From e17fc53b91ee336563fa2c6279d7de32a390949c Mon Sep 17 00:00:00 2001 From: yamamura-k Date: Tue, 2 Jul 2024 17:49:25 +0900 Subject: [PATCH 1/9] Implement Rescaling-ACG (ReACG), which is a improved version of Auto Conjugate Gradient (ACG) attack Signed-off-by: yamamura-k --- art/attacks/evasion/__init__.py | 1 + .../rescaling_auto_conjugate_gradient.py | 664 ++++++++++++++++++ .../test_rescaling_auto_conjugate_gradient.py | 166 +++++ 3 files changed, 831 insertions(+) create mode 100644 art/attacks/evasion/rescaling_auto_conjugate_gradient.py create mode 100644 tests/attacks/evasion/test_rescaling_auto_conjugate_gradient.py diff --git a/art/attacks/evasion/__init__.py b/art/attacks/evasion/__init__.py index 35c9e61df4..b7a2e0e87d 100644 --- a/art/attacks/evasion/__init__.py +++ b/art/attacks/evasion/__init__.py @@ -13,6 +13,7 @@ from art.attacks.evasion.auto_attack import AutoAttack from art.attacks.evasion.auto_projected_gradient_descent import AutoProjectedGradientDescent from art.attacks.evasion.auto_conjugate_gradient import AutoConjugateGradient +from art.attacks.evasion.rescaling_auto_conjugate_gradient import RescalingAutoConjugateGradient if importlib.util.find_spec("numba") is not None: from art.attacks.evasion.brendel_bethge import BrendelBethgeAttack diff --git a/art/attacks/evasion/rescaling_auto_conjugate_gradient.py b/art/attacks/evasion/rescaling_auto_conjugate_gradient.py new file mode 100644 index 0000000000..e38fce953e --- /dev/null +++ b/art/attacks/evasion/rescaling_auto_conjugate_gradient.py @@ -0,0 +1,664 @@ +# MIT License + +# Copyright (c) 2024 Keiichiro Yamamura + +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to deal +# in the Software without restriction, including without limitation the rights +# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +# copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: + +# The above copyright notice and this permission notice shall be included in all +# copies or substantial portions of the Software. + +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +# SOFTWARE. + +# MIT License +# +# Copyright (C) The Adversarial Robustness Toolbox (ART) Authors 2020 +# +# Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated +# documentation files (the "Software"), to deal in the Software without restriction, including without limitation the +# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit +# persons to whom the Software is furnished to do so, subject to the following conditions: +# +# The above copyright notice and this permission notice shall be included in all copies or substantial portions of the +# Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE +# WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, +# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +# SOFTWARE. +""" +This module implements the 'Auto Conjugate Gradient' attack. + +| Paper link: https://arxiv.org/abs/2206.09628 +""" +import abc +import logging +import math +from typing import Optional, Union, TYPE_CHECKING + +import numpy as np +from tqdm.auto import trange + +from art.config import ART_NUMPY_DTYPE +from art.attacks.attack import EvasionAttack +from art.estimators.estimator import BaseEstimator, LossGradientsMixin +from art.estimators.classification.classifier import ClassifierMixin +from art.utils import check_and_transform_label_format, projection, random_sphere, is_probability, get_labels_np_array + +if TYPE_CHECKING: + from art.utils import CLASSIFIER_LOSS_GRADIENTS_TYPE + +logger = logging.getLogger(__name__) + + +class RescalingAutoConjugateGradient(EvasionAttack): + """ + Implementation of the 'Rescaling-ACG' attack. + The original implementation is https://github.com/yamamura-k/ReACG. + + | Paper link: + """ + + attack_params = EvasionAttack.attack_params + [ + "norm", + "eps", + "eps_step", + "max_iter", + "targeted", + "nb_random_init", + "batch_size", + "loss_type", + "verbose", + ] + _estimator_requirements = (BaseEstimator, LossGradientsMixin, ClassifierMixin) + _predefined_losses = [None, "cross_entropy", "difference_logits_ratio"] + + def __init__( + self, + estimator: "CLASSIFIER_LOSS_GRADIENTS_TYPE", + norm: Union[int, float, str] = np.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 :class:`.RescalingAutoConjugateGradient` instance. + + :param estimator: An trained estimator. + :param norm: The norm of the adversarial perturbation. Possible values: "inf", np.inf, 1 or 2. + :param eps: Maximum perturbation that the attacker can introduce. + :param eps_step: Attack step size (input variation) at each iteration. + :param max_iter: The maximum number of iterations. + :param targeted: Indicates whether the attack is targeted (True) or untargeted (False). + :param nb_random_init: Number of random initialisations within the epsilon ball. For num_random_init=0 + starting at the original input. + :param batch_size: Size of the batch on which adversarial samples are generated. + :param loss_type: Defines the loss to attack. Available options: None (Use loss defined by