art.attacks.evasion

Module providing evasion attacks under a common interface.

Adversarial Patch

class art.attacks.evasion.AdversarialPatch(classifier: CLASSIFIER_NEURALNETWORK_TYPE, rotation_max: float = 22.5, scale_min: float = 0.1, scale_max: float = 1.0, learning_rate: float = 5.0, max_iter: int = 500, batch_size: int = 16, patch_shape: Optional[Tuple[int, int, int]] = None, verbose: bool = True)

Implementation of the adversarial patch attack for square and rectangular images and videos.

Paper link: https://arxiv.org/abs/1712.09665

__init__(classifier: CLASSIFIER_NEURALNETWORK_TYPE, rotation_max: float = 22.5, scale_min: float = 0.1, scale_max: float = 1.0, learning_rate: float = 5.0, max_iter: int = 500, batch_size: int = 16, patch_shape: Optional[Tuple[int, int, int]] = None, verbose: bool = True)

Create an instance of the AdversarialPatch.

Parameters

• classifier – A trained classifier.

• rotation_max (float) – The maximum rotation applied to random patches. The value is expected to be in the range [0, 180].

• scale_min (float) – The minimum scaling applied to random patches. The value should be in the range [0, 1], but less than scale_max.

• scale_max (float) – The maximum scaling applied to random patches. The value should be in the range [0, 1], but larger than scale_min.

• learning_rate (float) – The learning rate of the optimization.

• max_iter (int) – The number of optimization steps.

• batch_size (int) – The size of the training batch.

• patch_shape – The shape of the adversarial patch as a tuple of shape (width, height, nb_channels). Currently only supported for TensorFlowV2Classifier. For classifiers of other frameworks the patch_shape is set to the shape of the input samples.

• verbose (bool) – Show progress bars.

apply_patch(x: numpy.ndarray, scale: float, patch_external: Optional[numpy.ndarray] = None) → numpy.ndarray

A function to apply the learned adversarial patch to images or videos.

Return type

ndarray

Parameters

• x (ndarray) – Instances to apply randomly transformed patch.

• scale (float) – Scale of the applied patch in relation to the classifier input shape.

• patch_external – External patch to apply to images x.

Returns

The patched instances.

generate(*args, **kwargs)

Generate an adversarial patch and return the patch and its mask in arrays.

Parameters

• x – An array with the original input images of shape NHWC or NCHW or input videos of shape NFHWC or NFCHW.

• y – An array with the original true labels.

• mask (np.ndarray) – An boolean array of shape equal to the shape of a single samples (1, H, W) or the shape of x (N, H, W) without their channel dimensions. Any features for which the mask is True can be the center location of the patch during sampling.

Returns

An array with adversarial patch and an array of the patch mask.

set_params(**kwargs) → None

Take in a dictionary of parameters and apply attack-specific checks before saving them as attributes.

Parameters

kwargs – A dictionary of attack-specific parameters.

Adversarial Patch - Numpy

class art.attacks.evasion.AdversarialPatchNumpy(classifier: CLASSIFIER_NEURALNETWORK_TYPE, target: int = 0, rotation_max: float = 22.5, scale_min: float = 0.1, scale_max: float = 1.0, learning_rate: float = 5.0, max_iter: int = 500, clip_patch: Optional[Union[list, tuple]] = None, batch_size: int = 16, verbose: bool = True)

Implementation of the adversarial patch attack for square and rectangular images and videos in Numpy.

Paper link: https://arxiv.org/abs/1712.09665

__init__(classifier: CLASSIFIER_NEURALNETWORK_TYPE, target: int = 0, rotation_max: float = 22.5, scale_min: float = 0.1, scale_max: float = 1.0, learning_rate: float = 5.0, max_iter: int = 500, clip_patch: Optional[Union[list, tuple]] = None, batch_size: int = 16, verbose: bool = True) → None

Create an instance of the AdversarialPatchNumpy.

Parameters

• classifier – A trained classifier.

• target (int) – The target label for the created patch.

• rotation_max (float) – The maximum rotation applied to random patches. The value is expected to be in the range [0, 180].

• scale_min (float) – The minimum scaling applied to random patches. The value should be in the range [0, 1], but less than scale_max.

• scale_max (float) – The maximum scaling applied to random patches. The value should be in the range [0, 1], but larger than scale_min.

• learning_rate (float) – The learning rate of the optimization.

• max_iter (int) – The number of optimization steps.

• clip_patch – The minimum and maximum values for each channel in the form [(float, float), (float, float), (float, float)].

• batch_size (int) – The size of the training batch.

• verbose (bool) – Show progress bars.

apply_patch(x: numpy.ndarray, scale: float, patch_external: Optional[numpy.ndarray] = None, mask: Optional[numpy.ndarray] = None) → numpy.ndarray

A function to apply the learned adversarial patch to images or videos.

Return type

ndarray

Parameters

• x (ndarray) – Instances to apply randomly transformed patch.

• scale (float) – Scale of the applied patch in relation to the classifier input shape.

• patch_external (ndarray) – External patch to apply to images x.

• mask – An boolean array of shape equal to the shape of a single samples (1, H, W) or the shape of x (N, H, W) without their channel dimensions. Any features for which the mask is True can be the center location of the patch during sampling.

Returns

The patched instances.

generate(*args, **kwargs)

Generate an adversarial patch and return the patch and its mask in arrays.

Parameters

• x – An array with the original input images of shape NHWC or NCHW or input videos of shape NFHWC or NFCHW.

• y – An array with the original true labels.

• mask (np.ndarray) – An boolean array of shape equal to the shape of a single samples (1, H, W) or the shape of x (N, H, W) without their channel dimensions. Any features for which the mask is True can be the center location of the patch during sampling.

Returns

An array with adversarial patch and an array of the patch mask.

Adversarial Patch - TensorFlowV2

class art.attacks.evasion.AdversarialPatchTensorFlowV2(classifier: CLASSIFIER_NEURALNETWORK_TYPE, rotation_max: float = 22.5, scale_min: float = 0.1, scale_max: float = 1.0, learning_rate: float = 5.0, max_iter: int = 500, batch_size: int = 16, patch_shape: Optional[Tuple[int, int, int]] = None, verbose: bool = True)

Implementation of the adversarial patch attack for square and rectangular images and videos in TensorFlow v2.

Paper link: https://arxiv.org/abs/1712.09665

__init__(classifier: CLASSIFIER_NEURALNETWORK_TYPE, rotation_max: float = 22.5, scale_min: float = 0.1, scale_max: float = 1.0, learning_rate: float = 5.0, max_iter: int = 500, batch_size: int = 16, patch_shape: Optional[Tuple[int, int, int]] = None, verbose: bool = True)

Create an instance of the AdversarialPatchTensorFlowV2.

Parameters

• classifier – A trained classifier.

• rotation_max (float) – The maximum rotation applied to random patches. The value is expected to be in the range [0, 180].

• scale_min (float) – The minimum scaling applied to random patches. The value should be in the range [0, 1], but less than scale_max.

• scale_max (float) – The maximum scaling applied to random patches. The value should be in the range [0, 1], but larger than scale_min.

• learning_rate (float) – The learning rate of the optimization.

• max_iter (int) – The number of optimization steps.

• batch_size (int) – The size of the training batch.

• patch_shape – The shape of the adversarial patch as a tuple of shape HWC (width, height, nb_channels).

• verbose (bool) – Show progress bars.

apply_patch(x: numpy.ndarray, scale: float, patch_external: Optional[numpy.ndarray] = None, mask: Optional[numpy.ndarray] = None) → numpy.ndarray

A function to apply the learned adversarial patch to images or videos.

Return type

ndarray

Parameters

• x (ndarray) – Instances to apply randomly transformed patch.

• scale (float) – Scale of the applied patch in relation to the classifier input shape.

• patch_external – External patch to apply to images x.

• mask – An boolean array of shape equal to the shape of a single samples (1, H, W) or the shape of x (N, H, W) without their channel dimensions. Any features for which the mask is True can be the center location of the patch during sampling.

Returns

The patched samples.

generate(*args, **kwargs)

Generate an adversarial patch and return the patch and its mask in arrays.

Parameters

• x – An array with the original input images of shape NHWC or input videos of shape NFHWC.

• y – An array with the original true labels.

• mask (np.ndarray) – An boolean array of shape equal to the shape of a single samples (1, H, W) or the shape of x (N, H, W) without their channel dimensions. Any features for which the mask is True can be the center location of the patch during sampling.

Returns

An array with adversarial patch and an array of the patch mask.

reset_patch(initial_patch_value: numpy.ndarray) → None

Reset the adversarial patch.

Parameters

initial_patch_value (ndarray) – Patch value to use for resetting the patch.

Auto Attack

class art.attacks.evasion.AutoAttack(estimator: CLASSIFIER_TYPE, norm: Union[int, float, str] = inf, eps: float = 0.3, eps_step: float = 0.1, attacks: Optional[List[art.attacks.attack.EvasionAttack]] = None, batch_size: int = 32, estimator_orig: Optional[CLASSIFIER_TYPE] = None, targeted: bool = False)

Implementation of the AutoAttack attack.

Paper link: https://arxiv.org/abs/2003.01690

__init__(estimator: CLASSIFIER_TYPE, norm: Union[int, float, str] = inf, eps: float = 0.3, eps_step: float = 0.1, attacks: Optional[List[art.attacks.attack.EvasionAttack]] = None, batch_size: int = 32, estimator_orig: Optional[CLASSIFIER_TYPE] = None, targeted: bool = False)

Create a AutoAttack instance.

Parameters

• estimator – An trained estimator.

• norm – The norm of the adversarial perturbation. Possible values: “inf”, np.inf, 1 or 2.

• eps (float) – Maximum perturbation that the attacker can introduce.

• eps_step (float) – Attack step size (input variation) at each iteration.

• attacks – The list of art.attacks.EvasionAttack attacks to be used for AutoAttack. If it is None or empty the standard attacks (PGD, APGD-ce, APGD-dlr, DeepFool, Square) will be used.

• batch_size (int) – Size of the batch on which adversarial samples are generated.

• estimator_orig – Original estimator to be attacked by adversarial examples.

