论文笔记--DeepFool: a simple and accurate method to fool deep neural networks

论文原文：DeepFool: a simple and accurate method to fool deep neural networks arXiv:1511.04599 [cs.LG]

思路

deepfool提出两种产生对抗样本的算法，二分类和多分类情况。并实验比较EOT、FGSM和deepfool三种算法的鲁棒性。

1、二分类器

符号函数k^(x) = sign(f(x)) 其中 f(x) = wx + b。对样本添加扰动使得样本分类到距离最近的类。
r:样本到分类边界的最短距离*法线方向的单位向量

2、多分类器

k^(x)= fk(x)，fk(x) 是向量f(x)的第k个维度，即第k个子分类器。
计算样本到各个类的最小距离，取最近的一类，L为距离超平面最近的一类。

3、评估鲁棒性

通过扰动所占样本的比值来评估鲁棒性。下表为deepfool,EOT,FGSM三种算法的鲁棒性和运行时间对比

4、论文复现-多分类结果：

Evaluating on clean data
loss: 0.0294 acc: 0.9900
Evaluating on adversarial data
loss: 1.6897 acc: 0.1145

def _deepfool2(model, x, epochs, eta, clip_min, clip_max, min_prob):"""DeepFool二分类情况干净样本和对抗样本输出： +1/-1"""y0 = tf.stop_gradient(tf.reshape(model(x), [-1])[0])y0 = tf.to_int32(tf.greater(y0, 0.0))def _cond(i, z):xadv = tf.clip_by_value(x + z*(1+eta), clip_min, clip_max)y = tf.stop_gradient(tf.reshape(model(xadv), [-1])[0])y = tf.to_int32(tf.greater(y, 0.0))return tf.logical_and(tf.less(i, epochs), tf.equal(y0, y))def _body(i, z):xadv = tf.clip_by_value(x + z*(1+eta), clip_min, clip_max)y = tf.reshape(model(xadv), [-1])[0]g = tf.gradients(y, xadv)[0]dx = - y * g / (tf.norm(g) + 1e-10)  # 1范数：norm（1）return i+1, z+dx_, noise = tf.while_loop(_cond, _body, [0, tf.zeros_like(x)],name='_deepfool2', back_prop=False)return noise

def _deepfoolx(model, x, epochs, eta, clip_min, clip_max, min_prob):"""DeepFool多分类情况.分类到最大概率的标签."""y0 = tf.stop_gradient(model(x))y0 = tf.reshape(y0, [-1])k0 = tf.argmax(y0)ydim = y0.get_shape().as_list()[0]xdim = x.get_shape().as_list()[1:]xflat = _prod(xdim)def _cond(i, z):xadv = tf.clip_by_value(x + z*(1+eta), clip_min, clip_max)y = tf.reshape(model(xadv), [-1])p = tf.reduce_max(y)k = tf.argmax(y)return tf.logical_and(tf.less(i, epochs),tf.logical_or(tf.equal(k0, k),tf.less(p, min_prob)))def _body(i, z):xadv = tf.clip_by_value(x + z*(1+eta), clip_min, clip_max)y = tf.reshape(model(xadv), [-1])gs = [tf.reshape(tf.gradients(y[i], xadv)[0], [-1])for i in range(ydim)]g = tf.stack(gs, axis=0)yk, yo = y[k0], tf.concat((y[:k0], y[(k0+1):]), axis=0)gk, go = g[k0], tf.concat((g[:k0], g[(k0+1):]), axis=0)yo.set_shape(ydim - 1)go.set_shape([ydim - 1, xflat])a = tf.abs(yo - yk)b = go - gkc = tf.norm(b, axis=1)score = a / cind = tf.argmin(score)si, bi = score[ind], b[ind]dx = si * bidx = tf.reshape(dx, [-1] + xdim)return i+1, z+dx_, noise = tf.while_loop(_cond, _body, [0, tf.zeros_like(x)],name='_deepfoolx', back_prop=False)return noise

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论文笔记--DeepFool: a simple and accurate method to fool deep neural networks

思路

1、二分类器

2、多分类器

3、评估鲁棒性

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