estimator), + "cross_entropy", or "difference_logits_ratio" + :param verbose: Show progress bars. + """ + from art.estimators.classification import TensorFlowClassifier, TensorFlowV2Classifier, PyTorchClassifier + + if isinstance(estimator, TensorFlowClassifier): + raise ValueError("This attack does not support TensorFlow v1.") + + if loss_type not in self._predefined_losses: + raise ValueError( + f"The argument loss_type has an invalid value. The following options for `loss_type` are currently " + f"supported: {self._predefined_losses}" + ) + + if loss_type is None: + if hasattr(estimator, "predict") and is_probability( + estimator.predict(x=np.ones(shape=(1, *estimator.input_shape), dtype=np.float32)) + ): + raise ValueError( # pragma: no cover + "AutoProjectedGradientDescent is expecting logits as estimator output, the provided " + "estimator seems to predict probabilities." + ) + + estimator_acg = estimator + else: + if isinstance(estimator, TensorFlowV2Classifier): + import tensorflow as tf + + class TensorFlowV2Loss: + """abstract class of loss function of tensorflow v2""" + + @abc.abstractmethod + def __call__(self, y_true: tf.Tensor, y_pred: tf.Tensor, *args, **kwargs) -> tf.Tensor: + raise NotImplementedError + + if loss_type == "cross_entropy": + + class CrossEntropyLossV2(TensorFlowV2Loss): + """Class defining cross entropy loss with reduction options.""" + + def __init__(self, from_logits, reduction="sum"): + self.ce_loss = tf.keras.losses.CategoricalCrossentropy( + from_logits=from_logits, + reduction=tf.keras.losses.Reduction.NONE, + ) + self.reduction = reduction + + def __call__(self, y_true: tf.Tensor, y_pred: tf.Tensor, *args, **kwargs) -> tf.Tensor: + if self.reduction == "mean": + return tf.reduce_mean(self.ce_loss(y_true, y_pred)) + if self.reduction == "sum": + return tf.reduce_sum(self.ce_loss(y_true, y_pred)) + if self.reduction == "none": + return self.ce_loss(y_true, y_pred) + raise NotImplementedError() + + if is_probability(estimator.predict(x=np.ones(shape=(1, *estimator.input_shape)))): + _loss_object_tf: TensorFlowV2Loss = CrossEntropyLossV2(from_logits=False) + else: + _loss_object_tf = CrossEntropyLossV2(from_logits=True) + elif loss_type == "difference_logits_ratio": + if is_probability(estimator.predict(x=np.ones(shape=(1, *estimator.input_shape)))): + raise ValueError( # pragma: no cover + "The provided estimator seems to predict probabilities. " + "If loss_type='difference_logits_ratio' the estimator has to to predict logits." + ) + + class DifferenceLogitsRatioTensorFlowV2(TensorFlowV2Loss): + """ + Callable class for Difference Logits Ratio loss in TensorFlow v2. + """ + + def __init__(self): + self.reduction = "sum" + + def __call__(self, y_true: tf.Tensor, y_pred: tf.Tensor, *args, **kwargs) -> tf.Tensor: + i_y_true = tf.cast(tf.math.argmax(tf.cast(y_true, tf.int32), axis=1), tf.int32) + i_y_pred_arg = tf.argsort(y_pred, axis=1) + i_z_i_list = [] + + for i in range(y_true.shape[0]): + if i_y_pred_arg[i, -1] != i_y_true[i]: + i_z_i_list.append(i_y_pred_arg[i, -1]) + else: + i_z_i_list.append(i_y_pred_arg[i, -2]) + + i_z_i = tf.stack(i_z_i_list) + + z_1 = tf.gather(y_pred, i_y_pred_arg[:, -1], axis=1, batch_dims=0) + z_3 = tf.gather(y_pred, i_y_pred_arg[:, -3], axis=1, batch_dims=0) + z_i = tf.gather(y_pred, i_z_i, axis=1, batch_dims=0) + z_y = tf.gather(y_pred, i_y_true, axis=1, batch_dims=0) + + z_1 = tf.linalg.diag_part(z_1) + z_3 = tf.linalg.diag_part(z_3) + z_i = tf.linalg.diag_part(z_i) + z_y = tf.linalg.diag_part(z_y) + + dlr = -(z_y - z_i) / (z_1 - z_3) + if self.reduction == "mean": + return tf.reduce_mean(dlr) + if self.reduction == "sum": + return tf.reduce_sum(dlr) + if self.reduction == "none": + return dlr + raise NotImplementedError() + + _loss_object_tf = DifferenceLogitsRatioTensorFlowV2() + + estimator_acg = TensorFlowV2Classifier( + model=estimator.model, + nb_classes=estimator.nb_classes, + input_shape=estimator.input_shape, + loss_object=_loss_object_tf, + optimizer=estimator.optimizer, + train_step=estimator.train_step, + channels_first=estimator.channels_first, + clip_values=estimator.clip_values, + preprocessing_defences=estimator.preprocessing_defences, + postprocessing_defences=estimator.postprocessing_defences, + preprocessing=estimator.preprocessing, + ) + elif isinstance(estimator, PyTorchClassifier): + import torch + + if loss_type == "cross_entropy": + if is_probability( + estimator.predict(x=np.ones(shape=(1, *estimator.input_shape), dtype=np.float32)) + ): + raise ValueError( # pragma: no cover + "The provided estimator seems to predict probabilities. If loss_type='cross_entropy' " + "the estimator has to to predict logits." + ) + + class CrossEntropyLossTorch(torch.nn.modules.loss._Loss): # pylint: disable=W0212 + """Class defining cross entropy loss with reduction options.""" + + def __init__(self, reduction="sum"): + super().