深层学习基础 (DEEP LEARNING BASICS)

Aim of this article is to provide an intuitive understanding behind the inner working of key layers in a convolution neural network. The idea is to go beyond simply stating the facts and exploring how image manipulation actually works.

本文的目的是提供对卷积神经网络中关键层内部工作的直观了解。 这个想法不只是简单地陈述事实 ， 而是探索图像处理的实际作用 。

目标 (The Objective)

Out aim is to design a deep learning framework capable of classify cat and dog images like those shown below. Let us start by thinking about what challenges such an algorithm must overcome.

最终目的是设计一个能够对猫和狗图像进行分类的深度学习框架，如下所示。 让我们首先考虑一下这种算法必须克服的挑战。

It should be able to detect cats and dogs of different color, size, shape, and breed. It must be able to detect and classify animals even from pictures where the dog or the cat is not entirely visible. It must be sensitive to presence of more than one dog in the image. Most importantly, the algorithm must be spatially invariant — it must be able to recognise dogs physically located in any corner of the image.

它应该能够检测出不同颜色，大小，形状和品种的猫和狗。 即使从狗或猫不完全可见的图片中，它也必须能够对动物进行检测和分类。 它必须对图像中有不止一只狗的情况敏感。 最重要的是，该算法必须在空间上不变-它必须能够识别物理上位于图像任何角落的狗。

计算机如何读取图像。 (How computer reads images.)

Images are composed of pixels that have values ranging from 0–255 that depict brightness. 0 means black, 255 is white and everything else is some shade of grey. More the pixels, better the image quality.

图像由像素组成，其值在0-255之间，表示亮度。 0表示黑色，255表示白色，其他所有内容均为灰色。 像素越多，图像质量越好。

While a greyscale image is made of a single channel (i.e. a 2D array). A color image in the RBG format is composed of three different layers, stacked on top of each other

灰度图像由单个通道(即2D阵列)组成。 RBG格式的彩色图像由三个不同的层组成，彼此堆叠

多层感知器的局限性。 (Limitations of a multi-layered perceptron.)

The contents of each pixel are fed into the perceptron separately. Each neuron processes a pixel in the input layer. For a image of dimensions 350*720, the total number of parameters to be learned for the input layer alone will be (350*720*3 (three channels for each pixel)*2 (two parameters per neuron, weight and bias)) 1.5 million. This number will scale linearly with number of layers, making the MLP an incredibly computationally intensive to learn. This however is not the only challeng with MLPs.

每个像素的内容分别送入感知器。 每个神经元处理输入层中的一个像素。 对于尺寸为350 * 720的图像，仅输入层要学习的参数总数将为(350 * 720 * 3(每个像素三个通道)* 2(每个神经元两个参数，权重和偏差) 150万。 该数目将随层数线性增长，这使得MLP的计算量大到难以学习。 但是，这并不是MLP的唯一挑战。

MLPs have no inbuilt mechanism for being spatially invariant. If a MLP has been trained to detect dogs in the top right corner of the image, it will fail when dogs are located in other positions. This is a serious drawback and in the subsequent sections we will discuss how to overcome this challenge.

MLP没有内置的机制来保持空间不变。 如果已训练MLP在图像的右上角检测狗，则当狗位于其他位置时，它将失败。 这是一个严重的缺陷，在接下来的部分中，我们将讨论如何克服这一挑战。

A convolution neural network aims to ameliorate these drawbacks using built-in mechanism for (1) extracting different high level features (2) introducing spatial invariance (3) improving networks learning ability.

卷积神经网络旨在使用内置机制来缓解这些缺点，该机制用于 (1)提取不同的高级特征(2)引入空间不变性(3)改善网络学习能力。

图像特征提取。 (Image feature extraction.)

Convolution (discrete convolution to be specific) is based on use to linear transformations to extract the key features of input images while preserving the ordering of information. The input is convolved with a kernel to generate the output, similar to the response generated by a network of neurons in the visual cortex.

卷积(具体来说是离散卷积)基于线性变换的使用，以在保持信息有序的同时提取输入图像的关键特征。 输入与内核进行卷积以生成输出，类似于视觉皮层中神经元网络生成的响应。

Kernel

核心

The kernel (also known as a filter or a feature detector) samples the input image matrix with a pre-determined step size (known as stride) in both horizontal and vertical directions. As the kernel slides over the input image, the element-wise product between each element of the kernel and overlapping elements of the input image is calculated to obtain to the output for the current location. When the input image is composed of multiple channels (which is almost always the case), the kernel has the same depth as the number of channels in the input image. The dot product in such cases is added to arrive at a feature map composed of a single channel.

内核(也称为过滤器或特征检测器)在水平和垂直方向上以预定步长(称为步幅)对输入图像矩阵进行采样。 当内核在输入图像上滑动时，将计算内核的每个元素与输入图像的重叠元素之间的逐元素乘积，以获取当前位置的输出。 当输入图像由多个通道组成时(几乎总是这样)，内核的深度与输入图像中通道的数量相同。 在这种情况下，将点积相加即可得出由单个通道组成的特征图。

If you are new to matrix multiplication, check out this youtube video for a more detailed explanation.

