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pgd_attacks_pt.py
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pgd_attacks_pt.py
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#import tensorflow as tf
#import scipy.io
import numpy as np
from utils_pt import get_predictions, get_predictions_and_gradients
def project_L0_box(y, k, lb, ub):
''' projection of the batch y to a batch x such that:
- each image of the batch x has at most k pixels with non-zero channels
- lb <= x <= ub '''
x = np.copy(y)
p1 = np.sum(x**2, axis=-1)
p2 = np.minimum(np.minimum(ub - x, x - lb), 0)
p2 = np.sum(p2**2, axis=-1)
p3 = np.sort(np.reshape(p1-p2, [p2.shape[0],-1]))[:,-k]
x = x*(np.logical_and(lb <=x, x <= ub)) + lb*(lb > x) + ub*(x > ub)
x *= np.expand_dims((p1 - p2) >= p3.reshape([-1, 1, 1]), -1)
return x
def project_L0_sigma(y, k, sigma, kappa, x_nat):
''' projection of the batch y to a batch x such that:
- 0 <= x <= 1
- each image of the batch x differs from the corresponding one of
x_nat in at most k pixels
- (1 - kappa*sigma)*x_nat <= x <= (1 + kappa*sigma)*x_nat '''
x = np.copy(y)
p1 = 1.0/np.maximum(1e-12, sigma)*(x_nat > 0).astype(float) + 1e12*(x_nat == 0).astype(float)
p2 = 1.0/np.maximum(1e-12, sigma)*(1.0/np.maximum(1e-12, x_nat) - 1)*(x_nat > 0).astype(float) + 1e12*(x_nat == 0).astype(float) + 1e12*(sigma == 0).astype(float)
lmbd_l = np.maximum(-kappa, np.amax(-p1, axis=-1, keepdims=True))
lmbd_u = np.minimum(kappa, np.amin(p2, axis=-1, keepdims=True))
lmbd_unconstr = np.sum((y - x_nat)*sigma*x_nat, axis=-1, keepdims=True)/np.maximum(1e-12, np.sum((sigma*x_nat)**2, axis=-1, keepdims=True))
lmbd = np.maximum(lmbd_l, np.minimum(lmbd_unconstr, lmbd_u))
p12 = np.sum((y - x_nat)**2, axis=-1, keepdims=True)
p22 = np.sum((y - (1 + lmbd*sigma)*x_nat)**2, axis=-1, keepdims=True)
p3 = np.sort(np.reshape(p12 - p22, [x.shape[0],-1]))[:,-k]
x = x_nat + lmbd*sigma*x_nat*((p12 - p22) >= p3.reshape([-1, 1, 1, 1]))
return x
def perturb_L0_box(attack, x_nat, y_nat, lb, ub):
''' PGD attack wrt L0-norm + box constraints
it returns adversarial examples (if found) adv for the images x_nat, with correct labels y_nat,
such that:
- each image of the batch adv differs from the corresponding one of
x_nat in at most k pixels
- lb <= adv - x_nat <= ub
it returns also a vector of flags where 1 means no adversarial example found
(in this case the original image is returned in adv) '''
if attack.rs:
x2 = x_nat + np.random.uniform(lb, ub, x_nat.shape)
x2 = np.clip(x2, 0, 1)
else:
x2 = np.copy(x_nat)
adv_not_found = np.ones(y_nat.shape)
adv = np.zeros(x_nat.shape)
for i in range(attack.num_steps):
if i > 0:
#pred, grad = sess.run([attack.model.correct_prediction, attack.model.grad], feed_dict={attack.model.x_input: x2, attack.model.y_input: y_nat})
pred, grad = get_predictions_and_gradients(attack.model, x2, y_nat)
adv_not_found = np.minimum(adv_not_found, pred.astype(int))
adv[np.logical_not(pred)] = np.copy(x2[np.logical_not(pred)])
grad /= (1e-10 + np.sum(np.abs(grad), axis=(1,2,3), keepdims=True))
x2 = np.add(x2, (np.random.random_sample(grad.shape)-0.5)*1e-12 + attack.step_size * grad, casting='unsafe')
x2 = x_nat + project_L0_box(x2 - x_nat, attack.k, lb, ub)
return adv, adv_not_found
def perturb_L0_sigma(attack, x_nat, y_nat):
''' PGD attack wrt L0-norm + sigma-map constraints
it returns adversarial examples (if found) adv for the images x_nat, with correct labels y_nat,
such that:
- each image of the batch adv differs from the corresponding one of
x_nat in at most k pixels
- (1 - kappa*sigma)*x_nat <= adv <= (1 + kappa*sigma)*x_nat
it returns also a vector of flags where 1 means no adversarial example found
(in this case the original image is returned in adv) '''
if attack.rs:
x2 = x_nat + np.random.uniform(-attack.kappa, attack.kappa, x_nat.shape)