__init__() + self.ce_loss = torch.nn.CrossEntropyLoss(reduction="none") + self.reduction = reduction + + def __call__(self, y_true: torch.Tensor, y_pred: torch.Tensor, *args, **kwargs) -> torch.Tensor: + if self.reduction == "mean": + return self.ce_loss(y_true, y_pred).mean() + if self.reduction == "sum": + return self.ce_loss(y_true, y_pred).sum() + if self.reduction == "none": + return self.ce_loss(y_true, y_pred) + raise NotImplementedError() + + def forward( + self, input: torch.Tensor, target: torch.Tensor # pylint: disable=W0622 + ) -> torch.Tensor: + """ + Forward method. + :param input: Predicted labels of shape (nb_samples, nb_classes). + :param target: Target labels of shape (nb_samples, nb_classes). + :return: Difference Logits Ratio Loss. + """ + return self.__call__(y_true=target, y_pred=input) + + _loss_object_pt: torch.nn.modules.loss._Loss = CrossEntropyLossTorch(reduction="mean") + + elif loss_type == "difference_logits_ratio": + if is_probability( + estimator.predict(x=np.ones(shape=(1, *estimator.input_shape), dtype=ART_NUMPY_DTYPE)) + ): + raise ValueError( # pragma: no cover + "The provided estimator seems to predict probabilities. " + "If loss_type='difference_logits_ratio' the estimator has to to predict logits." + ) + + class DifferenceLogitsRatioPyTorch(torch.nn.modules.loss._Loss): # pylint: disable=W0212 + """ + Callable class for Difference Logits Ratio loss in PyTorch. + """ + + def __init__(self): + super().__init__() + self.reduction = "sum" + + def __call__(self, y_pred: torch.Tensor, y_true: torch.Tensor) -> torch.Tensor: + if isinstance(y_true, np.ndarray): + y_true = torch.from_numpy(y_true) + if isinstance(y_pred, np.ndarray): + y_pred = torch.from_numpy(y_pred) + + y_true = y_true.float() + + i_y_true = torch.argmax(y_true, dim=1) + i_y_pred_arg = torch.argsort(y_pred, dim=1) + i_z_i_list = [] + + for i in range(y_true.shape[0]): + if i_y_pred_arg[i, -1] != i_y_true[i]: + i_z_i_list.append(i_y_pred_arg[i, -1]) + else: + i_z_i_list.append(i_y_pred_arg[i, -2]) + + i_z_i = torch.stack(i_z_i_list) + + z_1 = y_pred[:, i_y_pred_arg[:, -1]] + z_3 = y_pred[:, i_y_pred_arg[:, -3]] + z_i = y_pred[:, i_z_i] + z_y = y_pred[:, i_y_true] + + z_1 = torch.diagonal(z_1) + z_3 = torch.diagonal(z_3) + z_i = torch.diagonal(z_i) + z_y = torch.diagonal(z_y) + + dlr = (-(z_y - z_i) / (z_1 - z_3)).float() + if self.reduction == "mean": + return dlr.mean() + if self.reduction == "sum": + return dlr.sum() + if self.reduction == "none": + return dlr + raise NotImplementedError() + + def forward( + self, input: torch.Tensor, target: torch.Tensor # pylint: disable=W0622 + ) -> torch.Tensor: + """ + Forward method. + :param input: Predicted labels of shape (nb_samples, nb_classes). + :param target: Target labels of shape (nb_samples, nb_classes). + :return: Difference Logits Ratio Loss. + """ + return self.__call__(y_true=target, y_pred=input) + + _loss_object_pt = DifferenceLogitsRatioPyTorch() + else: + raise NotImplementedError() + + estimator_acg = PyTorchClassifier( + model=estimator.model, + loss=_loss_object_pt, + input_shape=estimator.input_shape, + nb_classes=estimator.nb_classes, + optimizer=None, + channels_first=estimator.channels_first, + clip_values=estimator.clip_values, + preprocessing_defences=estimator.preprocessing_defences, + postprocessing_defences=estimator.postprocessing_defences, + preprocessing=estimator.preprocessing, + device_type=str(estimator._device), + ) + + else: # pragma: no cover + raise ValueError(f"The loss type {loss_type} is not supported for the provided estimator.") + + super().__init__(estimator=estimator_acg) + self.norm = norm + self.eps = eps + self.eps_step = eps_step + self.max_iter = max_iter + self.targeted = targeted + self.nb_random_init = nb_random_init + self.batch_size = batch_size + self.loss_type = loss_type + self.verbose = verbose + self._check_params() + + def generate(self, x: np.ndarray, y: Optional[np.ndarray] = None, **kwargs) -> np.ndarray: + """ + Generate adversarial samples and return them in an array. + + :param x: An array with the original inputs. + :param 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`. + :param mask: 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. + :type mask: `np.ndarray` + :return: An array holding the adversarial examples. + """ + mask = kwargs.get("mask") + + if y is not None: + y = check_and_transform_label_format(y, nb_classes=self.estimator.nb_classes) + + if y is None: + if self.targeted: + raise ValueError("Target labels `y` need to be provided for a targeted attack.") + y = get_labels_np_array(self.estimator.predict(x, batch_size=self.batch_size)).astype(int) + + if self.estimator.nb_classes == 2 and y.shape[1] == 1: + raise ValueError( + "This attack has not yet been tested for binary classification with a single output classifier." + ) + + x_adv = x.astype(ART_NUMPY_DTYPE) + + for _ in trange(max(1, self.nb_random_init), desc="ACG - restart", disable=not self.verbose): + # Determine correctly predicted samples + y_pred = self.estimator.predict(x_adv) + if self.targeted: + sample_is_robust = np.argmax(y_pred, axis=1) != np.argmax(y, axis=1) + elif not self.targeted: + sample_is_robust = np.argmax(y_pred, axis=1) == np.argmax(y, axis=1) + + if np.sum(sample_is_robust) == 0: + break + + x_robust = x_adv[sample_is_robust] + y_robust = y[sample_is_robust] + x_init = x[sample_is_robust] + + n = x_robust.shape[0] + m = np.prod(x_robust.shape[1:]).item() + random_perturbation = ( + random_sphere(n, m, self.eps, self.norm).reshape(x_robust.shape).astype(ART_NUMPY_DTYPE) + ) + + x_robust = x_robust + random_perturbation + + if self.estimator.clip_values is not None: + clip_min, clip_max = self.estimator.clip_values + x_robust = np.clip(x_robust, clip_min, clip_max) + + perturbation = projection(x_robust - x_init, self.eps, self.norm) + x_robust = x_init + perturbation + + # Compute perturbation with implicit batching + for batch_id in trange( + int(np.ceil(x_robust.shape[0] / float(self.batch_size))), + desc="ACG - batch", + leave=False, + disable=not self.verbose, + ): + batch_index_1, batch_index_2 = batch_id * self.batch_size, (batch_id + 1) * self.batch_size + x_k = x_robust[batch_index_1:batch_index_2].astype(ART_NUMPY_DTYPE) + x_init_batch = x_init[batch_index_1:batch_index_2].astype(ART_NUMPY_DTYPE) + y_batch = y_robust[batch_index_1:batch_index_2] + + p_0 = 0 + p_1 = 0.43 + var_w = [p_0, p_1] + + while True: + p_j_p_1 = var_w[-1] + max(var_w[-1] - var_w[-2] - 0.24, 0.08) + if p_j_p_1 > 1: + break + var_w.append(p_j_p_1) + + var_w = [math.ceil(p * self.max_iter) for p in var_w] + + # self.eta = np.full((self.batch_size, 1, 1, 1), 2 * self.eps_step).astype(ART_NUMPY_DTYPE) + _batch_size = x_k.shape[0] + eta = np.full((_batch_size,) + (1,) * len(self.estimator.input_shape), self.eps_step).astype( + ART_NUMPY_DTYPE + ) + self.count_condition_1 = np.zeros(shape=(_batch_size,)) + gradk_1 = np.zeros_like(x_k) + cgradk_1 = np.zeros_like(x_k) + cgradk = np.zeros_like(x_k) + gradk_1_best = np.zeros_like(x_k) + cgradk_1_best = np.zeros_like(x_k) + gradk_1_tmp = np.zeros_like(x_k) + cgradk_1_tmp = np.zeros_like(x_k) + + for k_iter in trange(self.max_iter, desc="ACG - iteration", leave=False, disable=not self.verbose): + + # Get perturbation, use small scalar to avoid division by 0 + tol = 10e-8 + + # Get gradient wrt loss; invert it if attack is targeted + grad = self.estimator.loss_gradient(x_k, y_batch) * (1 - 2 * int(self.targeted)) + if k_iter == 0: + gradk_1 = grad.copy() + cgradk_1 = grad.copy() + cgradk = grad.copy() + else: + beta = get_beta(grad, gradk_1, cgradk_1) + _beta_normalized = get_beta(grad / np.linalg.norm(grad), gradk_1 / np.linalg.norm(gradk_1), cgradk_1) + grad_ratio_value = np.abs(grad / cgradk_1).reshape((_batch_size, -1)) + grad_ratio = ( + grad_ratio_value.mean(1) + ) + normalize_inds = np.abs(beta).reshape((_batch_size,)) > grad_ratio + smaller_beta_inds = (np.abs(beta) > np.abs(_beta_normalized)).reshape((_batch_size,)) + normalize_inds = np.logical_and(normalize_inds, smaller_beta_inds) + beta[normalize_inds] = _beta_normalized[normalize_inds].copy() + cgradk = grad + beta * cgradk_1 + + # Apply norm bound + if self.norm in [np.inf, "inf"]: + grad = np.sign(cgradk) + elif self.norm == 1: + ind = tuple(range(1, len(x_k.shape))) + cgradk = cgradk / (np.sum(np.abs(cgradk), axis=ind, keepdims=True) + tol) + elif self.norm == 2: + ind = tuple(range(1, len(x_k.shape))) + cgradk = cgradk / (np.sqrt(np.sum(np.square(cgradk), axis=ind, keepdims=True)) + tol) + assert x_k.shape == cgradk.shape + + perturbation = cgradk + + if mask is not None: + perturbation = perturbation * (mask.astype(ART_NUMPY_DTYPE)) + + # Apply perturbation and clip + x_k_p_1 = x_k + eta * perturbation + + if self.estimator.clip_values is not None: + clip_min, clip_max = self.estimator.clip_values + x_k_p_1 = np.clip(x_k_p_1, clip_min, clip_max) + + if k_iter == 0: + x_1 = x_k_p_1 + perturbation = projection(x_1 - x_init_batch, self.eps, self.norm) + x_1 = x_init_batch + perturbation + + f_0 = self.estimator.compute_loss(x=x_k, y=y_batch, reduction="none") + f_1 = self.estimator.compute_loss(x=x_1, y=y_batch, reduction="none") + + self.eta_w_j_m_1 = eta.copy() + self.f_max_w_j_m_1 = f_0.copy() + + self.f_max = f_0.copy() + self.x_max = x_k.copy() + + f1_ge_f0 = f_1 >= f_0 + f_1_tmp = f_1[f1_ge_f0].copy() + self.f_max[f1_ge_f0] = f_1_tmp.copy() + x_1_tmp = x_1[f1_ge_f0].copy() + self.x_max[f1_ge_f0] = x_1_tmp.copy() + self.count_condition_1[f1_ge_f0] += 1 + + # Settings for next iteration k + x_k = x_1 + gradk_1_best = gradk_1.copy() + cgradk_1_best = cgradk_1.copy() + + else: + perturbation = projection(x_k_p_1 - x_init_batch, self.eps, self.norm) + x_k_p_1 = x_init_batch + perturbation + + if self.estimator.clip_values is not None: + clip_min, clip_max = self.estimator.clip_values + x_k_p_1 = np.clip(x_k_p_1, clip_min, clip_max) + + perturbation = projection(x_k_p_1 - x_init_batch, self.eps, self.norm) + x_k_p_1 = x_init_batch + perturbation + + f_k_p_1 = self.estimator.compute_loss(x=x_k_p_1, y=y_batch, reduction="none") + + if (f_k_p_1 == 0.0).all(): + x_k = x_k_p_1.copy() + break + + if self.targeted: + fk_ge_fm = f_k_p_1 < self.f_max # assume the loss function is cross-entropy + else: + fk_ge_fm = f_k_p_1 > self.f_max + + self.count_condition_1[fk_ge_fm] += 1 + # update the best points + x_k_p_1_tmp = x_k_p_1[fk_ge_fm].copy() + self.x_max[fk_ge_fm] = x_k_p_1_tmp.copy() + f_k_p_1_tmp = f_k_p_1[fk_ge_fm].copy() + self.f_max[fk_ge_fm] = f_k_p_1_tmp.copy() + gradk_1_tmp = gradk_1[fk_ge_fm].copy() + gradk_1_best[fk_ge_fm] = gradk_1_tmp.copy() + cgradk_1_tmp = cgradk_1[fk_ge_fm].copy() + cgradk_1_best[fk_ge_fm] = cgradk_1_tmp.copy() + + # update the search points + x_k = x_k_p_1.copy() + gradk_1 = grad.copy() + cgradk_1 = cgradk.copy() + + if k_iter in var_w: + + rho = 0.75 + + condition_1 = self.count_condition_1 < rho * (k_iter - var_w[var_w.index(k_iter) - 1]) + condition_2 = np.logical_and( + (self.eta_w_j_m_1 == eta).squeeze(), self.f_max_w_j_m_1 == self.f_max + ) + condition = np.logical_or(condition_1, condition_2) + + # halve the stepsize if the condition is satisfied + eta[condition] /= 2 + # move to the best point + x_max_tmp = self.x_max[condition].copy() + x_k[condition] = x_max_tmp.copy() + gradk_1_tmp = gradk_1_best[condition].copy() + gradk_1[condition] = gradk_1_tmp.copy() + cgradk_1_tmp = cgradk_1_best[condition].copy() + cgradk_1[condition] = cgradk_1_tmp.copy() + + self.count_condition_1[:] = 0 + self.eta_w_j_m_1 = eta.copy() + self.f_max_w_j_m_1 = self.f_max.copy() + + y_pred_adv_k = self.estimator.predict(x_k) + if self.targeted: + sample_is_not_robust_k = np.invert(np.argmax(y_pred_adv_k, axis=1) != np.argmax(y_batch, axis=1)) + elif not self.targeted: + sample_is_not_robust_k = np.invert(np.argmax(y_pred_adv_k, axis=1) == np.argmax(y_batch, axis=1)) + + x_robust[batch_index_1:batch_index_2][sample_is_not_robust_k] = x_k[sample_is_not_robust_k] + + x_adv[sample_is_robust] = x_robust + + return x_adv + + def _check_params(self) -> None: + if self.norm not in [1, 2, np.inf, "inf"]: + raise ValueError('The argument norm has to be either 1, 2, np.inf, or "inf".') + + if not isinstance(self.eps, (int, float)) or self.eps <= 0.0: + raise ValueError("The argument eps has to be either of type int or float and larger than zero.") + + if not isinstance(self.eps_step, (int, float)) or self.eps_step <= 0.0: + raise ValueError("The argument eps_step has to be either of type int or float and larger than zero.") + + if not isinstance(self.max_iter, int) or self.max_iter <= 0: + raise ValueError("The argument max_iter has to be of type int and larger than zero.") + + if not isinstance(self.targeted, bool): + raise ValueError("The argument targeted has to be of bool.") + + if not isinstance(self.nb_random_init, int) or self.nb_random_init <= 0: + raise ValueError("The argument nb_random_init has to be of type int and larger than zero.") + + if not isinstance(self.batch_size, int) or self.batch_size <= 0: + raise ValueError("The argument batch_size has to be of type int and larger than zero.") + + # if self.loss_type not in self._predefined_losses: + # raise ValueError("The argument loss_type has to be either {}.".format(self._predefined_losses)) + + if not isinstance(self.verbose, bool): + raise ValueError("The argument `verbose` has to be of type bool.") + + +def get_beta(gradk, gradk_1, cgradk_1): + """compute the coefficient beta required to update CG direction""" + _batch_size = gradk.shape[0] + _cgradk_1 = cgradk_1.reshape(_batch_size, -1) + _gradk = -gradk.reshape(_batch_size, -1) + _gradk_1 = -gradk_1.reshape(_batch_size, -1) + delta_gradk = _gradk - _gradk_1 + betak = -(_gradk * delta_gradk).sum(axis=1) / ( + (_cgradk_1 * delta_gradk).sum(axis=1) + np.finfo(ART_NUMPY_DTYPE).eps + ) + return betak.reshape((_batch_size,) + (1,) * (len(gradk.shape) - 1)) diff --git a/tests/attacks/evasion/test_rescaling_auto_conjugate_gradient.py b/tests/attacks/evasion/test_rescaling_auto_conjugate_gradient.py new file mode 100644 index 0000000000..436ec4936b --- /dev/null +++ b/tests/attacks/evasion/test_rescaling_auto_conjugate_gradient.py @@ -0,0 +1,166 @@ +# MIT License + +# Copyright (c) 2024 Keiichiro Yamamura + +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to deal +# in the Software without restriction, including without limitation the rights +# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +# copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: + +# The above copyright notice and this permission notice shall be included in all +# copies or substantial portions of the Software. + +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +# SOFTWARE. + +# MIT License +# +# Copyright (C) The Adversarial Robustness Toolbox (ART) Authors 2020 +# +# Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated +# documentation files (the "Software"), to deal in the Software without restriction, including without limitation the +# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit +# persons to whom the Software is furnished to do so, subject to the following conditions: +# +# The above copyright notice and this permission notice shall be included in all