• targeted (bool) – If False run only untargeted attacks, if True also run targeted attacks against each possible target.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs.

• y – Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,). 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.

• mask (np.ndarray) – An array with a mask broadcastable to input x defining where to apply adversarial perturbations. Shape needs to be broadcastable to the shape of x and can also be of the same shape as x. Any features for which the mask is zero will not be adversarially perturbed.

Returns

An array holding the adversarial examples.

Auto Projected Gradient Descent (Auto-PGD)

class art.attacks.evasion.AutoProjectedGradientDescent(estimator: CLASSIFIER_LOSS_GRADIENTS_TYPE, norm: Union[int, float, str] = inf, eps: float = 0.3, eps_step: float = 0.1, max_iter: int = 100, targeted: bool = False, nb_random_init: int = 5, batch_size: int = 32, loss_type: Optional[str] = None, verbose: bool = True)

Implementation of the Auto Projected Gradient Descent attack.

Paper link: https://arxiv.org/abs/2003.01690

__init__(estimator: CLASSIFIER_LOSS_GRADIENTS_TYPE, norm: Union[int, float, str] = inf, eps: float = 0.3, eps_step: float = 0.1, max_iter: int = 100, targeted: bool = False, nb_random_init: int = 5, batch_size: int = 32, loss_type: Optional[str] = None, verbose: bool = True)

Create a AutoProjectedGradientDescent instance.

Parameters

• estimator – An trained estimator.

• norm – The norm of the adversarial perturbation. Possible values: “inf”, np.inf, 1 or 2.

• eps (float) – Maximum perturbation that the attacker can introduce.

• eps_step (float) – Attack step size (input variation) at each iteration.

• max_iter (int) – The maximum number of iterations.

• targeted (bool) – Indicates whether the attack is targeted (True) or untargeted (False).

• nb_random_init (int) – Number of random initialisations within the epsilon ball. For num_random_init=0 starting at the original input.

• batch_size (int) – Size of the batch on which adversarial samples are generated.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs.

• y – Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,). 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.

• mask (np.ndarray) – An array with a mask broadcastable to input x defining where to apply adversarial perturbations. Shape needs to be broadcastable to the shape of x and can also be of the same shape as x. Any features for which the mask is zero will not be adversarially perturbed.

Returns

An array holding the adversarial examples.

Boundary Attack / Decision-Based Attack

class art.attacks.evasion.BoundaryAttack(estimator: CLASSIFIER_TYPE, targeted: bool = True, delta: float = 0.01, epsilon: float = 0.01, step_adapt: float = 0.667, max_iter: int = 5000, num_trial: int = 25, sample_size: int = 20, init_size: int = 100, min_epsilon: Optional[float] = None, verbose: bool = True)

Implementation of the boundary attack from Brendel et al. (2018). This is a powerful black-box attack that only requires final class prediction.

Paper link: https://arxiv.org/abs/1712.04248

__init__(estimator: CLASSIFIER_TYPE, targeted: bool = True, delta: float = 0.01, epsilon: float = 0.01, step_adapt: float = 0.667, max_iter: int = 5000, num_trial: int = 25, sample_size: int = 20, init_size: int = 100, min_epsilon: Optional[float] = None, verbose: bool = True) → None

Create a boundary attack instance.

Parameters

• estimator – A trained classifier.

• targeted (bool) – Should the attack target one specific class.

• delta (float) – Initial step size for the orthogonal step.

• epsilon (float) – Initial step size for the step towards the target.

• step_adapt (float) – Factor by which the step sizes are multiplied or divided, must be in the range (0, 1).

• max_iter (int) – Maximum number of iterations.

• num_trial (int) – Maximum number of trials per iteration.

• sample_size (int) – Number of samples per trial.

• init_size (int) – Maximum number of trials for initial generation of adversarial examples.

• min_epsilon – Stop attack if perturbation is smaller than min_epsilon.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs to be attacked.

• y – Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,). If self.targeted is true, then y represents the target labels.

• x_adv_init (np.ndarray) – Initial array to act as initial adversarial examples. Same shape as x.

Returns

An array holding the adversarial examples.

Brendel and Bethge Attack

class art.attacks.evasion.BrendelBethgeAttack(estimator: CLASSIFIER_LOSS_GRADIENTS_TYPE, norm: Union[int, float, str] = inf, targeted: bool = False, overshoot: float = 1.1, steps: int = 1000, lr: float = 0.001, lr_decay: float = 0.5, lr_num_decay: int = 20, momentum: float = 0.8, binary_search_steps: int = 10, init_size: int = 100, batch_size: int = 32)

__init__(estimator: CLASSIFIER_LOSS_GRADIENTS_TYPE, norm: Union[int, float, str] = inf, targeted: bool = False, overshoot: float = 1.1, steps: int = 1000, lr: float = 0.001, lr_decay: float = 0.5, lr_num_decay: int = 20, momentum: float = 0.8, binary_search_steps: int = 10, init_size: int = 100, batch_size: int = 32)

Parameters

estimator – An estimator.

generate(*args, **kwargs)

Applies the Brendel & Bethge attack.

Parameters

• x – The original clean inputs.

• y – The labels for inputs x.

• starting_points – Adversarial inputs to use as a starting points, in particular for targeted attacks.

• early_stop – Early-stopping criteria.

mid_points(x0: numpy.ndarray, x1: numpy.ndarray, epsilons: numpy.ndarray, bounds: Tuple[float, float]) → numpy.ndarray

returns a point between x0 and x1 where epsilon = 0 returns x0 and epsilon = 1 returns x1

Carlini and Wagner L_2 Attack

class art.attacks.evasion.CarliniL2Method(classifier: CLASSIFIER_CLASS_LOSS_GRADIENTS_TYPE, confidence: float = 0.0, targeted: bool = False, learning_rate: float = 0.01, binary_search_steps: int = 10, max_iter: int = 10, initial_const: float = 0.01, max_halving: int = 5, max_doubling: int = 5, batch_size: int = 1, verbose: bool = True)

The L_2 optimized attack of Carlini and Wagner (2016). This attack is among the most effective and should be used among the primary attacks to evaluate potential defences. A major difference wrt to the original implementation (https://github.com/carlini/nn_robust_attacks) is that we use line search in the optimization of the attack objective.

Paper link: https://arxiv.org/abs/1608.04644

__init__(classifier: CLASSIFIER_CLASS_LOSS_GRADIENTS_TYPE, confidence: float = 0.0, targeted: bool = False, learning_rate: float = 0.01, binary_search_steps: int = 10, max_iter: int = 10, initial_const: float = 0.01, max_halving: int = 5, max_doubling: int = 5, batch_size: int = 1, verbose: bool = True) → None

Create a Carlini L_2 attack instance.

Parameters

• classifier – A trained classifier.

• confidence (float) – Confidence of adversarial examples: a higher value produces examples that are farther away, from the original input, but classified with higher confidence as the target class.

• targeted (bool) – Should the attack target one specific class.

• learning_rate (float) – The initial learning rate for the attack algorithm. Smaller values produce better results but are slower to converge.

• binary_search_steps (int) – Number of times to adjust constant with binary search (positive value). If binary_search_steps is large, then the algorithm is not very sensitive to the value of initial_const. Note that the values gamma=0.999999 and c_upper=10e10 are hardcoded with the same values used by the authors of the method.

• max_iter (int) – The maximum number of iterations.

• initial_const (float) – The initial trade-off constant c to use to tune the relative importance of distance and confidence. If binary_search_steps is large, the initial constant is not important, as discussed in Carlini and Wagner (2016).

• max_halving (int) – Maximum number of halving steps in the line search optimization.

• max_doubling (int) – Maximum number of doubling steps in the line search optimization.

• batch_size (int) – Size of the batch on which adversarial samples are generated.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs to be attacked.

• y – Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,). If self.targeted is true, then y represents the target labels. If self.targeted is true, then y_val represents the target labels. Otherwise, the targets are the original class labels.

Returns

An array holding the adversarial examples.

Carlini and Wagner L_inf Attack

class art.attacks.evasion.CarliniLInfMethod(classifier: CLASSIFIER_CLASS_LOSS_GRADIENTS_TYPE, confidence: float = 0.0, targeted: bool = False, learning_rate: float = 0.01, max_iter: int = 10, max_halving: int = 5, max_doubling: int = 5, eps: float = 0.3, batch_size: int = 128, verbose: bool = True)

This is a modified version of the L_2 optimized attack of Carlini and Wagner (2016). It controls the L_Inf norm, i.e. the maximum perturbation applied to each pixel.

__init__(classifier: CLASSIFIER_CLASS_LOSS_GRADIENTS_TYPE, confidence: float = 0.0, targeted: bool = False, learning_rate: float = 0.01, max_iter: int = 10, max_halving: int = 5, max_doubling: int = 5, eps: float = 0.3, batch_size: int = 128, verbose: bool = True) → None

Create a Carlini L_Inf attack instance.

Parameters

• classifier – A trained classifier.

• confidence (float) – Confidence of adversarial examples: a higher value produces examples that are farther away, from the original input, but classified with higher confidence as the target class.

• targeted (bool) – Should the attack target one specific class.

• learning_rate (float) – The initial learning rate for the attack algorithm. Smaller values produce better results but are slower to converge.

• max_iter (int) – The maximum number of iterations.

• max_halving (int) – Maximum number of halving steps in the line search optimization.

• max_doubling (int) – Maximum number of doubling steps in the line search optimization.

• eps (float) – An upper bound for the L_0 norm of the adversarial perturbation.

• batch_size (int) – Size of the batch on which adversarial samples are generated.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs to be attacked.

• y – Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,). If self.targeted is true, then y_val represents the target labels. Otherwise, the targets are the original class labels.

Returns

An array holding the adversarial examples.

Decision Tree Attack

class art.attacks.evasion.DecisionTreeAttack(classifier: art.estimators.classification.scikitlearn.ScikitlearnDecisionTreeClassifier, offset: float = 0.001, verbose: bool = True)

Close implementation of Papernot’s attack on decision trees following Algorithm 2 and communication with the authors.