x2 = np.clip(x2, 0, 1)
else:
x2 = np.copy(x_nat)
adv_not_found = np.ones(y_nat.shape)
adv = np.zeros(x_nat.shape)
for i in range(attack.num_steps):
if i > 0:
#pred, grad = sess.run([attack.model.correct_prediction, attack.model.grad], feed_dict={attack.model.x_input: x2, attack.model.y_input: y_nat})
pred, grad = get_predictions_and_gradients(attack.model, x2, y_nat)
adv_not_found = np.minimum(adv_not_found, pred.astype(int))
adv[np.logical_not(pred)] = np.copy(x2[np.logical_not(pred)])
grad /= (1e-10 + np.sum(np.abs(grad), axis=(1,2,3), keepdims=True))
x2 = np.add(x2, (np.random.random_sample(grad.shape)-0.5)*1e-12 + attack.step_size * grad, casting='unsafe')
x2 = project_L0_sigma(x2, attack.k, attack.sigma, attack.kappa, x_nat)
return adv, adv_not_found
def sigma_map(x):
''' creates the sigma-map for the batch x '''
sh = [4]
sh.extend(x.shape)
t = np.zeros(sh)
t[0,:,:-1] = x[:,1:]
t[0,:,-1] = x[:,-1]
t[1,:,1:] = x[:,:-1]
t[1,:,0] = x[:,0]
t[2,:,:,:-1] = x[:,:,1:]
t[2,:,:,-1] = x[:,:,-1]
t[3,:,:,1:] = x[:,:,:-1]
t[3,:,:,0] = x[:,:,0]
mean1 = (t[0] + x + t[1])/3
sd1 = np.sqrt(((t[0]-mean1)**2 + (x-mean1)**2 + (t[1]-mean1)**2)/3)
mean2 = (t[2] + x + t[3])/3
sd2 = np.sqrt(((t[2]-mean2)**2 + (x-mean2)**2 + (t[3]-mean2)**2)/3)
sd = np.minimum(sd1, sd2)
sd = np.sqrt(sd)
return sd
class PGDattack():
def __init__(self, model, args):
self.model = model
self.type_attack = args['type_attack'] # 'L0', 'L0+Linf', 'L0+sigma'
self.num_steps = args['num_steps'] # number of iterations of gradient descent for each restart
self.step_size = args['step_size'] # step size for gradient descent (\eta in the paper)
self.n_restarts = args['n_restarts'] # number of random restarts to perform
self.rs = True # random starting point
self.epsilon = args['epsilon'] # for L0+Linf, the bound on the Linf-norm of the perturbation
self.kappa = args['kappa'] # for L0+sigma (see kappa in the paper), larger kappa means easier and more visible attacks
self.k = args['sparsity'] # maximum number of pixels that can be modified (k_max in the paper)
def perturb(self, x_nat, y_nat):
adv = np.copy(x_nat)
if self.type_attack == 'L0+sigma': self.sigma = sigma_map(x_nat)
for counter in range(self.n_restarts):
if counter == 0:
#corr_pred = sess.run(self.model.correct_prediction, {self.model.x_input: x_nat, self.model.y_input: y_nat})
corr_pred = get_predictions(self.model, x_nat, y_nat)
pgd_adv_acc = np.copy(corr_pred)
if self.type_attack == 'L0':
x_batch_adv, curr_pgd_adv_acc = perturb_L0_box(self, x_nat, y_nat, -x_nat, 1.0 - x_nat)
elif self.type_attack == 'L0+Linf':
x_batch_adv, curr_pgd_adv_acc = perturb_L0_box(self, x_nat, y_nat, np.maximum(-self.epsilon, -x_nat), np.minimum(self.epsilon, 1.0 - x_nat))
elif self.type_attack == 'L0+sigma' and x_nat.shape[3] == 3:
x_batch_adv, curr_pgd_adv_acc = perturb_L0_sigma(self, x_nat, y_nat)
elif self.type_attack == 'L0+sigma' and x_nat.shape[3] == 1:
x_batch_adv, curr_pgd_adv_acc = perturb_L0_box(self, x_nat, y_nat, np.maximum(-self.kappa*self.sigma, -x_nat), np.minimum(self.kappa*self.sigma, 1.0 - x_nat))
pgd_adv_acc = np.minimum(pgd_adv_acc, curr_pgd_adv_acc)
print("Restart {} - Robust accuracy: {}".format(counter + 1, np.sum(pgd_adv_acc)/x_nat.shape[0]))
adv[np.logical_not(curr_pgd_adv_acc)] = x_batch_adv[np.logical_not(curr_pgd_adv_acc)]
pixels_changed = np.sum(np.amax(np.abs(adv - x_nat) > 1e-10, axis=-1), axis=(1,2))
print('Pixels changed: ', pixels_changed)
#corr_pred = sess.run(self.model.correct_prediction, {self.model.x_input: adv, self.model.y_input: y_nat})
corr_pred = get_predictions(self.model, adv, y_nat)
print('Robust accuracy at {} pixels: {:.2f}%'.format(self.k, np.sum(corr_pred)/x_nat.shape[0]*100.0))
print('Maximum perturbation size: {:.5f}'.format(np.amax(np.abs(adv - x_nat))))
return adv, pgd_adv_acc