copies or substantial portions of the +# Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE +# WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, +# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +# SOFTWARE. +import logging +import pytest + +import numpy as np + +from art.attacks.evasion import RescalingAutoConjugateGradient +from art.estimators.estimator import BaseEstimator, LossGradientsMixin +from art.estimators.classification.classifier import ClassifierMixin + +from tests.attacks.utils import backend_test_classifier_type_check_fail +from tests.utils import ARTTestException + +logger = logging.getLogger(__name__) + + +@pytest.fixture() +def fix_get_mnist_subset(get_mnist_dataset): + (x_train_mnist, y_train_mnist), (x_test_mnist, y_test_mnist) = get_mnist_dataset + n_train = 100 + n_test = 10 + yield x_train_mnist[:n_train], y_train_mnist[:n_train], x_test_mnist[:n_test], y_test_mnist[:n_test] + + +@pytest.mark.parametrize("loss_type", ["cross_entropy", "difference_logits_ratio"]) +@pytest.mark.parametrize("norm", ["inf", np.inf, 1, 2]) +@pytest.mark.skip_framework("keras", "non_dl_frameworks", "mxnet", "kerastf", "tensorflow1", "tensorflow2v1") +def test_generate(art_warning, fix_get_mnist_subset, image_dl_estimator_for_attack, framework, loss_type, norm): + print("test_generate") + try: + classifier = image_dl_estimator_for_attack(RescalingAutoConjugateGradient, from_logits=True) + + print("framework", framework) + + if framework in ["tensorflow1", "tensorflow2v1"] and loss_type == "difference_logits_ratio": + with pytest.raises(ValueError): + _ = RescalingAutoConjugateGradient( + estimator=classifier, + norm=norm, + eps=0.3, + eps_step=0.1, + max_iter=5, + targeted=False, + nb_random_init=1, + batch_size=32, + loss_type=loss_type, + verbose=False, + ) + else: + + attack = RescalingAutoConjugateGradient( + estimator=classifier, + norm=norm, + eps=0.3, + eps_step=0.1, + max_iter=5, + targeted=False, + nb_random_init=1, + batch_size=32, + loss_type=loss_type, + verbose=False, + ) + + (x_train_mnist, y_train_mnist, x_test_mnist, y_test_mnist) = fix_get_mnist_subset + + x_train_mnist_adv = attack.generate(x=x_train_mnist, y=y_train_mnist) + + assert np.max(np.abs(x_train_mnist_adv - x_train_mnist)) > 0.0 + + except ARTTestException as e: + art_warning(e) + + +@pytest.mark.framework_agnostic +def test_check_params(art_warning, image_dl_estimator_for_attack): + try: + + classifier = image_dl_estimator_for_attack(RescalingAutoConjugateGradient, from_logits=True) + + with pytest.raises(ValueError): + _ = RescalingAutoConjugateGradient(classifier, norm=0) + + with pytest.raises(ValueError): + _ = RescalingAutoConjugateGradient(classifier, eps="1") + with pytest.raises(ValueError): + _ = RescalingAutoConjugateGradient(classifier, eps=-1.0) + + with pytest.raises(ValueError): + _ = RescalingAutoConjugateGradient(classifier, eps_step="1") + with pytest.raises(ValueError): + _ = RescalingAutoConjugateGradient(classifier, eps_step=-1.0) + + with pytest.raises(ValueError): + _ = RescalingAutoConjugateGradient(classifier, max_iter=1.0) + with pytest.raises(ValueError): + _ = RescalingAutoConjugateGradient(classifier, max_iter=-1) + + with pytest.raises(ValueError): + _ = RescalingAutoConjugateGradient(classifier, targeted="true") + + with pytest.raises(ValueError): + _ = RescalingAutoConjugateGradient(classifier, nb_random_init=1.0) + with pytest.raises(ValueError): + _ = RescalingAutoConjugateGradient(classifier, nb_random_init=-1) + + with pytest.raises(ValueError): + _ = RescalingAutoConjugateGradient(classifier, batch_size=1.0) + with pytest.raises(ValueError): + _ = RescalingAutoConjugateGradient(classifier, batch_size=-1) + + with pytest.raises(ValueError): + _ = RescalingAutoConjugateGradient(classifier, loss_type="test") + + with pytest.raises(ValueError): + _ = RescalingAutoConjugateGradient(classifier, verbose="true") + + except ARTTestException as e: + art_warning(e) + + +@pytest.mark.framework_agnostic +def test_classifier_type_check_fail(art_warning): + try: + backend_test_classifier_type_check_fail( + RescalingAutoConjugateGradient, [BaseEstimator, LossGradientsMixin, ClassifierMixin] + ) + except ARTTestException as e: + art_warning(e) From 4d22c12d305279724837861dd613d492d9f366cd Mon Sep 17 00:00:00 2001 From: yamamura-k Date: Tue, 2 Jul 2024 21:51:05 +0900 Subject: [PATCH 2/9] formatting Signed-off-by: yamamura-k --- art/attacks/evasion/rescaling_auto_conjugate_gradient.py | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/art/attacks/evasion/rescaling_auto_conjugate_gradient.py b/art/attacks/evasion/rescaling_auto_conjugate_gradient.py index e38fce953e..64bcd7e614 100644 --- a/art/attacks/evasion/rescaling_auto_conjugate_gradient.py +++ b/art/attacks/evasion/rescaling_auto_conjugate_gradient.py @@ -67,7 +67,7 @@ class RescalingAutoConjugateGradient(EvasionAttack): Implementation of the 'Rescaling-ACG' attack. The original implementation is https://github.com/yamamura-k/ReACG. - | Paper link: + | Paper link: """ attack_params = EvasionAttack.attack_params + [ @@ -488,7 +488,9 @@ def generate(self, x: np.ndarray, y: Optional[np.ndarray] = None, **kwargs) -> n cgradk = grad.copy() else: beta = get_beta(grad, gradk_1, cgradk_1) - _beta_normalized = get_beta(grad / np.linalg.norm(grad), gradk_1 / np.linalg.norm(gradk_1), cgradk_1) + _beta_normalized = get_beta( + grad / np.linalg.norm(grad), gradk_1 / np.linalg.norm(gradk_1), cgradk_1 + ) grad_ratio_value = np.abs(grad / cgradk_1).reshape((_batch_size, -1)) grad_ratio = ( grad_ratio_value.mean(1) From 0291898d8cd36c154740c589cb9c9096676e6fdb Mon Sep 17 00:00:00 2001 From: yamamura-k Date: Tue, 2 Jul 2024 22:12:32 +0900 Subject: [PATCH 3/9] Add comments Signed-off-by: yamamura-k --- .../rescaling_auto_conjugate_gradient.py | 19 ++++++++++--------- 1 file changed, 10 insertions(+), 9 deletions(-) diff --git a/art/attacks/evasion/rescaling_auto_conjugate_gradient.py b/art/attacks/evasion/rescaling_auto_conjugate_gradient.py index 64bcd7e614..9c2cce0f81 100644 --- a/art/attacks/evasion/rescaling_auto_conjugate_gradient.py +++ b/art/attacks/evasion/rescaling_auto_conjugate_gradient.py @@ -38,9 +38,9 @@ # TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE # SOFTWARE. """ -This module implements the 'Auto Conjugate Gradient' attack. +This module implements the 'Rescaling-ACG' attack. -| Paper link: https://arxiv.org/abs/2206.09628 +| Paper link: """ import abc import logging @@ -133,7 +133,7 @@ def __init__( "estimator seems to predict probabilities." ) - estimator_acg = estimator + estimator_reacg = estimator else: if isinstance(estimator, TensorFlowV2Classifier): import tensorflow as tf @@ -219,7 +219,7 @@ def __call__(self, y_true: tf.Tensor, y_pred: tf.Tensor, *args, **kwargs) -> tf. _loss_object_tf = DifferenceLogitsRatioTensorFlowV2() - estimator_acg = TensorFlowV2Classifier( + estimator_reacg = TensorFlowV2Classifier( model=estimator.model, nb_classes=estimator.nb_classes, input_shape=estimator.input_shape, @@ -346,7 +346,7 @@ def forward( else: raise NotImplementedError() - estimator_acg = PyTorchClassifier( + estimator_reacg = PyTorchClassifier( model=estimator.model, loss=_loss_object_pt, input_shape=estimator.input_shape, @@ -363,7 +363,7 @@ def forward( else: # pragma: no cover raise ValueError(f"The loss type {loss_type} is not supported for the provided estimator.") - super().__init__(estimator=estimator_acg) + super().__init__(estimator=estimator_reacg) self.norm = norm self.eps = eps self.eps_step = eps_step @@ -407,7 +407,7 @@ def generate(self, x: np.ndarray, y: Optional[np.ndarray] = None, **kwargs) -> n x_adv = x.astype(ART_NUMPY_DTYPE) - for _ in trange(max(1, self.nb_random_init), desc="ACG - restart", disable=not self.verbose): + for _ in trange(max(1, self.nb_random_init), desc="ReACG - restart", disable=not self.verbose): # Determine correctly predicted samples y_pred = self.estimator.predict(x_adv) if self.targeted: @@ -440,7 +440,7 @@ def generate(self, x: np.ndarray, y: Optional[np.ndarray] = None, **kwargs) -> n # Compute perturbation with implicit batching for batch_id in trange( int(np.ceil(x_robust.shape[0] / float(self.batch_size))), - desc="ACG - batch", + desc="ReACG - batch", leave=False, disable=not self.verbose, ): @@ -475,7 +475,7 @@ def generate(self, x: np.ndarray, y: Optional[np.ndarray] = None, **kwargs) -> n gradk_1_tmp = np.zeros_like(x_k) cgradk_1_tmp = np.zeros_like(x_k) - for k_iter in trange(self.max_iter, desc="ACG - iteration", leave=False, disable=not self.verbose): + for k_iter in trange(self.max_iter, desc="ReACG - iteration", leave=False, disable=not self.verbose): # Get perturbation, use small scalar to avoid division by 0 tol = 10e-8 @@ -488,6 +488,7 @@ def generate(self, x: np.ndarray, y: Optional[np.ndarray] = None, **kwargs) -> n cgradk = grad.copy() else: beta = get_beta(grad, gradk_1, cgradk_1) + # Modify the coefficient beta when |beta| >> avg.(|grad / cgradk_1|) _beta_normalized = get_beta( grad / np.linalg.norm(grad), gradk_1 / np.linalg.norm(gradk_1), cgradk_1 ) From 2615500a2eef789a179bc2ea9a9b486af1166a31 Mon Sep 17 00:00:00 2001 From: yamamura-k Date: Tue, 2 Jul 2024 22:16:01 +0900 Subject: [PATCH 4/9] update documentation Signed-off-by: yamamura-k --- docs/modules/attacks/evasion.rst | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/docs/modules/attacks/evasion.rst b/docs/modules/attacks/evasion.rst index f6f41ad95c..39531bcea3 100644 --- a/docs/modules/attacks/evasion.rst +++ b/docs/modules/attacks/evasion.rst @@ -50,6 +50,12 @@ Auto Conjugate Gradient (Auto-CG) :members: :special-members: +Rescaling-Auto Conjugate Gradient (ReACG) +--------------------------------- +.. autoclass:: RescalingAutoConjugateGradient + :members: + :special-members: + Boundary Attack / Decision-Based Attack --------------------------------------- .. autoclass:: BoundaryAttack From 2ceb11f65bbacb14cb4430955192beed451c40ec Mon Sep 17 00:00:00 2001 From: yamamura-k Date: Wed, 3 Jul 2024 07:48:27 +0900 Subject: [PATCH 5/9] formatting with black Signed-off-by: yamamura-k --- art/attacks/evasion/rescaling_auto_conjugate_gradient.py | 4 +--- 1 file changed, 1 insertion(+), 3 deletions(-) diff --git a/art/attacks/evasion/rescaling_auto_conjugate_gradient.py b/art/attacks/evasion/rescaling_auto_conjugate_gradient.py index 9c2cce0f81..774c4c4989 100644 --- a/art/attacks/evasion/rescaling_auto_conjugate_gradient.py +++ b/art/attacks/evasion/rescaling_auto_conjugate_gradient.py @@ -493,9 +493,7 @@ def generate(self, x: np.ndarray, y: Optional[np.ndarray] = None, **kwargs) -> n grad / np.linalg.norm(grad), gradk_1 / np.linalg.norm(gradk_1), cgradk_1 ) grad_ratio_value = np.abs(grad / cgradk_1).reshape((_batch_size, -1)) - grad_ratio = ( - grad_ratio_value.mean(1) - ) + grad_ratio = grad_ratio_value.mean(1) normalize_inds = np.abs(beta).reshape((_batch_size,)) > grad_ratio smaller_beta_inds = (np.abs(beta) > np.abs(_beta_normalized)).reshape((_batch_size,)) normalize_inds = np.logical_and(normalize_inds, smaller_beta_inds) From ce4228891e7d0699d8e9d436f2b7a03fee2008c2 Mon Sep 17 00:00:00 2001 From: yamamura-k Date: Wed, 3 Jul 2024 07:55:20 +0900 Subject: [PATCH 6/9] raise NotImplementedError if the unexpected loss type is specified Signed-off-by: yamamura-k --- art/attacks/evasion/rescaling_auto_conjugate_gradient.py | 2 ++ 1 file changed, 2 insertions(+) diff --git a/art/attacks/evasion/rescaling_auto_conjugate_gradient.py b/art/attacks/evasion/rescaling_auto_conjugate_gradient.py index 774c4c4989..24e250bdc7 100644 --- a/art/attacks/evasion/rescaling_auto_conjugate_gradient.py +++ b/art/attacks/evasion/rescaling_auto_conjugate_gradient.py @@ -218,6 +218,8 @@ def __call__(self, y_true: tf.Tensor, y_pred: tf.Tensor, *args, **kwargs) -> tf. raise NotImplementedError() _loss_object_tf = DifferenceLogitsRatioTensorFlowV2() + else: + raise NotImplementedError() estimator_reacg = TensorFlowV2Classifier( model=estimator.model, From 0ed7f6907aea58b62e6ef881d4950ce89fc57556 Mon Sep 17 00:00:00 2001 From: yamamura-k Date: Mon, 22 Jul 2024 10:47:07 +0900 Subject: [PATCH 7/9] remove comments and update license Signed-off-by: yamamura-k --- art/attacks/evasion/rescaling_auto_conjugate_gradient.py | 5 +---- 1 file changed, 1 insertion(+), 4 deletions(-) diff --git a/art/attacks/evasion/rescaling_auto_conjugate_gradient.py b/art/attacks/evasion/rescaling_auto_conjugate_gradient.py index 24e250bdc7..f80ae43773 100644 --- a/art/attacks/evasion/rescaling_auto_conjugate_gradient.py +++ b/art/attacks/evasion/rescaling_auto_conjugate_gradient.py @@ -22,7 +22,7 @@ # MIT License # -# Copyright (C) The Adversarial Robustness Toolbox (ART) Authors 2020 +# Copyright (C) The Adversarial Robustness Toolbox (ART) Authors 2024 # # Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated # documentation files (the "Software"), to deal in the Software without restriction, including without limitation the @@ -647,9 +647,6 @@ def _check_params(self) -> None: if not isinstance(self.batch_size, int) or self.batch_size <= 0: raise ValueError("The argument batch_size has to be of type int and larger than zero.") - # if self.loss_type not in self._predefined_losses: - # raise ValueError("The argument loss_type has to be either {}.".format(self._predefined_losses)) - if not isinstance(self.verbose, bool): raise ValueError("The argument `verbose` has to be of type bool.") From a5a61d3761edfa71c645c652d30f212308c4a8c9 Mon Sep 17 00:00:00 2001 From: yamamura-k Date: Mon, 22 Jul 2024 10:50:45 +0900 Subject: [PATCH 8/9] update license Signed-off-by: yamamura-k --- tests/attacks/evasion/test_rescaling_auto_conjugate_gradient.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/tests/attacks/evasion/test_rescaling_auto_conjugate_gradient.py b/tests/attacks/evasion/test_rescaling_auto_conjugate_gradient.py index 436ec4936b..9bb9026b1c 100644 --- a/tests/attacks/evasion/test_rescaling_auto_conjugate_gradient.py +++ b/tests/attacks/evasion/test_rescaling_auto_conjugate_gradient.py @@ -22,7 +22,7 @@ # MIT License # -# Copyright (C) The Adversarial Robustness Toolbox (ART) Authors 2020 +# Copyright (C) The Adversarial Robustness Toolbox (ART) Authors 2024 # # Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated # documentation files (the "Software"), to deal in the Software without restriction, including without limitation the From 2ee873d1874c198028da8515bd451b0d20ca2f04 Mon Sep 17 00:00:00 2001 From: yamamura-k Date: Thu, 15 Aug 2024 14:57:09 +0900 Subject: [PATCH 9/9] add link to paper Signed-off-by: yamamura-k --- art/attacks/evasion/rescaling_auto_conjugate_gradient.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/art/attacks/evasion/rescaling_auto_conjugate_gradient.py b/art/attacks/evasion/rescaling_auto_conjugate_gradient.py index f80ae43773..2b2e53a595 100644 --- a/art/attacks/evasion/rescaling_auto_conjugate_gradient.py +++ b/art/attacks/evasion/rescaling_auto_conjugate_gradient.py @@ -40,7 +40,7 @@ """ This module implements the 'Rescaling-ACG' attack. -| Paper link: +| Paper link: https://arxiv.org/abs/2408.03972 """ import abc import logging