min, clip_max)
rv = (perturbed - sample) / delta
# query the model.
decisions = decision_function(model, perturbed, params)
decision_shape = [len(decisions)] + [1] * len(params['shape'])
fval = 2 * decisions.astype(float).reshape(decision_shape) - 1.0
# Baseline subtraction (when fval differs)
if np.mean(fval) == 1.0: # label changes.
gradf = np.mean(rv, axis = 0)
elif np.mean(fval) == -1.0: # label not change.
gradf = - np.mean(rv, axis = 0)
else:
fval -= np.mean(fval)
gradf = np.mean(fval * rv, axis = 0)
# Get the gradient direction.
gradf = gradf / np.linalg.norm(gradf)
return gradf
def project(original_image, perturbed_images, alphas, params):
alphas_shape = [len(alphas)] + [1] * len(params['shape'])
alphas = alphas.reshape(alphas_shape)
if params['constraint'] == 'l2':
return (1-alphas) * original_image + alphas * perturbed_images
elif params['constraint'] == 'linf':
out_images = clip_image(
perturbed_images,
original_image - alphas,
original_image + alphas
)
return out_images
def binary_search_batch(original_image, perturbed_images, model, params):
""" Binary search to approach the boundar. """
# Compute distance between each of perturbed image and original image.
dists_post_update = np.array([
compute_distance(
original_image,
perturbed_image,
params['constraint']
)
for perturbed_image in perturbed_images])
# Choose upper thresholds in binary searchs based on constraint.
if params['constraint'] == 'linf':
highs = dists_post_update
# Stopping criteria.
thresholds = np.minimum(dists_post_update * params['theta'], params['theta'])
else:
highs = np.ones(len(perturbed_images))
thresholds = params['theta']
lows = np.zeros(len(perturbed_images))
# Call recursive function.
while np.max((highs - lows) / thresholds) > 1:
# projection to mids.
mids = (highs + lows) / 2.0
mid_images = project(original_image, perturbed_images, mids, params)
# Update highs and lows based on model decisions.
decisions = decision_function(model, mid_images, params)
lows = np.where(decisions == 0, mids, lows)
highs = np.where(decisions == 1, mids, highs)
out_images = project(original_image, perturbed_images, highs, params)
# Compute distance of the output image to select the best choice.
# (only used when stepsize_search is grid_search.)
dists = np.array([
compute_distance(
original_image,
out_image,
params['constraint']
)
for out_image in out_images])
idx = np.argmin(dists)
dist = dists_post_update[idx]
out_image = out_images[idx]
return out_image, dist
def initialize(model, sample, params):
"""
Efficient Implementation of BlendedUniformNoiseAttack in Foolbox.
"""
success = 0
num_evals = 0
if params['target_image'] is None:
# Find a misclassified random noise.
while True:
random_noise = np.random.uniform(params['clip_min'],
params['clip_max'], size = params['shape'])
success = decision_function(model,random_noise[None], params)[0]
num_evals += 1
if success:
break
assert num_evals < 1e4,"Initialization failed! "
"Use a misclassified image as `target_image`"
# Binary search to minimize l2 distance to original image.
low = 0.0
high = 1.0
while high - low > 0.001:
mid = (high + low) / 2.0
blended = (1 - mid) * sample + mid * random_noise
success = decision_function(model, blended[None], params)
if success:
high = mid
else:
low = mid
initialization = (1 - high) * sample + high * random_noise
else:
initialization = params['target_image']
return initialization
def geometric_progression_for_stepsize(x, update, dist, model, params):
"""
Geometric progression to search for stepsize.
Keep decreasing stepsize by half until reaching
the desired side of the boundary,
"""
epsilon = dist / np.sqrt(params['cur_iter'])
def phi(epsilon):
new = x + epsilon * update
success = decision_function(model, new[None], params)
return success
while not phi(epsilon):
epsilon /= 2.0
return epsilon
def select_delta(params, dist_post_update):
"""
Choose the delta at the scale of distance
between x and perturbed sample.
"""
if params['cur_iter'] == 1:
delta = 0.1 * (params['clip_max'] - params['clip_min'])
else:
if params['constraint'] == 'l2':
delta = np.sqrt(params['d']) * params['theta'] * dist_post_update
elif params['constraint'] == 'linf':
delta = params['d'] * params['theta'] * dist_post_update
return delta