Paper link: https://arxiv.org/abs/1605.07277

__init__(classifier: art.estimators.classification.scikitlearn.ScikitlearnDecisionTreeClassifier, offset: float = 0.001, verbose: bool = True) → None

Parameters

• classifier (ScikitlearnDecisionTreeClassifier) – A trained scikit-learn decision tree model.

• offset (float) – How much the value is pushed away from tree’s threshold.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial examples and return them as an array.

Parameters

• x – An array with the original inputs to be attacked.

• y – Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).

Returns

An array holding the adversarial examples.

DeepFool

class art.attacks.evasion.DeepFool(classifier: CLASSIFIER_CLASS_LOSS_GRADIENTS_TYPE, max_iter: int = 100, epsilon: float = 1e-06, nb_grads: int = 10, batch_size: int = 1, verbose: bool = True)

Implementation of the attack from Moosavi-Dezfooli et al. (2015).

Paper link: https://arxiv.org/abs/1511.04599

__init__(classifier: CLASSIFIER_CLASS_LOSS_GRADIENTS_TYPE, max_iter: int = 100, epsilon: float = 1e-06, nb_grads: int = 10, batch_size: int = 1, verbose: bool = True) → None

Create a DeepFool attack instance.

Parameters

• classifier – A trained classifier.

• max_iter (int) – The maximum number of iterations.

• epsilon (float) – Overshoot parameter.

• nb_grads (int) – The number of class gradients (top nb_grads w.r.t. prediction) to compute. This way only the most likely classes are considered, speeding up the computation.

• batch_size (int) – Batch size

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs to be attacked.

• y – An array with the original labels to be predicted.

Returns

An array holding the adversarial examples.

DPatch

class art.attacks.evasion.DPatch(estimator: OBJECT_DETECTOR_TYPE, patch_shape: Tuple[int, int, int] = (40, 40, 3), learning_rate: float = 5.0, max_iter: int = 500, batch_size: int = 16, verbose: bool = True)

Implementation of the DPatch attack.

Paper link: https://arxiv.org/abs/1806.02299v4

__init__(estimator: OBJECT_DETECTOR_TYPE, patch_shape: Tuple[int, int, int] = (40, 40, 3), learning_rate: float = 5.0, max_iter: int = 500, batch_size: int = 16, verbose: bool = True)

Create an instance of the DPatch.

Parameters

• estimator – A trained object detector.

• patch_shape (Tuple) – The shape of the adversarial path as a tuple of shape (height, width, nb_channels).

• learning_rate (float) – The learning rate of the optimization.

• max_iter (int) – The number of optimization steps.

• batch_size (int) – The size of the training batch.

• verbose (bool) – Show progress bars.

apply_patch(x: numpy.ndarray, patch_external: Optional[numpy.ndarray] = None, random_location: bool = False, mask: Optional[numpy.ndarray] = None) → numpy.ndarray

Apply the adversarial patch to images.

Return type

ndarray

Parameters

• x (ndarray) – Images to be patched.

• patch_external – External patch to apply to images x. If None the attacks patch will be applied.

• random_location (bool) – True if patch location should be random.

• mask – An boolean array of shape equal to the shape of a single samples (1, H, W) or the shape of x (N, H, W) without their channel dimensions. Any features for which the mask is True can be the center location of the patch during sampling.

Returns

The patched images.

generate(*args, **kwargs)

Generate DPatch.

Parameters

• x – Sample images.

• y – Target labels for object detector.

• target_label – The target label of the DPatch attack.

• mask (np.ndarray) – An boolean array of shape equal to the shape of a single samples (1, H, W) or the shape of x (N, H, W) without their channel dimensions. Any features for which the mask is True can be the center location of the patch during sampling.

Returns

Adversarial patch.

RobustDPatch

class art.attacks.evasion.RobustDPatch(estimator: OBJECT_DETECTOR_TYPE, patch_shape: Tuple[int, int, int] = (40, 40, 3), patch_location: Tuple[int, int] = (0, 0), crop_range: Tuple[int, int] = (0, 0), brightness_range: Tuple[float, float] = (1.0, 1.0), rotation_weights: Union[Tuple[float, float, float, float], Tuple[int, int, int, int]] = (1, 0, 0, 0), sample_size: int = 1, learning_rate: float = 5.0, max_iter: int = 500, batch_size: int = 16, verbose: bool = True)

Implementation of a particular variation of the DPatch attack. It follows Lee & Kolter (2019) in using sign gradients with expectations over transformations. The particular transformations supported in this implementation are cropping, rotations by multiples of 90 degrees, and changes in the brightness of the image.

Paper link (original DPatch): https://arxiv.org/abs/1806.02299v4

Paper link (physical-world patch from Lee & Kolter): https://arxiv.org/abs/1906.11897

__init__(estimator: OBJECT_DETECTOR_TYPE, patch_shape: Tuple[int, int, int] = (40, 40, 3), patch_location: Tuple[int, int] = (0, 0), crop_range: Tuple[int, int] = (0, 0), brightness_range: Tuple[float, float] = (1.0, 1.0), rotation_weights: Union[Tuple[float, float, float, float], Tuple[int, int, int, int]] = (1, 0, 0, 0), sample_size: int = 1, learning_rate: float = 5.0, max_iter: int = 500, batch_size: int = 16, verbose: bool = True)

Create an instance of the RobustDPatch.

Parameters

• estimator – A trained object detector.

• patch_shape (Tuple) – The shape of the adversarial patch as a tuple of shape (height, width, nb_channels).

• patch_location (Tuple) – The location of the adversarial patch as a tuple of shape (upper left x, upper left y).

• crop_range (Tuple) – By how much the images may be cropped as a tuple of shape (height, width).

• brightness_range (Tuple) – Range for randomly adjusting the brightness of the image.

• rotation_weights – Sampling weights for random image rotations by (0, 90, 180, 270) degrees clockwise.

• sample_size (int) – Number of samples to be used in expectations over transformation.

• learning_rate (float) – The learning rate of the optimization.

• max_iter (int) – The number of optimization steps.

• batch_size (int) – The size of the training batch.

• verbose (bool) – Show progress bars.

apply_patch(x: numpy.ndarray, patch_external: Optional[numpy.ndarray] = None) → numpy.ndarray

Apply the adversarial patch to images.

Return type

ndarray

Parameters

• x (ndarray) – Images to be patched.

• patch_external – External patch to apply to images x. If None the attacks patch will be applied.

Returns

The patched images.

generate(*args, **kwargs)

Generate RobustDPatch.

Parameters

• x – Sample images.

• y – Target labels for object detector.

Returns

Adversarial patch.

Elastic Net Attack

class art.attacks.evasion.ElasticNet(classifier: CLASSIFIER_CLASS_LOSS_GRADIENTS_TYPE, confidence: float = 0.0, targeted: bool = False, learning_rate: float = 0.01, binary_search_steps: int = 9, max_iter: int = 100, beta: float = 0.001, initial_const: float = 0.001, batch_size: int = 1, decision_rule: str = 'EN', verbose: bool = True)

The elastic net attack of Pin-Yu Chen et al. (2018).

Paper link: https://arxiv.org/abs/1709.04114

__init__(classifier: CLASSIFIER_CLASS_LOSS_GRADIENTS_TYPE, confidence: float = 0.0, targeted: bool = False, learning_rate: float = 0.01, binary_search_steps: int = 9, max_iter: int = 100, beta: float = 0.001, initial_const: float = 0.001, batch_size: int = 1, decision_rule: str = 'EN', verbose: bool = True) → None

Create an ElasticNet attack instance.

Parameters

• classifier – A trained classifier.

• confidence (float) – Confidence of adversarial examples: a higher value produces examples that are farther away, from the original input, but classified with higher confidence as the target class.

• targeted (bool) – Should the attack target one specific class.

• learning_rate (float) – The initial learning rate for the attack algorithm. Smaller values produce better results but are slower to converge.

• binary_search_steps (int) – Number of times to adjust constant with binary search (positive value).

• max_iter (int) – The maximum number of iterations.

• beta (float) – Hyperparameter trading off L2 minimization for L1 minimization.

• initial_const (float) – The initial trade-off constant c to use to tune the relative importance of distance and confidence. If binary_search_steps is large, the initial constant is not important, as discussed in Carlini and Wagner (2016).

• batch_size (int) – Internal size of batches on which adversarial samples are generated.

• decision_rule (str) – Decision rule. ‘EN’ means Elastic Net rule, ‘L1’ means L1 rule, ‘L2’ means L2 rule.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs to be attacked.

• y – Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,). If self.targeted is true, then y represents the target labels. Otherwise, the targets are the original class labels.

Returns

An array holding the adversarial examples.

Fast Gradient Method (FGM)

class art.attacks.evasion.FastGradientMethod(estimator: CLASSIFIER_LOSS_GRADIENTS_TYPE, norm: Union[int, float, str] = inf, eps: Union[int, float, numpy.ndarray] = 0.3, eps_step: Union[int, float, numpy.ndarray] = 0.1, targeted: bool = False, num_random_init: int = 0, batch_size: int = 32, minimal: bool = False)

This attack was originally implemented by Goodfellow et al. (2015) with the infinity norm (and is known as the “Fast Gradient Sign Method”). This implementation extends the attack to other norms, and is therefore called the Fast Gradient Method.

Paper link: https://arxiv.org/abs/1412.6572

__init__(estimator: CLASSIFIER_LOSS_GRADIENTS_TYPE, norm: Union[int, float, str] = inf, eps: Union[int, float, numpy.ndarray] = 0.3, eps_step: Union[int, float, numpy.ndarray] = 0.1, targeted: bool = False, num_random_init: int = 0, batch_size: int = 32, minimal: bool = False) → None

Create a FastGradientMethod instance.

Parameters

• estimator – A trained classifier.

• norm – The norm of the adversarial perturbation. Possible values: “inf”, np.inf, 1 or 2.

• eps – Attack step size (input variation).

• eps_step – Step size of input variation for minimal perturbation computation.

• targeted (bool) – Indicates whether the attack is targeted (True) or untargeted (False)

• num_random_init (int) – Number of random initialisations within the epsilon ball. For random_init=0 starting at the original input.

• batch_size (int) – Size of the batch on which adversarial samples are generated.