如果您不熟悉矩阵乘法，请 观看 此 youtube视频以获取更详细的说明。

While a CNN made of a single convolution layer would only be able to extract/learn low level features of the input image, adding successive convolution layers significantly improves the ability of the CNN to learn high level features.

尽管由单个卷积层构成的CNN仅能够提取/学习输入图像的低级特征，但是添加连续的卷积层会显着提高CNN学习高级特征的能力。

Rectifier

整流器

To introduce non-linearity into the system and improve the learning capacity, the output from the convolution operation is passed through a non-saturating activation function like sigmoid or rectified linear unit (ReLU). Check out this excellent article about these and several other commonly used activation functions.

为了将非线性引入系统并提高学习能力，卷积运算的输出将通过非饱和激活函数(如S型或整流线性单元(ReLU))传递。 查看 关于这些以及其他几个常用激活功能的 出色文章 。

Padding

填充

The feature map resulting from convolution is smaller in size compared to the input image. For an input image of I*I that is convolved with a kernel of size K*K with a stride S, the output will be [(I-F)/S + 1]* [(I-F)/S + 1]. This can result in substantial reduction in image size in large CovNets made of several convolution layers. A zero padding of [(F-1)/2] all around the output image can be used to preserve the convolution output. Alternatively, the padding size itself can be turned into one of the hyperparameters that is learned during the training of the CNN.

与输入图像相比，由卷积产生的特征图的大小较小。 对于 I * I 的输入图像， 它 与步长为 S 的大小为 K * K 的内核卷积 ，输出将为 [(IF)/ S + 1] * [(IF)/ S +1] 。 在由多个卷积层组成的大型CovNet中，这可能会导致图像大小的显着减小。 输出图像周围的 [[F-1)/ 2] 零填充 可用于保留卷积输出。 备选地，填充大小本身可以变成在CNN的训练期间学习的超参数之一。

For the most general case where an input image of size I*I is convolved with a filter of size K*K with a stride S and padding P, the output will have the dimension [(I+2P-K)/S +1]*[(I+2P-K)/S +1].

对于最一般的情况，其中输入大小为 I * I的 图像与大小 为 K * K 且步幅为 S 且填充为 P 的滤波器进行卷积时 ，输出将具有 [[I + 2P-K)/ S +1 ] * [(I + 2P-K)/ S +1] 。

Pooling

汇集

The convolution output is pooled so as to introduce spatial invariance i.e the ability to detect the same feature in different images. The idea here is to retain key information corresponding to important features that the CNN must learn and at the same time reduce image size by getting rid of insignificant information. While there are several variation, max pooling is the most commonly used strategy. The convolution product is split into non-overlapping patches of size K*K and only the maximum value of each patch is recorded in the output.

合并卷积输出以引入空间不变性，即在不同图像中检测相同特征的能力。 这里的想法是保留与CNN必须学习的重要功能相对应的关键信息，同时通过摆脱无关紧要的信息来减小图像尺寸。 尽管存在多种变体，但最大池化是最常用的策略。 卷积积被拆分为大小为 K * K的 非重叠面片， 并且仅每个面片的最大值记录在输出中。

Other less frequently used pooling strategies include average pooling, ‘mixed’ max-average pooling, stochastic pooling, spatial pyramid pooling etc.

其他不常用的合并策略包括平均合并，“混合”最大平均合并，随机合并，空间金字塔合并等。

Let us summarise the concepts discussed so far as they apply to the VGGNet 16 architecture. Show below are the convolution layers of this network.

让我们总结一下所讨论的概念，直到它们适用于VGGNet 16架构。 下面显示的是该网络的卷积层。

This network excepts a image made of 224*224 pixels and 3 channels (corresponding to red, green and blue) as input. It is then processes through a series of convolution layers (shown in black), not all of which are followed by a max pooling step. Five distinct convolution blocks are depicted in the image above. All convolution steps use 3*3 kernels and all max pooling steps use a 2*2 kernel. The number of kernels used in each convolution block gradually increases, from 64 in first to 512 in the fourth and fifth convolution block. Initially two and later three convolution layers are used per block. This is important for increasing the receptive field since the kernel size is mantained constant throughout this architecture. The output of block five is passed through a maxpooling layer at the end, resulting in a 7*7*512 output. The output from the last convolution block is then fed into the fully connected layer discussed in the subsequent section. For a more detailed understanding of VGGNet, read the original paper.

该网络不包括由224 * 224像素和3个通道(分别对应于红色，绿色和蓝色)作为输入的图像。 然后，它通过一系列卷积层(以黑色显示)进行处理，并非所有卷积层之后都是最大池化步骤。 上图中描绘了五个不同的卷积块。 所有卷积步骤都使用3 * 3内核，所有最大池化步骤都使用2 * 2内核。 每个卷积块中使用的内核数量逐渐增加，从最初的64个增加到第四个和第五个卷积块中的512个。 最初，每个块使用两个和后来的三个卷积层。 这对于增加接收场很重要，因为在整个体系结构中内核大小保持恒定。 块5的输出最后通过maxpooling层，产生7 * 7 * 512的输出。 然后，最后一个卷积块的输出将馈送到下一节中讨论的完全连接的层中。 为了更详细地了解VGGNet，请阅读 原始文章 。