如何根据某个类计算图像的渐变？
在Breaking Linear Classifiers on ImageNet中，作者提出了以下方法来创建欺骗ConvNets的对抗图像：
简而言之，为了创造一个愚蠢的形象，我们从任何形象开始 想要（实际图像，甚至噪音模式），然后使用 反向传播计算任何图像像素的梯度 课程成绩，并轻轻一推。我们可以，但不必，重复 过程几次。您可以在此解释反向传播 设置为使用动态编程来计算最具破坏性的 对输入的局部扰动。请注意，这个过程非常好 如果你有权访问，那么效率很高，时间可以忽略不计 ConvNet的参数（backprop很快），但有可能做到 这即使您无法访问参数，也只能访问 课程成绩最后。在这种情况下，可以计算 数据梯度数字，或使用其他本地随机搜索 策略等。请注意，由于后一种方法，甚至 不可微分类（例如随机森林）并不安全（但是 我还没见过有人凭经验证实这一点。
我知道我可以像这样计算图像的渐变：
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渐变？可能我需要做一些与流程in this tutorial类似的事情？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}))
但我不确定具体如何......具体来说，我有一个数字2的图像如下：
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如何计算此图像相对于数字6图像类的渐变（下面显示了一个示例）？ （我想我需要使用反向传播来计算所有数字6图像的渐变。）
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提前感谢您的帮助！
这里提到了我提出的两个相关问题：
How to use image and weight matrix to create adversarial images in TensorFlow?
How to create adversarial images for ConvNet?
这里my script。
1 个答案:
答案 0 :(得分：1)
仅分类
如果您只能访问任何图像的课程分数，那么您建议您真正计算渐变的目的并不多。
如果返回的内容可以被视为每个类别的相对分数，则它是一个向量v，它是某个函数f作用于包含所有类别的向量A的结果有关图像的信息*。函数的真实梯度由矩阵D(A)给出，它取决于A，因此任何D(A)*B = (f(A + epsilon*B) -f(A))/epsilon的{{1}}限制为epsilon。 。你可以使用epsilon的一些小值和一些测试矩阵B（B的每个元素一个应该足够）来数值近似，但这可能是不必要的昂贵。
您要做的是最大化算法识别图像的难度。也就是说，对于给定的算法A，您希望最大化一些适当的度量，以确定算法识别每个图像f的差异程度。有很多方法可以解决这个问题。我对它们不是很熟悉，但我最近看到的一个话题有一些有趣的内容（https://wsc.project.cwi.nl/woudschoten-conferences/2016-woudschoten-conference/PRtalk1.pdf，见第24页及以后）。如果您具有高维输入，则计算整个梯度通常太昂贵。相反，你只需要修改一个随机选择的坐标，然后在正确的方向上或多或少地采取许多（很多）小而便宜的步骤，而不是以某种方式实现最佳的大而昂贵的步骤。
型号可用且适用
如果您完全了解模型并且可以明确地将其写为A，那么您可以计算函数v = f(A)的梯度。如果您尝试击败的算法是线性回归，可能是多层，则会出现这种情况。渐变的形式应该比你在这里写下来更容易弄清楚。
使用此渐变可以非常便宜地评估其对不同图像f的值，您可以继续使用最陡的下降（或上升）方法来使图像对算法不易识别。
重要提示
最好不要忘记你的方法也不应该让图像对人类难以理解，这样做会使一切都毫无意义。
- 我认为出于本次讨论的目的，最好将图像视为向量
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