• minimal (bool) – Indicates if computing the minimal perturbation (True). If True, also define eps_step for the step size and eps for the maximum perturbation.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs.

• y – Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,). 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.

• mask (np.ndarray) – An array with a mask broadcastable to input x defining where to apply adversarial perturbations. Shape needs to be broadcastable to the shape of x and can also be of the same shape as x. Any features for which the mask is zero will not be adversarially perturbed.

Returns

An array holding the adversarial examples.

Feature Adversaries

class art.attacks.evasion.FeatureAdversaries(classifier: CLASSIFIER_NEURALNETWORK_TYPE, delta: Optional[float] = None, layer: Optional[int] = None, batch_size: int = 32)

This class represent a Feature Adversaries evasion attack.

Paper link: https://arxiv.org/abs/1511.05122

__init__(classifier: CLASSIFIER_NEURALNETWORK_TYPE, delta: Optional[float] = None, layer: Optional[int] = None, batch_size: int = 32)

Create a FeatureAdversaries instance.

Parameters

• classifier – A trained classifier.

• delta – The maximum deviation between source and guide images.

• layer – Index of the representation layer.

• batch_size (int) – Batch size.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – Source samples.

• y – Guide samples.

• kwargs –

  The kwargs are used as options for the minimisation with scipy.optimize.minimize using method=”L-BFGS-B”. Valid options are based on the output of scipy.optimize.show_options(solver=’minimize’, method=’L-BFGS-B’): Minimize a scalar function of one or more variables using the L-BFGS-B algorithm.

  dispNone or int

  If disp is None (the default), then the supplied version of iprint is used. If disp is not None, then it overrides the supplied version of iprint with the behaviour you outlined.

  maxcorint

  The maximum number of variable metric corrections used to define the limited memory matrix. (The limited memory BFGS method does not store the full hessian but uses this many terms in an approximation to it.)

  ftolfloat

  The iteration stops when (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= ftol.

  gtolfloat

  The iteration will stop when max{|proj g_i | i = 1, ..., n} <= gtol where pg_i is the i-th component of the projected gradient.

  epsfloat

  Step size used for numerical approximation of the Jacobian.

  maxfunint

  Maximum number of function evaluations.

  maxiterint

  Maximum number of iterations.

  iprintint, optional

  Controls the frequency of output. iprint < 0 means no output; iprint = 0 print only one line at the last iteration; 0 < iprint < 99 print also f and |proj g| every iprint iterations; iprint = 99 print details of every iteration except n-vectors; iprint = 100 print also the changes of active set and final x; iprint > 100 print details of every iteration including x and g.

  callbackcallable, optional

  Called after each iteration, as callback(xk), where xk is the current parameter vector.

  maxlsint, optional

  Maximum number of line search steps (per iteration). Default is 20.

  The option ftol is exposed via the scipy.optimize.minimize interface, but calling scipy.optimize.fmin_l_bfgs_b directly exposes factr. The relationship between the two is ftol = factr * numpy.finfo(float).eps. I.e., factr multiplies the default machine floating-point precision to arrive at ftol.

Returns

Adversarial examples.

Raises

KeyError – The argument {} in kwargs is not allowed as option for scipy.optimize.minimize using method=”L-BFGS-B”.

Frame Saliency Attack

class art.attacks.evasion.FrameSaliencyAttack(classifier: CLASSIFIER_NEURALNETWORK_TYPE, attacker: art.attacks.attack.EvasionAttack, method: str = 'iterative_saliency', frame_index: int = 1, batch_size: int = 1, verbose: bool = True)

Implementation of the attack framework proposed by Inkawhich et al. (2018). Prioritizes the frame of a sequential input to be adversarially perturbed based on the saliency score of each frame.

Paper link: https://arxiv.org/abs/1811.11875

__init__(classifier: CLASSIFIER_NEURALNETWORK_TYPE, attacker: art.attacks.attack.EvasionAttack, method: str = 'iterative_saliency', frame_index: int = 1, batch_size: int = 1, verbose: bool = True)

Parameters

• classifier – A trained classifier.

• attacker (EvasionAttack) – An adversarial evasion attacker which supports masking. Currently supported: ProjectedGradientDescent, BasicIterativeMethod, FastGradientMethod.

• method (str) – Specifies which method to use: “iterative_saliency” (adds perturbation iteratively to frame with highest saliency score until attack is successful), “iterative_saliency_refresh” (updates perturbation after each iteration), “one_shot” (adds all perturbations at once, i.e. defaults to original attack).

• frame_index (int) – Index of the axis in input (feature) array x representing the frame dimension.

• batch_size (int) – Size of the batch on which adversarial samples are generated.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs.

• y – An array with the original labels to be predicted.

Returns

An array holding the adversarial examples.

High Confidence Low Uncertainty Attack

class art.attacks.evasion.HighConfidenceLowUncertainty(classifier: art.estimators.classification.GPy.GPyGaussianProcessClassifier, conf: float = 0.95, unc_increase: float = 100.0, min_val: float = 0.0, max_val: float = 1.0, verbose: bool = True)

Implementation of the High-Confidence-Low-Uncertainty (HCLU) adversarial example formulation by Grosse et al. (2018)

Paper link: https://arxiv.org/abs/1812.02606

__init__(classifier: art.estimators.classification.GPy.GPyGaussianProcessClassifier, conf: float = 0.95, unc_increase: float = 100.0, min_val: float = 0.0, max_val: float = 1.0, verbose: bool = True) → None

Parameters

• classifier (GPyGaussianProcessClassifier) – A trained model of type GPYGaussianProcessClassifier.

• conf (float) – Confidence that examples should have, if there were to be classified as 1.0 maximally.

• unc_increase (float) – Value uncertainty is allowed to deviate, where 1.0 is original value.

• min_val (float) – minimal value any feature can take.

• max_val (float) – maximal value any feature can take.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial examples and return them as an array.

Parameters

• x – An array with the original inputs to be attacked.

• y – Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).

Returns

An array holding the adversarial examples.

HopSkipJump Attack

class art.attacks.evasion.HopSkipJump(classifier: CLASSIFIER_TYPE, targeted: bool = False, norm: Union[int, float, str] = 2, max_iter: int = 50, max_eval: int = 10000, init_eval: int = 100, init_size: int = 100, verbose: bool = True)

Implementation of the HopSkipJump attack from Jianbo et al. (2019). This is a powerful black-box attack that only requires final class prediction, and is an advanced version of the boundary attack.

Paper link: https://arxiv.org/abs/1904.02144

__init__(classifier: CLASSIFIER_TYPE, targeted: bool = False, norm: Union[int, float, str] = 2, max_iter: int = 50, max_eval: int = 10000, init_eval: int = 100, init_size: int = 100, verbose: bool = True) → None

Create a HopSkipJump attack instance.

Parameters

• classifier – A trained classifier.

• targeted (bool) – Should the attack target one specific class.

• norm – Order of the norm. Possible values: “inf”, np.inf or 2.

• max_iter (int) – Maximum number of iterations.

• max_eval (int) – Maximum number of evaluations for estimating gradient.

• init_eval (int) – Initial number of evaluations for estimating gradient.

• init_size (int) – Maximum number of trials for initial generation of adversarial examples.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs to be attacked.

• y – Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).

• mask (np.ndarray) – An array with a mask broadcastable to input x defining where to apply adversarial perturbations. Shape needs to be broadcastable to the shape of x and can also be of the same shape as x. Any features for which the mask is zero will not be adversarially perturbed.

• x_adv_init (np.ndarray) – Initial array to act as initial adversarial examples. Same shape as x.

• resume (bool) – Allow users to continue their previous attack.

Returns

An array holding the adversarial examples.

Imperceptible ASR Attack

class art.attacks.evasion.ImperceptibleASR(estimator: SPEECH_RECOGNIZER_TYPE, masker: Optional[PsychoacousticMasker], eps: float = 2000.0, learning_rate_1: float = 100.0, max_iter_1: int = 1000, alpha: float = 0.05, learning_rate_2: float = 1.0, max_iter_2: int = 4000, batch_size: int = 16)

Implementation of the imperceptible attack against a speech recognition model.

Paper link: http://proceedings.mlr.press/v97/qin19a.html

__init__(estimator: SPEECH_RECOGNIZER_TYPE, masker: Optional[PsychoacousticMasker], eps: float = 2000.0, learning_rate_1: float = 100.0, max_iter_1: int = 1000, alpha: float = 0.05, learning_rate_2: float = 1.0, max_iter_2: int = 4000, batch_size: int = 16) → None

Create an instance of the ImperceptibleASR.

Parameters

• estimator – A trained speech recognition estimator.

• masker – A Psychoacoustic masker.

• eps (float) – Initial max norm bound for adversarial perturbation.

• learning_rate_1 (float) – Learning rate for stage 1 of attack.

• max_iter_1 (int) – Number of iterations for stage 1 of attack.

• alpha (float) – Initial alpha value for balancing stage 2 loss.

• learning_rate_2 (float) – Learning rate for stage 2 of attack.

• max_iter_2 (int) – Number of iterations for stage 2 of attack.

• batch_size (int) – Batch size.

generate(*args, **kwargs)

Generate imperceptible, adversarial examples.

Parameters

• x – An array with the original inputs to be attacked.

• y – Target values of shape (batch_size,). Each sample in y is a string and it may possess different lengths. A possible example of y could be: y = np.array([‘SIXTY ONE’, ‘HELLO’]).

Returns

An array holding the adversarial examples.

Imperceptible ASR Attack - PyTorch

class art.attacks.evasion.ImperceptibleASRPyTorch(estimator: art.estimators.speech_recognition.pytorch_deep_speech.PyTorchDeepSpeech, initial_eps: float = 0.001, max_iter_1st_stage: int = 1000, max_iter_2nd_stage: int = 4000, learning_rate_1st_stage: float = 0.1, learning_rate_2nd_stage: float = 0.001, optimizer_1st_stage: Optional[torch.optim.Optimizer] = None, optimizer_2nd_stage: Optional[torch.optim.Optimizer] = None, global_max_length: int = 10000, initial_rescale: float = 1.0, rescale_factor: float = 0.8, num_iter_adjust_rescale: int = 10, initial_alpha: float = 0.05, increase_factor_alpha: float = 1.2, num_iter_increase_alpha: int = 20, decrease_factor_alpha: float = 0.8, num_iter_decrease_alpha: int = 50, batch_size: int = 32, use_amp: bool = False, opt_level: str = 'O1')

This class implements the imperceptible, robust, and targeted attack to generate adversarial examples for automatic speech recognition models. This attack will be implemented specifically for DeepSpeech model and is framework dependent, specifically for PyTorch.

