如何根据某个类计算图像的梯度？
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【中文标题】如何根据某个类计算图像的梯度？【英文标题】：How to compute the gradient of an image based on a certain class? 【发布时间】：2017-05-09 15:42:16 【问题描述】：在Breaking Linear Classifiers on ImageNet中，作者提出了以下方法来创建欺骗ConvNets的对抗性图像：
简而言之，要创建一个愚蠢的图像，我们从我们的任何图像开始 想要（实际图像，甚至是噪声模式），然后使用 反向传播来计算任何图像像素的梯度 班级分数，然后轻推它。我们可以但不必重复 该过程几次。您可以在此解释反向传播 设置为使用动态规划来计算最具破坏性的 输入的局部扰动。注意这个过程非常 如果您可以访问 ConvNet 的参数（反向传播速度很快），但可以这样做 即使您无权访问参数，但只能访问 最后的班级成绩。在这种情况下，可以计算 数据梯度数值，或使用其他局部随机搜索 策略等。请注意，由于后一种方法，即使 不可微分类器（例如随机森林）不安全（但 我还没有看到任何人凭经验证实这一点）。
我知道我可以像这样计算图像的梯度：
np.gradient(img)
但是如何使用 TensorFlow 或 Numpy 计算图像相对于另一个图像类的梯度？可能我需要做一些类似于in this tutorial 的过程？如：
cross_entropy = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(y_conv, y_))
train_step = tf.train.AdamOptimizer(1e-4).minimize(cross_entropy)
correct_prediction = tf.equal(tf.argmax(y_conv,1), tf.argmax(y_,1))
accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
sess.run(tf.initialize_all_variables())
for i in range(20000):
batch = mnist.train.next_batch(50)
if i%100 == 0:
train_accuracy = accuracy.eval(feed_dict=
x:batch[0], y_: batch[1], keep_prob: 1.0)
print("step %d, training accuracy %g"%(i, train_accuracy))
train_step.run(feed_dict=x: batch[0], y_: batch[1], keep_prob: 0.5)
print("test accuracy %g"%accuracy.eval(feed_dict=
x: mnist.test.images, y_: mnist.test.labels, keep_prob: 1.0))
但我不确定具体是如何...具体来说，我有一个数字 2 的图像，如下所示：
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如何计算此图像相对于数字 6 图像类的梯度（示例如下）？ （我想我需要使用反向传播来计算所有 6 位图像的梯度。）
array([[ 0. , 0. , 0. , 0. , 0. ,
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[ 0. , 0. , 0. , 0. , 0. ,
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0.95686281, 0.19607845, 0. , 0. , 0. ,
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[ 0. , 0. , 0. , 0. , 0. ,
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0.99215692, 0.94117653, 0.71764708, 0.34901962, 0.27058825,
0.02745098, 0.27058825, 0.67058825, 0.98823535, 0.98823535,
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0.62352943, 0.98823535, 0.60392159, 0.03529412, 0. ,
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0.37254903, 0. , 0. , 0. , 0. ,
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[ 0. , 0. , 0. , 0. , 0. ,
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0.06666667, 0.89019614, 0.98823535, 0.60392159, 0.27450982,
0.31764707, 0.89411771, 0.98823535, 0.89019614, 0.50980395,
0. , 0. , 0. , 0. , 0. ,
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[ 0. , 0. , 0. , 0. , 0. ,
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0.99215692, 0.98823535, 0.72549021, 0.19607845, 0. ,
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[ 0. , 0. , 0. , 0. , 0. ,
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提前感谢您的帮助！
我问了两个相关的问题：
How to use image and weight matrix to create adversarial images in TensorFlow?
How to create adversarial images for ConvNet?
这里是my script。
【问题讨论】：
“图像相对于其他图像的渐变”是什么意思？你是说两者的区别吗？您是指图像的渐变吗？ 你只能计算一个函数的梯度。例如，如果函数将图像（输入）映射到类别分数（输出）的向量，您可以计算输出相对于输入的梯度。但是在这里你说你想计算一个图像相对于另一个图像的梯度，你需要一个将图像映射到图像的函数来做到这一点。 This answer 可能会帮助你理解。 @GeorgeLiu：关于深度梦想的 tensorflow 教程有一个示例，该示例将图像相对于某个层的梯度。特别是 [this section] (nbviewer.jupyter.org/github/tensorflow/tensorflow/blob/master/…) 应该会有所帮助（即 t_grad = tf.gradients(t_score, t_input)[0]）。注意：您引用的博客没有采用一张图像相对于另一张图像的渐变。它正在获取图像相对于类分数的梯度。而在深切的梦想中，班级成绩只是另一层。 这个链接有一个对抗网络的视频和一个有据可查的例子。 github.com/Hvass-Labs/TensorFlow-Tutorials @chris_anderson 分类器神经网络的输出通常是一个向量，每个类有一个元素，其中每个元素（有效地）近似于输入图像属于该类的概率（或最小化训练图像上的日志损失）。给一个猫对狗分类器网络，一张猫的图像可能会产生一个输出 (0.9, 0.1) 或 90% 的猫。这个问题询问的梯度是输入图像的像素相对于网络输出的元素之一（类概率）。它不是空间坐标的图像梯度。 【参考方案1】：仅限班级成绩
如果您只能访问您建议的任何图像的班级分数，那么您就无法真正计算梯度。
如果返回的内容可以看作是每个类别的相对分数，则它是一个向量 v，它是某个函数 f 作用于包含图像上所有信息的向量 A 的结果* .函数的真实梯度由矩阵D(A) 给出，该矩阵取决于A，因此D(A)*B = (f(A + epsilon*B) -f(A))/epsilon 在小epsilon 的限制中对于任何B。您可以使用一些小的 epsilon 值和多个测试矩阵 B（A 的每个元素一个就足够了）来近似此数值，但这可能会不必要地昂贵。
您要做的是最大限度地提高算法识别图像的难度。也就是说，对于给定的算法f，您希望最大化一些适当的度量来衡量该算法识别您的每个图像A 的糟糕程度。有很多方法可以做到这一点。我对它们不太熟悉，但我最近看到的一个演讲有一些有趣的材料（https://wsc.project.cwi.nl/woudschoten-conferences/2016-woudschoten-conference/PRtalk1.pdf，见第 24 页及以后）。如果你有高维输入，计算整个梯度通常太昂贵了。相反，您只需修改一个随机选择的坐标，并在正确的方向上或多或少地采取许多（许多）小而便宜的步骤，而不是采取某种最佳的大而昂贵的步骤。
型号可用且合适
如果您完全了解模型并且可以明确写为v = f(A)，那么您可以计算函数f 的梯度。如果您尝试击败的算法是线性回归，可能是多层的，就会出现这种情况。渐变的形式应该比我在这里写的更容易理解。
有了这个梯度可用并且相当便宜地评估它对不同图像的价值A，您可以继续使用例如最陡下降（或上升）方法来使算法难以识别图像。
重要提示
最好不要忘记您的方法也不应该使图像对人类难以辨认，这会使这一切变得毫无意义。
我认为，出于本次讨论的目的，最好将图像视为矢量【讨论】：
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