diff --git a/README.md b/README.md index 0daed10ed33eb7904feb31ec4ec1cb53411e8e97..2f7b6d3c467c5615968bda552e85e5a77dbe9007 100644 --- a/README.md +++ b/README.md @@ -177,6 +177,7 @@ pipeline，流水线 size，大小 +transformation，变换 ## 样式规范 diff --git a/chapter_crashcourse/ndarray.md b/chapter_crashcourse/ndarray.md index 5faf6ed2c337096a7be1a823c92688ded29e47db..eb17315ef552169acd78c761a15eada05a67c498 100644 --- a/chapter_crashcourse/ndarray.md +++ b/chapter_crashcourse/ndarray.md @@ -2,7 +2,7 @@ 在深度学习中，我们通常会频繁地对数据进行操作。作为动手学深度学习的基础，本节将介绍如何对内存中的数据进行操作。 -在MXNet中，NDArray是存储和转换数据的主要工具。如果你之前用过NumPy，你会发现NDArray和NumPy的多维数组非常类似。然而，NDArray提供更多的功能，例如CPU和GPU的异步计算，以及自动求导。这些都使得NDArray更加适合深度学习。 +在MXNet中，NDArray是存储和变换数据的主要工具。如果你之前用过NumPy，你会发现NDArray和NumPy的多维数组非常类似。然而，NDArray提供更多的功能，例如CPU和GPU的异步计算，以及自动求导。这些都使得NDArray更加适合深度学习。 ## 创建NDArray @@ -196,22 +196,22 @@ x[1:2, 1:3] = 10 x ``` -## NDArray和NumPy相互转换 +## NDArray和NumPy相互变换 我们可以通过`array`和`asnumpy`函数令数据在NDArray和Numpy格式之间相互转换。以下是一个例子。 ```{.python .input n=22} import numpy as np x = np.ones((2, 3)) -y = nd.array(x) # NumPy转换成NDArray。 -z = y.asnumpy() # NDArray转换成NumPy。 +y = nd.array(x) # NumPy变换成NDArray。 +z = y.asnumpy() # NDArray变换成NumPy。 z, y ``` ## 小结 -* NDArray是MXNet中存储和转换数据的主要工具。 -* 我们可以轻松地对NDArray进行创建、运算、指定索引和与NumPy之间的相互转换。 +* NDArray是MXNet中存储和变换数据的主要工具。 +* 我们可以轻松地对NDArray进行创建、运算、指定索引和与NumPy之间的相互变换。 ## 练习 diff --git a/chapter_supervised-learning/multi-layer.md b/chapter_supervised-learning/multi-layer.md index 26ed8db84506e3027f5f3a9c574d9090914013e8..bac70817cad4594f3b41629537de41f7d083553e 100644 --- a/chapter_supervised-learning/multi-layer.md +++ b/chapter_supervised-learning/multi-layer.md @@ -14,7 +14,7 @@ 在图3.3的多层感知机中，输入和输出个数分别为4和3，中间的隐藏层中包含了5个隐藏单元（hidden unit）。由于输入层不涉及计算，图3.3中的多层感知机的层数为2。由图3.3可见，隐藏层中的神经元和输入层中各个输入完全连接，输出层中的神经元和隐藏层中的各个神经元也完全连接。因此，多层感知机中的隐藏层和输出层都是全连接层。 -## 线性转换 +## 仿射变换 在描述隐藏层的计算之前，让我们看看多层感知机输出层是怎样计算的。它的计算和之前介绍的单层神经网络的输出层的计算类似：只是输出层的输入变成了隐藏层的输出。我们通常将隐藏层的输出称为隐藏层变量或隐藏变量。 @@ -24,22 +24,23 @@ $$ \boldsymbol{O} = \boldsymbol{H} \boldsymbol{W}_o + \boldsymbol{b}_o, $$ -其中的加法运算使用了广播机制，$\boldsymbol{O} \in \mathbb{R}^{n \times y}$。可见，多层感知机的输出$\boldsymbol{O}$是对上一层的输出$\boldsymbol{H}$的线性转换。 +其中的加法运算使用了广播机制，$\boldsymbol{O} \in \mathbb{R}^{n \times y}$。实际上，多层感知机的输出$\boldsymbol{O}$是对上一层的输出$\boldsymbol{H}$的仿射变换（affine transformation）。它包括一次通过乘以权重参数的线性变换和一次通过加上偏差参数的平移。 -那么，如果隐藏层也对输入做线性转换会怎么样呢？为了便于描述这一问题，让我们暂时忽略每一层的偏差参数。设批量特征为$\boldsymbol{X} \in \mathbb{R}^{n \times x}$，隐藏层的权重参数$\boldsymbol{W}_h \in \mathbb{R}^{x \times h}$。假设$\boldsymbol{H} = \boldsymbol{X} \boldsymbol{W}_h$且$\boldsymbol{O} = \boldsymbol{H} \boldsymbol{W}_o$，联立两式可得$\boldsymbol{O} = \boldsymbol{X} \boldsymbol{W}_h \boldsymbol{W}_o$：它等价于$\boldsymbol{O} = \boldsymbol{X} \boldsymbol{W}^\prime$，其中$\boldsymbol{W}^\prime = \boldsymbol{W}_h \boldsymbol{W}_o$。因此，使用线性转换的隐藏层使多层感知机与前面介绍的单层神经网络没什么区别。 +那么，如果隐藏层也只对输入做仿射变换会怎么样呢？设单个样本的特征为$\boldsymbol{x} \in \mathbb{R}^{1 \times x}$，隐藏层的权重参数和偏差参数分别为$\boldsymbol{W}_h \in \mathbb{R}^{x \times h}, \boldsymbol{b}_h \in \mathbb{R}^{1 \times h}$。 +假设$\boldsymbol{h} = \boldsymbol{x} \boldsymbol{W}_h + \boldsymbol{b}_h$且$\boldsymbol{o} = \boldsymbol{h} \boldsymbol{W}_o + \boldsymbol{b}_o$，联立两式可得$\boldsymbol{o} = \boldsymbol{x} \boldsymbol{W}_h \boldsymbol{W}_o + \boldsymbol{b}_h \boldsymbol{W}_o + \boldsymbol{b}_o$：它等价于单层神经网络的输出$\boldsymbol{o} = \boldsymbol{x} \boldsymbol{W}^\prime + \boldsymbol{b}^\prime$，其中$\boldsymbol{W}^\prime = \boldsymbol{W}_h \boldsymbol{W}_o, \boldsymbol{b}^\prime = \boldsymbol{b}_h \boldsymbol{W}_o + \boldsymbol{b}_o$。因此，仅使用仿射变换的隐藏层使多层感知机与前面介绍的单层神经网络没什么区别。 ## 激活函数 -由上面的例子可以看出，我们必须在隐藏层中添加非线性转换，这样才能使多层感知机变得有意义。我们将这些非线性转换称为激活函数（activation function）。激活函数能对任意形状的输入按元素操作且不改变输入的形状。以下列举了三种常用的激活函数。 +由上面的例子可以看出，我们必须在隐藏层中使用其他变换，例如添加非线性变换，这样才能使多层感知机变得有意义。我们将这些非线性变换称为激活函数（activation function）。激活函数能对任意形状的输入按元素操作且不改变输入的形状。以下列举了三种常用的激活函数。 ### ReLU函数 -ReLU（rectified linear unit）函数提供了一个很简单的非线性转换。给定元素$x$，该函数的输出是 +ReLU（rectified linear unit）函数提供了一个很简单的非线性变换。给定元素$x$，该函数的输出是 $$\text{relu}(x) = \max(x, 0).$$ -ReLU函数只保留正数元素，并将负数元素清零。为了直观地观察这一非线性转换，让我们先导入一些包或模块。 +ReLU函数只保留正数元素，并将负数元素清零。为了直观地观察这一非线性变换，让我们先导入一些包或模块。 ```{.python .input n=1} %matplotlib inline @@ -51,7 +52,7 @@ import matplotlib.pyplot as plt from mxnet import nd ``` -下面，让我们绘制ReLU函数。当元素值非负时，ReLU函数实际上在做线性转换。 +下面，让我们绘制ReLU函数。当元素值非负时，ReLU函数实际上在做线性变换。 ```{.python .input n=2} gb.set_fig_size(mpl) @@ -63,33 +64,15 @@ plt.ylabel('relu(x)') plt.show() ``` -```{.json .output n=2} -[ - { - "data": { - "image/png": "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\n", - "text/plain": "