Paper link: https://arxiv.org/abs/1903.10346

__init__(estimator: art.estimators.speech_recognition.pytorch_deep_speech.PyTorchDeepSpeech, initial_eps: float = 0.001, max_iter_1st_stage: int = 1000, max_iter_2nd_stage: int = 4000, learning_rate_1st_stage: float = 0.1, learning_rate_2nd_stage: float = 0.001, optimizer_1st_stage: Optional[torch.optim.Optimizer] = None, optimizer_2nd_stage: Optional[torch.optim.Optimizer] = None, global_max_length: int = 10000, initial_rescale: float = 1.0, rescale_factor: float = 0.8, num_iter_adjust_rescale: int = 10, initial_alpha: float = 0.05, increase_factor_alpha: float = 1.2, num_iter_increase_alpha: int = 20, decrease_factor_alpha: float = 0.8, num_iter_decrease_alpha: int = 50, batch_size: int = 32, use_amp: bool = False, opt_level: str = 'O1')

Create a ImperceptibleASRPyTorch instance.

Parameters

• estimator (PyTorchDeepSpeech) – A trained estimator.

• initial_eps (float) – Initial maximum perturbation that the attacker can introduce.

• max_iter_1st_stage (int) – The maximum number of iterations applied for the first stage of the optimization of the attack.

• max_iter_2nd_stage (int) – The maximum number of iterations applied for the second stage of the optimization of the attack.

• learning_rate_1st_stage (float) – The initial learning rate applied for the first stage of the optimization of the attack.

• learning_rate_2nd_stage (float) – The initial learning rate applied for the second stage of the optimization of the attack.

• optimizer_1st_stage – The optimizer applied for the first stage of the optimization of the attack. If None attack will use torch.optim.SGD.

• optimizer_2nd_stage – The optimizer applied for the second stage of the optimization of the attack. If None attack will use torch.optim.SGD.

• global_max_length (int) – The length of the longest audio signal allowed by this attack.

• initial_rescale (float) – Initial rescale coefficient to speedup the decrease of the perturbation size during the first stage of the optimization of the attack.

• rescale_factor (float) – The factor to adjust the rescale coefficient during the first stage of the optimization of the attack.

• num_iter_adjust_rescale (int) – Number of iterations to adjust the rescale coefficient.

• initial_alpha (float) – The initial value of the alpha coefficient used in the second stage of the optimization of the attack.

• increase_factor_alpha (float) – The factor to increase the alpha coefficient used in the second stage of the optimization of the attack.

• num_iter_increase_alpha (int) – Number of iterations to increase alpha.

• decrease_factor_alpha (float) – The factor to decrease the alpha coefficient used in the second stage of the optimization of the attack.

• num_iter_decrease_alpha (int) – Number of iterations to decrease alpha.

• batch_size (int) – Size of the batch on which adversarial samples are generated.

• use_amp (bool) – Whether to use the automatic mixed precision tool to enable mixed precision training or gradient computation, e.g. with loss gradient computation. When set to True, this option is only triggered if there are GPUs available.

• opt_level (str) – Specify a pure or mixed precision optimization level. Used when use_amp is True. Accepted values are O0, O1, O2, and O3.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – Samples of shape (nb_samples, seq_length). Note that, it is allowable that sequences in the batch could have different lengths. A possible example of x could be: x = np.array([np.array([0.1, 0.2, 0.1, 0.4]), np.array([0.3, 0.1])]).

• y – Target values of shape (nb_samples). Each sample in y is a string and it may possess different lengths. A possible example of y could be: y = np.array([‘SIXTY ONE’, ‘HELLO’]). Note that, this class only supports targeted attack.

Returns

An array holding the adversarial examples.

Basic Iterative Method (BIM)

class art.attacks.evasion.BasicIterativeMethod(estimator: CLASSIFIER_LOSS_GRADIENTS_TYPE, eps: Union[int, float, numpy.ndarray] = 0.3, eps_step: Union[int, float, numpy.ndarray] = 0.1, max_iter: int = 100, targeted: bool = False, batch_size: int = 32)

The Basic Iterative Method is the iterative version of FGM and FGSM.

Paper link: https://arxiv.org/abs/1607.02533

__init__(estimator: CLASSIFIER_LOSS_GRADIENTS_TYPE, eps: Union[int, float, numpy.ndarray] = 0.3, eps_step: Union[int, float, numpy.ndarray] = 0.1, max_iter: int = 100, targeted: bool = False, batch_size: int = 32) → None

Create a ProjectedGradientDescent instance.

Parameters

• estimator – A trained classifier.

• eps – Maximum perturbation that the attacker can introduce.

• eps_step – Attack step size (input variation) at each iteration.

• max_iter (int) – The maximum number of iterations.

• targeted (bool) – Indicates whether the attack is targeted (True) or untargeted (False).

• batch_size (int) – Size of the batch on which adversarial samples are generated.

Projected Gradient Descent (PGD)

class art.attacks.evasion.ProjectedGradientDescent(estimator: CLASSIFIER_LOSS_GRADIENTS_TYPE, norm: Union[int, float, str] = inf, eps: Union[int, float, numpy.ndarray] = 0.3, eps_step: Union[int, float, numpy.ndarray] = 0.1, max_iter: int = 100, targeted: bool = False, num_random_init: int = 0, batch_size: int = 32, random_eps: bool = False, verbose: bool = True)

The Projected Gradient Descent attack is an iterative method in which, after each iteration, the perturbation is projected on an lp-ball of specified radius (in addition to clipping the values of the adversarial sample so that it lies in the permitted data range). This is the attack proposed by Madry et al. for adversarial training.

Paper link: https://arxiv.org/abs/1706.06083

__init__(estimator: CLASSIFIER_LOSS_GRADIENTS_TYPE, norm: Union[int, float, str] = inf, eps: Union[int, float, numpy.ndarray] = 0.3, eps_step: Union[int, float, numpy.ndarray] = 0.1, max_iter: int = 100, targeted: bool = False, num_random_init: int = 0, batch_size: int = 32, random_eps: bool = False, verbose: bool = True)

Create a ProjectedGradientDescent instance.

Parameters

• estimator – An trained estimator.

• norm – The norm of the adversarial perturbation supporting “inf”, np.inf, 1 or 2.

• eps – Maximum perturbation that the attacker can introduce.

• eps_step – Attack step size (input variation) at each iteration.

• random_eps (bool) – When True, epsilon is drawn randomly from truncated normal distribution. The literature suggests this for FGSM based training to generalize across different epsilons. eps_step is modified to preserve the ratio of eps / eps_step. The effectiveness of this method with PGD is untested (https://arxiv.org/pdf/1611.01236.pdf).

• max_iter (int) – The maximum number of iterations.

• targeted (bool) – Indicates whether the attack is targeted (True) or untargeted (False).

• num_random_init (int) – Number of random initialisations within the epsilon ball. For num_random_init=0 starting at the original input.

• batch_size (int) – Size of the batch on which adversarial samples are generated.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs.

• y – Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,). 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.

• mask (np.ndarray) – An array with a mask broadcastable to input x defining where to apply adversarial perturbations. Shape needs to be broadcastable to the shape of x and can also be of the same shape as x. Any features for which the mask is zero will not be adversarially perturbed.

Returns

An array holding the adversarial examples.

set_params(**kwargs) → None

Take in a dictionary of parameters and apply attack-specific checks before saving them as attributes.

Parameters

kwargs – A dictionary of attack-specific parameters.

Projected Gradient Descent (PGD) - Numpy

class art.attacks.evasion.ProjectedGradientDescentNumpy(estimator: Union[CLASSIFIER_LOSS_GRADIENTS_TYPE, OBJECT_DETECTOR_TYPE], norm: Union[int, float, str] = inf, eps: Union[int, float, numpy.ndarray] = 0.3, eps_step: Union[int, float, numpy.ndarray] = 0.1, max_iter: int = 100, targeted: bool = False, num_random_init: int = 0, batch_size: int = 32, random_eps: bool = False, verbose: bool = True)

The Projected Gradient Descent attack is an iterative method in which, after each iteration, the perturbation is projected on an lp-ball of specified radius (in addition to clipping the values of the adversarial sample so that it lies in the permitted data range). This is the attack proposed by Madry et al. for adversarial training.

Paper link: https://arxiv.org/abs/1706.06083

__init__(estimator: Union[CLASSIFIER_LOSS_GRADIENTS_TYPE, OBJECT_DETECTOR_TYPE], norm: Union[int, float, str] = inf, eps: Union[int, float, numpy.ndarray] = 0.3, eps_step: Union[int, float, numpy.ndarray] = 0.1, max_iter: int = 100, targeted: bool = False, num_random_init: int = 0, batch_size: int = 32, random_eps: bool = False, verbose: bool = True) → None

Create a ProjectedGradientDescentNumpy instance.

Parameters

• estimator – An trained estimator.

• norm – The norm of the adversarial perturbation supporting “inf”, np.inf, 1 or 2.

• eps – Maximum perturbation that the attacker can introduce.

• eps_step – Attack step size (input variation) at each iteration.

• random_eps (bool) – When True, epsilon is drawn randomly from truncated normal distribution. The literature suggests this for FGSM based training to generalize across different epsilons. eps_step is modified to preserve the ratio of eps / eps_step. The effectiveness of this method with PGD is untested (https://arxiv.org/pdf/1611.01236.pdf).

• max_iter (int) – The maximum number of iterations.

• targeted (bool) – Indicates whether the attack is targeted (True) or untargeted (False)

• num_random_init (int) – Number of random initialisations within the epsilon ball. For num_random_init=0 starting at the original input.

• batch_size (int) – Size of the batch on which adversarial samples are generated.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs.

• y – Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,). 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.

