可视化自编码器训练结果
From Ufldl
Line 1: | Line 1: | ||
- | |||
:【原文】: | :【原文】: | ||
- | Having trained a (sparse) autoencoder, we would now like to visualize the function | + | :Having trained a (sparse) autoencoder, we would now like to visualize the function |
learned by the algorithm, to try to understand what it has learned. | learned by the algorithm, to try to understand what it has learned. | ||
Consider the case of training an autoencoder on <math>\textstyle 10 \times 10</math> images, so that <math>\textstyle n = 100</math>. | Consider the case of training an autoencoder on <math>\textstyle 10 \times 10</math> images, so that <math>\textstyle n = 100</math>. | ||
Each hidden unit <math>\textstyle i</math> computes a function of the input: | Each hidden unit <math>\textstyle i</math> computes a function of the input: | ||
- | 【初译】: | + | :【初译】: |
得到了训练好的(稀疏)自编码器,我们就可以将通过算法习得的函数进行可视化,以便于了解学习的结果。我们以使用10×10的图像来训练自编码器为例,此时n=100。针对每个隐藏单元i,将输入值代入以下方程: | 得到了训练好的(稀疏)自编码器,我们就可以将通过算法习得的函数进行可视化,以便于了解学习的结果。我们以使用10×10的图像来训练自编码器为例,此时n=100。针对每个隐藏单元i,将输入值代入以下方程: | ||
- | 【一校】: | + | :【一校】: |
在得到了已经训练好的(稀疏)自编码器之后,我们希望可以将通过学习算法得到的函数进行可视化处理,以便于了解学习的结果。对于可视化过程,我们以一个通过对10×10的图像进行训练而得到的自编码器为例来进行说明,此例中n=100。在该自编码器中,每个隐藏单元i将输入代入到以下函数进行计算: | 在得到了已经训练好的(稀疏)自编码器之后,我们希望可以将通过学习算法得到的函数进行可视化处理,以便于了解学习的结果。对于可视化过程,我们以一个通过对10×10的图像进行训练而得到的自编码器为例来进行说明,此例中n=100。在该自编码器中,每个隐藏单元i将输入代入到以下函数进行计算: | ||
- | 【二校】: | + | :【二校】: |
我们得到训练好的(稀疏)自编码器后,希望通过可视化学习算法习得的函数,理解学习结果。考虑在10×10的图像上训练自编码器的例子,n=100。在该自编码器中,每个隐藏单元i将输入代入到以下函数进行计算: | 我们得到训练好的(稀疏)自编码器后,希望通过可视化学习算法习得的函数,理解学习结果。考虑在10×10的图像上训练自编码器的例子,n=100。在该自编码器中,每个隐藏单元i将输入代入到以下函数进行计算: | ||
- | 【三校】: | + | :【三校】: |
训练完(稀疏)自编码器,我们还想把这自编码器学到的函数可视化出来,好弄明白它到底学到了什么。我们以在10×10图像(即n=100)上训练自编码器为例。在该自编码器中,每个隐藏单元i对如下关于输入的函数进行计算: | 训练完(稀疏)自编码器,我们还想把这自编码器学到的函数可视化出来,好弄明白它到底学到了什么。我们以在10×10图像(即n=100)上训练自编码器为例。在该自编码器中,每个隐藏单元i对如下关于输入的函数进行计算: | ||
- | + | :<math>\begin{align} | |
- | 【原文】: | + | a^{(2)}_i = f\left(\sum_{j=1}^{100} W^{(1)}_{ij} x_j + b^{(1)}_i \right). |
+ | \end{align}</math> | ||
+ | <!-- This is the activation function <math>\textstyle g(\cdot)</math> applied to an affine function of the input.!--> | ||
+ | :【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 (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 | ||
【初译】: | 【初译】: |