" - }, - "metadata": { - "image/png": { - "height": 182, - "width": 238 - } - }, - "output_type": "display_data" - } -] -``` - ### Sigmoid函数 -Sigmoid函数可以将元素的值转换到0和1之间： +Sigmoid函数可以将元素的值变换到0和1之间： $$\text{sigmoid}(x) = \frac{1}{1 + \exp(-x)}.$$ 我们会在后面“循环神经网络”一章中介绍如何利用sigmoid函数值域在0到1之间这一特性来控制信息在神经网络中的流动。 -下面绘制了sigmoid函数。当元素值接近0时，sigmoid函数接近线性转换。 +下面绘制了sigmoid函数。当元素值接近0时，sigmoid函数接近线性变换。 ```{.python .input n=3} plt.plot(x.asnumpy(), x.sigmoid().asnumpy()) @@ -98,31 +81,13 @@ plt.ylabel('sigmoid(x)') plt.show() ``` -```{.json .output n=3} -[ - { - "data": { - "image/png": "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\n", - "text/plain": "
" - }, - "metadata": { - "image/png": { - "height": 182, - "width": 247 - } - }, - "output_type": "display_data" - } -] -``` - ### Tanh函数 -Tanh（双曲正切）函数可以将元素的值转换到-1和1之间： +Tanh（双曲正切）函数可以将元素的值变换到-1和1之间： $$\text{tanh}(x) = \frac{1 - \exp(-2x)}{1 + \exp(-2x)}.$$ -下面绘制了tanh函数。当元素值接近0时，tanh函数接近线性转换。值得一提的是，它的形状和sigmoid函数很像，且当元素在实数域上均匀分布时，tanh函数值的均值为0。 +下面绘制了tanh函数。当元素值接近0时，tanh函数接近线性变换。值得一提的是，它的形状和sigmoid函数很像，且当元素在实数域上均匀分布时，tanh函数值的均值为0。 ```{.python .input n=4} plt.plot(x.asnumpy(), x.tanh().asnumpy()) @@ -131,44 +96,13 @@ plt.ylabel('tanh(x)') plt.show() ``` -```{.json .output n=4} -[ - { - "data": { - "image/png": "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\n", - "text/plain": "
" - }, - "metadata": { - "image/png": { - "height": 182, - "width": 256 - } - }, - "output_type": "display_data" - } -] -``` - -下面，我们使用三种激活函数来转换输入。按元素操作后，输入和输出形状相同。 +下面，我们使用三种激活函数来变换输入。按元素操作后，输入和输出形状相同。 ```{.python .input n=5} X = nd.array([[[0,1], [-2,3], [4,-5]], [[6,-7], [8,-9], [10,-11]]]) X.relu(), X.sigmoid(), X.tanh() ``` -```{.json .output n=5} -[ - { - "data": { - "text/plain": "(\n [[[ 0. 1.]\n [ 0. 3.]\n [ 4. 0.]]\n \n [[ 6. 0.]\n [ 8. 0.]\n [10. 0.]]]\n , \n [[[5.0000000e-01 7.3105860e-01]\n [1.1920292e-01 9.5257413e-01]\n [9.8201376e-01 6.6928510e-03]]\n \n [[9.9752742e-01 9.1105117e-04]\n [9.9966466e-01 1.2339458e-04]\n [9.9995458e-01 1.6701422e-05]]]\n , \n [[[ 0. 0.7615942 ]\n [-0.9640276 0.9950548 ]\n [ 0.9993293 -0.9999092 ]]\n \n [[ 0.9999877 -0.99999833]\n [ 0.99999976 -0.99999994]\n [ 1. -1. ]]]\n )" - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } -] -``` - ## 多层感知机 现在，我们可以给出多层感知机的矢量计算表达式了。 @@ -224,7 +158,7 @@ $$U(-\sqrt{\frac{6}{a+b}}, \sqrt{\frac{6}{a+b}}).$$ ## 小结 -* 多层感知机本质上是对输入做一系列线性和非线性的转换。 +* 多层感知机对输入做了一系列的线性和非线性的变换。 * 常用的激活函数包括ReLU函数、sigmoid函数和tanh函数。 * 我们需要随机初始化神经网络的模型参数。