• mask (np.ndarray) – An array with a mask broadcastable to input x defining where to apply adversarial perturbations. Shape needs to be broadcastable to the shape of x and can also be of the same shape as x. Any features for which the mask is zero will not be adversarially perturbed.

Returns

An array holding the adversarial examples.

Projected Gradient Descent (PGD) - PyTorch

class art.attacks.evasion.ProjectedGradientDescentPyTorch(estimator: PyTorchClassifier, norm: Union[int, float, str] = inf, eps: Union[int, float, numpy.ndarray] = 0.3, eps_step: Union[int, float, numpy.ndarray] = 0.1, max_iter: int = 100, targeted: bool = False, num_random_init: int = 0, batch_size: int = 32, random_eps: bool = False, verbose: bool = True)

The Projected Gradient Descent attack is an iterative method in which, after each iteration, the perturbation is projected on an lp-ball of specified radius (in addition to clipping the values of the adversarial sample so that it lies in the permitted data range). This is the attack proposed by Madry et al. for adversarial training.

Paper link: https://arxiv.org/abs/1706.06083

__init__(estimator: PyTorchClassifier, norm: Union[int, float, str] = inf, eps: Union[int, float, numpy.ndarray] = 0.3, eps_step: Union[int, float, numpy.ndarray] = 0.1, max_iter: int = 100, targeted: bool = False, num_random_init: int = 0, batch_size: int = 32, random_eps: bool = False, verbose: bool = True)

Create a ProjectedGradientDescentPyTorch instance.

Parameters

• estimator – An trained estimator.

• norm – The norm of the adversarial perturbation. Possible values: “inf”, np.inf, 1 or 2.

• eps – Maximum perturbation that the attacker can introduce.

• eps_step – Attack step size (input variation) at each iteration.

• random_eps (bool) – When True, epsilon is drawn randomly from truncated normal distribution. The literature suggests this for FGSM based training to generalize across different epsilons. eps_step is modified to preserve the ratio of eps / eps_step. The effectiveness of this method with PGD is untested (https://arxiv.org/pdf/1611.01236.pdf).

• max_iter (int) – The maximum number of iterations.

• targeted (bool) – Indicates whether the attack is targeted (True) or untargeted (False).

• num_random_init (int) – Number of random initialisations within the epsilon ball. For num_random_init=0 starting at the original input.

• batch_size (int) – Size of the batch on which adversarial samples are generated.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs.

• y – Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,). 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.

• mask (np.ndarray) – An array with a mask broadcastable to input x defining where to apply adversarial perturbations. Shape needs to be broadcastable to the shape of x and can also be of the same shape as x. Any features for which the mask is zero will not be adversarially perturbed.

Returns

An array holding the adversarial examples.

Projected Gradient Descent (PGD) - TensorFlowV2

class art.attacks.evasion.ProjectedGradientDescentTensorFlowV2(estimator: TensorFlowV2Classifier, norm: Union[int, float, str] = inf, eps: Union[int, float, numpy.ndarray] = 0.3, eps_step: Union[int, float, numpy.ndarray] = 0.1, max_iter: int = 100, targeted: bool = False, num_random_init: int = 0, batch_size: int = 32, random_eps: bool = False, verbose: bool = True)

The Projected Gradient Descent attack is an iterative method in which, after each iteration, the perturbation is projected on an lp-ball of specified radius (in addition to clipping the values of the adversarial sample so that it lies in the permitted data range). This is the attack proposed by Madry et al. for adversarial training.

Paper link: https://arxiv.org/abs/1706.06083

__init__(estimator: TensorFlowV2Classifier, norm: Union[int, float, str] = inf, eps: Union[int, float, numpy.ndarray] = 0.3, eps_step: Union[int, float, numpy.ndarray] = 0.1, max_iter: int = 100, targeted: bool = False, num_random_init: int = 0, batch_size: int = 32, random_eps: bool = False, verbose: bool = True)

Create a ProjectedGradientDescentTensorFlowV2 instance.

Parameters

• estimator – An trained estimator.

• norm – The norm of the adversarial perturbation. Possible values: np.inf, 1 or 2.

• eps – Maximum perturbation that the attacker can introduce.

• eps_step – Attack step size (input variation) at each iteration.

• random_eps (bool) – When True, epsilon is drawn randomly from truncated normal distribution. The literature suggests this for FGSM based training to generalize across different epsilons. eps_step is modified to preserve the ratio of eps / eps_step. The effectiveness of this method with PGD is untested (https://arxiv.org/pdf/1611.01236.pdf).

• max_iter (int) – The maximum number of iterations.

• targeted (bool) – Indicates whether the attack is targeted (True) or untargeted (False).

• num_random_init (int) – Number of random initialisations within the epsilon ball. For num_random_init=0 starting at the original input.

• batch_size (int) – Size of the batch on which adversarial samples are generated.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs.

• y – Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,). 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.

• mask (np.ndarray) – An array with a mask broadcastable to input x defining where to apply adversarial perturbations. Shape needs to be broadcastable to the shape of x and can also be of the same shape as x. Any features for which the mask is zero will not be adversarially perturbed.

Returns

An array holding the adversarial examples.

NewtonFool

class art.attacks.evasion.NewtonFool(classifier: CLASSIFIER_CLASS_LOSS_GRADIENTS_TYPE, max_iter: int = 100, eta: float = 0.01, batch_size: int = 1, verbose: bool = True)

Implementation of the attack from Uyeong Jang et al. (2017).

Paper link: http://doi.acm.org/10.1145/3134600.3134635

__init__(classifier: CLASSIFIER_CLASS_LOSS_GRADIENTS_TYPE, max_iter: int = 100, eta: float = 0.01, batch_size: int = 1, verbose: bool = True) → None

Create a NewtonFool attack instance.

Parameters

• classifier – A trained classifier.

• max_iter (int) – The maximum number of iterations.

• eta (float) – The eta coefficient.

• batch_size (int) – Size of the batch on which adversarial samples are generated.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in a Numpy array.

Parameters

• x – An array with the original inputs to be attacked.

• y – An array with the original labels to be predicted.

Returns

An array holding the adversarial examples.

PixelAttack

class art.attacks.evasion.PixelAttack(classifier: CLASSIFIER_NEURALNETWORK_TYPE, th: Optional[int] = None, es: int = 0, targeted: bool = False, verbose: bool = False)

This attack was originally implemented by Vargas et al. (2019). It is generalisation of One Pixel Attack originally implemented by Su et al. (2019).

One Pixel Attack Paper link: https://ieeexplore.ieee.org/abstract/document/8601309/citations#citations (arXiv link: https://arxiv.org/pdf/1710.08864.pdf)

Pixel Attack Paper link: https://arxiv.org/abs/1906.06026

__init__(classifier: CLASSIFIER_NEURALNETWORK_TYPE, th: Optional[int] = None, es: int = 0, targeted: bool = False, verbose: bool = False) → None

Create a PixelAttack instance.

Parameters

• classifier – A trained classifier.

• th – threshold value of the Pixel/ Threshold attack. th=None indicates finding a minimum threshold.

• es (int) – Indicates whether the attack uses CMAES (0) or DE (1) as Evolutionary Strategy.

• targeted (bool) – Indicates whether the attack is targeted (True) or untargeted (False).

• verbose (bool) – Indicates whether to print verbose messages of ES used.

ThresholdAttack

class art.attacks.evasion.ThresholdAttack(classifier: CLASSIFIER_NEURALNETWORK_TYPE, th: Optional[int] = None, es: int = 0, targeted: bool = False, verbose: bool = False)

This attack was originally implemented by Vargas et al. (2019).

Paper link: https://arxiv.org/abs/1906.06026

__init__(classifier: CLASSIFIER_NEURALNETWORK_TYPE, th: Optional[int] = None, es: int = 0, targeted: bool = False, verbose: bool = False) → None

Create a PixelThreshold instance.

Parameters

• classifier – A trained classifier.

• th – threshold value of the Pixel/ Threshold attack. th=None indicates finding a minimum threshold.

• es (int) – Indicates whether the attack uses CMAES (0) or DE (1) as Evolutionary Strategy.

• targeted (bool) – Indicates whether the attack is targeted (True) or untargeted (False).

• verbose (bool) – Indicates whether to print verbose messages of ES used.

Jacobian Saliency Map Attack (JSMA)

class art.attacks.evasion.SaliencyMapMethod(classifier: CLASSIFIER_CLASS_LOSS_GRADIENTS_TYPE, theta: float = 0.1, gamma: float = 1.0, batch_size: int = 1, verbose: bool = True)

Implementation of the Jacobian-based Saliency Map Attack (Papernot et al. 2016).

Paper link: https://arxiv.org/abs/1511.07528

__init__(classifier: CLASSIFIER_CLASS_LOSS_GRADIENTS_TYPE, theta: float = 0.1, gamma: float = 1.0, batch_size: int = 1, verbose: bool = True) → None

Create a SaliencyMapMethod instance.

Parameters

• classifier – A trained classifier.

• theta (float) – Amount of Perturbation introduced to each modified feature per step (can be positive or negative).

• gamma (float) – Maximum fraction of features being perturbed (between 0 and 1).

• batch_size (int) – Size of the batch on which adversarial samples are generated.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs to be attacked.

• y – Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).

Returns

An array holding the adversarial examples.

Shadow Attack

class art.attacks.evasion.ShadowAttack(estimator: Union[art.estimators.classification.tensorflow.TensorFlowV2Classifier, art.estimators.classification.pytorch.PyTorchClassifier], sigma: float = 0.5, nb_steps: int = 300, learning_rate: float = 0.1, lambda_tv: float = 0.3, lambda_c: float = 1.0, lambda_s: float = 0.5, batch_size: int = 400, targeted: bool = False, verbose: bool = True)

Implementation of the Shadow Attack.

Paper link: https://arxiv.org/abs/2003.08937

__init__(estimator: Union[art.estimators.classification.tensorflow.TensorFlowV2Classifier, art.estimators.classification.pytorch.PyTorchClassifier], sigma: float = 0.5, nb_steps: int = 300, learning_rate: float = 0.1, lambda_tv: float = 0.3, lambda_c: float = 1.0, lambda_s: float = 0.5, batch_size: int = 400, targeted: bool = False, verbose: bool = True)

Create an instance of the ShadowAttack.

