深度学习基础（二）—— 从多层感知机（MLP）到卷积神经网络（CNN）

经典的多层感知机（Multi-Layer Perceptron）形式上是全连接（fully-connected）的邻接网络（adjacent network）。

That is, every neuron in the network is connected to every neuron in adjacent layers.

Local receptive fields

全连接的多层感知机中，输入视为（或者需转化为）一个列向量。而在卷积神经网络中，以手写字符识别为例，输入不再 reshape 为 (28*28, 1) 的列向量，而是作为 28×28 的像素灰度矩阵。

That region in the input image is called the local receptive field for the hidden neuron. It’s a little window on the input pixels. Each connection learns a weight（one single weight，也即整个 5×5 的 region 共享同一个 weight）. And the hidden neuron learns an overall bias as well.

Shared weights and biases

注意对应关系，是左上角对应左上角，后四列是利用不到的？

28×28(5×5)⇒24×24

第 j 行 k 列的隐层神经元的输入为：

b+∑ℓ=04∑m=04wℓ,maj+ℓ,k+m

该隐层神经元的输出为：

σ(b+∑ℓ=04∑m=04wℓ,maj+ℓ,k+m)

The network structure I’ve described so far can detect just a single kind of localized feature. To do image recognition we’ll need more than one feature map（特征映射）. And so a complete convolutional layer consists of several different feature maps:

feature map：filter，kernel

In the example shown, there are 3 feature maps. Each feature map is defined by a set of 5×5 shared weights, and a single shared bias. The result is that the network can detect 3 different kinds of features（特征检测）, with each feature being detectable across the entire image.

I’ve shown just 3 feature maps, to keep the diagram above simple. However, in practice convolutional networks may use more (and perhaps many more) feature maps. One of the early convolutional networks, LeNet-5, used 6 feature maps, each associated to a 5×5 local receptive field, to recognize MNIST digits. So the example illustrated above is actually pretty close to LeNet-5. In the examples we develop later in the chapter we’ll use convolutional layers with 20 and 40 feature maps. Let’s take a quick peek at some of the features which are learned*