# 可视化自编码器训练结果

 Revision as of 10:51, 7 March 2013 (view source)Kandeng (Talk | contribs)← Older edit Revision as of 11:05, 7 March 2013 (view source)Kandeng (Talk | contribs) Newer edit → Line 14: Line 14: :【原文】： :【原文】： - We will visualize the function computed by hidden unit  ---which depends on the parameters   (ignoring the bias term for now)---using a 2D image. In particular, we think of   as some non-linear feature of the input . We ask: What input image   would cause   to be maximally activated? (Less formally, what is the feature that hidden unit   is looking for?) For this question to have a non-trivial answer, we must impose some constraints on . If we suppose that the input is norm constrained by , then one can show (try doing this yourself) that the input which maximally activates hidden unit   is given by setting pixel   (for all 100 pixels, ) to + :We will visualize the function computed by hidden unit  ---which depends on the parameters $\textstyle W^{(1)}_{ij}$ (ignoring the bias term for now)---using a 2D image. In particular, we think of $\textstyle a^{(2)}_i$ as some non-linear feature of the input $\textstyle x$. We ask: What input image $\textstyle x$ would cause $\textstyle a^{(2)}_i$ to be maximally activated? (Less formally, what is the feature that hidden unit $\textstyle i$ is looking for?) For this question to have a non-trivial answer, we must impose some constraints on $\textstyle x$. If we suppose that the input is norm constrained by $\textstyle ||x||^2 = \sum_{i=1}^{100} x_i^2 \leq 1$, then one can show (try doing this yourself) that the input which maximally activates hidden unit $\textstyle i$ is given by setting pixel $\textstyle x_j$ (for all 100 pixels, $\textstyle j=1,\ldots, 100$) to + :\begin{align} + x_j = \frac{W^{(1)}_{ij}}{\sqrt{\sum_{j=1}^{100} (W^{(1)}_{ij})^2}}. + \end{align} 【初译】： 【初译】： 我们将用2D图像对这个由隐藏单元i计算出的函数进行可视化，这个函数依赖于参数 （忽略掉偏置项b_i）。此时，如果我们将 理解为输入向量 的某个非线性特征值，我们需要思考：什么样的输入图像 会使得激励 取得最大值？（也就是说，隐藏单元i找到的是一个什么样的特征值？）。因为这个问题需要有一个有实际意义的解，所以我们必须对 加以限制。我们采用输入向量长度的平方 进行归一化限制，于是可以得到（请读者尝试自行推导。），当输入对隐藏单元产生最大的激励时，其输入像素 （对所有100个输入像素，j=1,…,100）所取的值应为： 我们将用2D图像对这个由隐藏单元i计算出的函数进行可视化，这个函数依赖于参数 （忽略掉偏置项b_i）。此时，如果我们将 理解为输入向量 的某个非线性特征值，我们需要思考：什么样的输入图像 会使得激励 取得最大值？（也就是说，隐藏单元i找到的是一个什么样的特征值？）。因为这个问题需要有一个有实际意义的解，所以我们必须对 加以限制。我们采用输入向量长度的平方 进行归一化限制，于是可以得到（请读者尝试自行推导。），当输入对隐藏单元产生最大的激励时，其输入像素 （对所有100个输入像素，j=1,…,100）所取的值应为：