Parameters

• estimator – A trained classifier.

• sigma (float) – Standard deviation random Gaussian Noise.

• nb_steps (int) – Number of SGD steps.

• learning_rate (float) – Learning rate for SGD.

• lambda_tv (float) – Scalar penalty weight for total variation of the perturbation.

• lambda_c (float) – Scalar penalty weight for change in the mean of each color channel of the perturbation.

• lambda_s (float) – Scalar penalty weight for similarity of color channels in perturbation.

• batch_size (int) – The size of the training batch.

• targeted (bool) – True if the attack is targeted.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array. This requires a lot of memory, therefore it accepts only a single samples as input, e.g. a batch of size 1.

Parameters

• x – An array of a single original input sample.

• y – An array of a single target label.

Returns

An array with the adversarial examples.

ShapeShifter Attack

class art.attacks.evasion.ShapeShifter(estimator: art.estimators.object_detection.tensorflow_faster_rcnn.TensorFlowFasterRCNN, random_transform: collections.abc.Callable, box_classifier_weight: float = 1.0, box_localizer_weight: float = 2.0, rpn_classifier_weight: float = 1.0, rpn_localizer_weight: float = 2.0, box_iou_threshold: float = 0.5, box_victim_weight: float = 0.0, box_target_weight: float = 0.0, box_victim_cw_weight: float = 0.0, box_victim_cw_confidence: float = 0.0, box_target_cw_weight: float = 0.0, box_target_cw_confidence: float = 0.0, rpn_iou_threshold: float = 0.5, rpn_background_weight: float = 0.0, rpn_foreground_weight: float = 0.0, rpn_cw_weight: float = 0.0, rpn_cw_confidence: float = 0.0, similarity_weight: float = 0.0, learning_rate: float = 1.0, optimizer: str = 'GradientDescentOptimizer', momentum: float = 0.0, decay: float = 0.0, sign_gradients: bool = False, random_size: int = 10, max_iter: int = 10, texture_as_input: bool = False, use_spectral: bool = True, soft_clip: bool = False)

Implementation of the ShapeShifter attack. This is a robust physical adversarial attack on Faster R-CNN object detector and is developed in TensorFlow.

Paper link: https://arxiv.org/abs/1804.05810

__init__(estimator: art.estimators.object_detection.tensorflow_faster_rcnn.TensorFlowFasterRCNN, random_transform: collections.abc.Callable, box_classifier_weight: float = 1.0, box_localizer_weight: float = 2.0, rpn_classifier_weight: float = 1.0, rpn_localizer_weight: float = 2.0, box_iou_threshold: float = 0.5, box_victim_weight: float = 0.0, box_target_weight: float = 0.0, box_victim_cw_weight: float = 0.0, box_victim_cw_confidence: float = 0.0, box_target_cw_weight: float = 0.0, box_target_cw_confidence: float = 0.0, rpn_iou_threshold: float = 0.5, rpn_background_weight: float = 0.0, rpn_foreground_weight: float = 0.0, rpn_cw_weight: float = 0.0, rpn_cw_confidence: float = 0.0, similarity_weight: float = 0.0, learning_rate: float = 1.0, optimizer: str = 'GradientDescentOptimizer', momentum: float = 0.0, decay: float = 0.0, sign_gradients: bool = False, random_size: int = 10, max_iter: int = 10, texture_as_input: bool = False, use_spectral: bool = True, soft_clip: bool = False)

Create an instance of the ShapeShifter.

Parameters

• estimator (TensorFlowFasterRCNN) – A trained object detector.

• random_transform – A function applies random transformations to images/textures.

• box_classifier_weight (float) – Weight of box classifier loss.

• box_localizer_weight (float) – Weight of box localizer loss.

• rpn_classifier_weight (float) – Weight of RPN classifier loss.

• rpn_localizer_weight (float) – Weight of RPN localizer loss.

• box_iou_threshold (float) – Box intersection over union threshold.

• box_victim_weight (float) – Weight of box victim loss.

• box_target_weight (float) – Weight of box target loss.

• box_victim_cw_weight (float) – Weight of box victim CW loss.

• box_victim_cw_confidence (float) – Confidence of box victim CW loss.

• box_target_cw_weight (float) – Weight of box target CW loss.

• box_target_cw_confidence (float) – Confidence of box target CW loss.

• rpn_iou_threshold (float) – RPN intersection over union threshold.

• rpn_background_weight (float) – Weight of RPN background loss.

• rpn_foreground_weight (float) – Weight of RPN foreground loss.

• rpn_cw_weight (float) – Weight of RPN CW loss.

• rpn_cw_confidence (float) – Confidence of RPN CW loss.

• similarity_weight (float) – Weight of similarity loss.

• learning_rate (float) – Learning rate.

• optimizer (str) – Optimizer including one of the following choices: GradientDescentOptimizer, MomentumOptimizer, RMSPropOptimizer, AdamOptimizer.

• momentum (float) – Momentum for RMSPropOptimizer, MomentumOptimizer.

• decay (float) – Learning rate decay for RMSPropOptimizer.

• sign_gradients (bool) – Whether to use the sign of gradients for optimization.

• random_size (int) – Random sample size.

• max_iter (int) – Maximum number of iterations.

• texture_as_input (bool) – Whether textures are used as inputs instead of images.

• use_spectral (bool) – Whether to use spectral with textures.

• soft_clip (bool) – Whether to apply soft clipping on textures.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – Sample image/texture.

• y – Not used.

• label (Dict[str, List[np.ndarray]]) –

  A dictionary of target labels for object detector. The fields of the dictionary are as follows:

  • groundtruth_boxes_list: A list of nb_samples size of 2-D tf.float32 tensors of shape

    [num_boxes, 4] containing coordinates of the groundtruth boxes. Groundtruth boxes are provided in [y_min, x_min, y_max, x_max] format and also assumed to be normalized as well as clipped relative to the image window with conditions y_min <= y_max and x_min <= x_max.

  • groundtruth_classes_list: A list of nb_samples size of 1-D tf.float32 tensors of shape

    [num_boxes] containing the class targets with the zero index assumed to map to the first non-background class.

  • groundtruth_weights_list: A list of nb_samples size of 1-D tf.float32 tensors of shape

    [num_boxes] containing weights for groundtruth boxes.

• mask (np.ndarray.) – Input mask.

• target_class (int) – Target class.

• victim_class (int) – Victim class.

• custom_loss (Tensor) – Custom loss function from users.

• rendering_function (Callable) – A rendering function to use textures as input.

Returns

Adversarial image/texture.

SimBA Attack

class art.attacks.evasion.SimBA(classifier: CLASSIFIER_TYPE, attack: str = 'dct', max_iter: int = 3000, order: str = 'random', epsilon: float = 0.1, freq_dim: int = 4, stride: int = 1, targeted: bool = False, batch_size: int = 1)

__init__(classifier: CLASSIFIER_TYPE, attack: str = 'dct', max_iter: int = 3000, order: str = 'random', epsilon: float = 0.1, freq_dim: int = 4, stride: int = 1, targeted: bool = False, batch_size: int = 1)

Create a SimBA (dct) attack instance.

Parameters

• classifier – A trained classifier.

• attack (str) – attack type: pixel (px) or DCT (dct) attacks

• max_iter (int) – The maximum number of iterations.

• epsilon (float) – Overshoot parameter.

• order (str) – order of pixel attacks: random or diagonal (diag)

• freq_dim (int) – dimensionality of 2D frequency space (DCT).

• stride (int) – stride for block order (DCT).

• targeted (bool) – perform targeted attack

• batch_size (int) – Batch size (but, batch process unavailable in this implementation)

diagonal_order(image_size, channels)

Defines a diagonal order for pixel attacks. order is fixed across diagonals but are randomized across channels and within the diagonal e.g. [1, 2, 5] [3, 4, 8] [6, 7, 9]

Parameters

• image_size – image size (i.e., width or height)

• channels – the number of channels

Return z

An array holding the diagonal order of pixel attacks.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs to be attacked.

• y – An array with the original labels to be predicted.

Returns

An array holding the adversarial examples.

Spatial Transformations Attack

class art.attacks.evasion.SpatialTransformation(classifier: CLASSIFIER_NEURALNETWORK_TYPE, max_translation: float = 0.0, num_translations: int = 1, max_rotation: float = 0.0, num_rotations: int = 1, verbose: bool = True)

Implementation of the spatial transformation attack using translation and rotation of inputs. The attack conducts black-box queries to the target model in a grid search over possible translations and rotations to find optimal attack parameters.

Paper link: https://arxiv.org/abs/1712.02779

__init__(classifier: CLASSIFIER_NEURALNETWORK_TYPE, max_translation: float = 0.0, num_translations: int = 1, max_rotation: float = 0.0, num_rotations: int = 1, verbose: bool = True) → None

Parameters

• classifier – A trained classifier.

• max_translation (float) – The maximum translation in any direction as percentage of image size. The value is expected to be in the range [0, 100].

• num_translations (int) – The number of translations to search on grid spacing per direction.

• max_rotation (float) – The maximum rotation in either direction in degrees. The value is expected to be in the range [0, 180].

• num_rotations (int) – The number of rotations to search on grid spacing.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs.

• y – An array with the original labels to be predicted.

Returns

An array holding the adversarial examples.

Square Attack

class art.attacks.evasion.SquareAttack(estimator: CLASSIFIER_TYPE, norm: Union[int, float, str] = inf, max_iter: int = 100, eps: float = 0.3, p_init: float = 0.8, nb_restarts: int = 1, batch_size: int = 128, verbose: bool = True)

__init__(estimator: CLASSIFIER_TYPE, norm: Union[int, float, str] = inf, max_iter: int = 100, eps: float = 0.3, p_init: float = 0.8, nb_restarts: int = 1, batch_size: int = 128, verbose: bool = True)

Create a SquareAttack instance.

Parameters

• estimator – An trained estimator.

• norm – The norm of the adversarial perturbation. Possible values: “inf”, np.inf, 1 or 2.

• max_iter (int) – Maximum number of iterations.

• eps (float) – Maximum perturbation that the attacker can introduce.

• p_init (float) – Initial fraction of elements.

• nb_restarts (int) – Number of restarts.

• batch_size (int) – Batch size for estimator evaluations.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs.

• y – Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,). 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.

Returns

An array holding the adversarial examples.

Targeted Universal Perturbation Attack

class art.attacks.evasion.TargetedUniversalPerturbation(classifier: CLASSIFIER_TYPE, attacker: str = 'fgsm', attacker_params: Optional[Dict[str, Any]] = None, delta: float = 0.2, max_iter: int = 20, eps: float = 10.0, norm: Union[int, float, str] = inf)

Implementation of the attack from Hirano and Takemoto (2019). Computes a fixed perturbation to be applied to all future inputs. To this end, it can use any adversarial attack method.

Paper link: https://arxiv.org/abs/1911.06502

__init__(classifier: CLASSIFIER_TYPE, attacker: str = 'fgsm', attacker_params: Optional[Dict[str, Any]] = None, delta: float = 0.2, max_iter: int = 20, eps: float = 10.0, norm: Union[int, float, str] = inf)

Parameters

• classifier – A trained classifier.

• attacker (str) – Adversarial attack name. Default is ‘deepfool’. Supported names: ‘fgsm’.

• attacker_params – Parameters specific to the adversarial attack. If this parameter is not specified, the default parameters of the chosen attack will be used.

• delta (float) – desired accuracy

• max_iter (int) – The maximum number of iterations for computing universal perturbation.

• eps (float) – Attack step size (input variation)

• norm – The norm of the adversarial perturbation. Possible values: “inf”, np.inf, 2

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs.

• y – An array with the targeted labels.

Returns

An array holding the adversarial examples.

Universal Perturbation Attack

class art.attacks.evasion.UniversalPerturbation(classifier: CLASSIFIER_TYPE, attacker: str = 'deepfool', attacker_params: Optional[Dict[str, Any]] = None, delta: float = 0.2, max_iter: int = 20, eps: float = 10.0, norm: Union[int, float, str] = inf, batch_size: int = 32, verbose: bool = True)

Implementation of the attack from Moosavi-Dezfooli et al. (2016). Computes a fixed perturbation to be applied to all future inputs. To this end, it can use any adversarial attack method.

Paper link: https://arxiv.org/abs/1610.08401

__init__(classifier: CLASSIFIER_TYPE, attacker: str = 'deepfool', attacker_params: Optional[Dict[str, Any]] = None, delta: float = 0.2, max_iter: int = 20, eps: float = 10.0, norm: Union[int, float, str] = inf, batch_size: int = 32, verbose: bool = True) → None

Parameters

• classifier – A trained classifier.

• attacker (str) – Adversarial attack name. Default is ‘deepfool’. Supported names: ‘carlini’, ‘carlini_inf’, ‘deepfool’, ‘fgsm’, ‘bim’, ‘pgd’, ‘margin’, ‘ead’, ‘newtonfool’, ‘jsma’, ‘vat’, ‘simba’.

• attacker_params – Parameters specific to the adversarial attack. If this parameter is not specified, the default parameters of the chosen attack will be used.

• delta (float) – desired accuracy

• max_iter (int) – The maximum number of iterations for computing universal perturbation.

• eps (float) – Attack step size (input variation).

• norm – The norm of the adversarial perturbation. Possible values: “inf”, np.inf, 2.

• batch_size (int) – Batch size for model evaluations in UniversalPerturbation.

• verbose (bool) – Show progress bars.

property converged

The convergence of universal perturbation generation.

Returns

True if generation of universal perturbation has converged.

property fooling_rate

The fooling rate of the universal perturbation on the most recent call to generate.

Returns

Fooling Rate.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs.

• y – An array with the original labels to be predicted.

Returns

An array holding the adversarial examples.

property noise

The universal perturbation.

Returns

Universal perturbation.

Virtual Adversarial Method

class art.attacks.evasion.VirtualAdversarialMethod(classifier: CLASSIFIER_TYPE, max_iter: int = 10, finite_diff: float = 1e-06, eps: float = 0.1, batch_size: int = 1, verbose: bool = True)

This attack was originally proposed by Miyato et al. (2016) and was used for virtual adversarial training.

Paper link: https://arxiv.org/abs/1507.00677

__init__(classifier: CLASSIFIER_TYPE, max_iter: int = 10, finite_diff: float = 1e-06, eps: float = 0.1, batch_size: int = 1, verbose: bool = True) → None

Create a VirtualAdversarialMethod instance.

Parameters

• classifier – A trained classifier.

• eps (float) – Attack step (max input variation).

• finite_diff (float) – The finite difference parameter.

• max_iter (int) – The maximum number of iterations.

• batch_size (int) – Size of the batch on which adversarial samples are generated.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs to be attacked.

• y – An array with the original labels to be predicted.

Returns

An array holding the adversarial examples.

Wasserstein Attack

class art.attacks.evasion.Wasserstein(estimator: CLASSIFIER_LOSS_GRADIENTS_TYPE, targeted: bool = False, regularization: float = 3000.0, p: int = 2, kernel_size: int = 5, eps_step: float = 0.1, norm: str = 'wasserstein', ball: str = 'wasserstein', eps: float = 0.3, eps_iter: int = 10, eps_factor: float = 1.1, max_iter: int = 400, conjugate_sinkhorn_max_iter: int = 400, projected_sinkhorn_max_iter: int = 400, batch_size: int = 1, verbose: bool = True)

Implements Wasserstein Adversarial Examples via Projected Sinkhorn Iterations as evasion attack.

Paper link: https://arxiv.org/abs/1902.07906

__init__(estimator: CLASSIFIER_LOSS_GRADIENTS_TYPE, targeted: bool = False, regularization: float = 3000.0, p: int = 2, kernel_size: int = 5, eps_step: float = 0.1, norm: str = 'wasserstein', ball: str = 'wasserstein', eps: float = 0.3, eps_iter: int = 10, eps_factor: float = 1.1, max_iter: int = 400, conjugate_sinkhorn_max_iter: int = 400, projected_sinkhorn_max_iter: int = 400, batch_size: int = 1, verbose: bool = True)

Create a Wasserstein attack instance.

Parameters

• estimator – A trained estimator.

• targeted (bool) – Indicates whether the attack is targeted (True) or untargeted (False).

• regularization (float) – Entropy regularization.

• p (int) – The p-wasserstein distance.

• kernel_size (int) – Kernel size for computing the cost matrix.

• eps_step (float) – Attack step size (input variation) at each iteration.

• norm (str) – The norm of the adversarial perturbation. Possible values: inf, 1, 2 or wasserstein.

• ball (str) – The ball of the adversarial perturbation. Possible values: inf, 1, 2 or wasserstein.

• eps (float) – Maximum perturbation that the attacker can introduce.

• eps_iter (int) – Number of iterations to increase the epsilon.

• eps_factor (float) – Factor to increase the epsilon.

• max_iter (int) – The maximum number of iterations.

• conjugate_sinkhorn_max_iter (int) – The maximum number of iterations for the conjugate sinkhorn optimizer.

• projected_sinkhorn_max_iter (int) – The maximum number of iterations for the projected sinkhorn optimizer.

• batch_size (int) – Size of batches.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs.

• y – Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,). 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.

• cost_matrix (np.ndarray) – A non-negative cost matrix.

Returns

An array holding the adversarial examples.

Zeroth-Order Optimization (ZOO) Attack

class art.attacks.evasion.ZooAttack(classifier: CLASSIFIER_TYPE, confidence: float = 0.0, targeted: bool = False, learning_rate: float = 0.01, max_iter: int = 10, binary_search_steps: int = 1, initial_const: float = 0.001, abort_early: bool = True, use_resize: bool = True, use_importance: bool = True, nb_parallel: int = 128, batch_size: int = 1, variable_h: float = 0.0001, verbose: bool = True)

The black-box zeroth-order optimization attack from Pin-Yu Chen et al. (2018). This attack is a variant of the C&W attack which uses ADAM coordinate descent to perform numerical estimation of gradients.

Paper link: https://arxiv.org/abs/1708.03999

__init__(classifier: CLASSIFIER_TYPE, confidence: float = 0.0, targeted: bool = False, learning_rate: float = 0.01, max_iter: int = 10, binary_search_steps: int = 1, initial_const: float = 0.001, abort_early: bool = True, use_resize: bool = True, use_importance: bool = True, nb_parallel: int = 128, batch_size: int = 1, variable_h: float = 0.0001, verbose: bool = True)

Create a ZOO attack instance.

Parameters

• classifier – A trained classifier.

• confidence (float) – Confidence of adversarial examples: a higher value produces examples that are farther away, from the original input, but classified with higher confidence as the target class.

• targeted (bool) – Should the attack target one specific class.

• learning_rate (float) – The initial learning rate for the attack algorithm. Smaller values produce better results but are slower to converge.

• max_iter (int) – The maximum number of iterations.

• binary_search_steps (int) – Number of times to adjust constant with binary search (positive value).

• initial_const (float) – The initial trade-off constant c to use to tune the relative importance of distance and confidence. If binary_search_steps is large, the initial constant is not important, as discussed in Carlini and Wagner (2016).

• abort_early (bool) – True if gradient descent should be abandoned when it gets stuck.

• use_resize (bool) – True if to use the resizing strategy from the paper: first, compute attack on inputs resized to 32x32, then increase size if needed to 64x64, followed by 128x128.

• use_importance (bool) – True if to use importance sampling when choosing coordinates to update.

• nb_parallel (int) – Number of coordinate updates to run in parallel. A higher value for nb_parallel should be preferred over a large batch size.

• batch_size (int) – Internal size of batches on which adversarial samples are generated. Small batch sizes are encouraged for ZOO, as the algorithm already runs nb_parallel coordinate updates in parallel for each sample. The batch size is a multiplier of nb_parallel in terms of memory consumption.

• variable_h (float) – Step size for numerical estimation of derivatives.

• verbose (bool) – Show progress bars.

generate(*args, **kwargs)

Generate adversarial samples and return them in an array.

Parameters

• x – An array with the original inputs to be attacked.

• y – Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).

Returns

An array holding the adversarial examples.