Here we will introduce these extensive implementation details, i.e., tricks or tips, for building and training your own deep networks.
主要以下面八个部分展开介绍：
mainly in eight
aspects: 1) data
augmentation; 2) pre-processing
on images; 3) initializations
of Networks; 4) some
tips during training; 5) selections
of activation functions; 6) diverse
regularizations; 7)some
insights found from figures and finally 8) methods
of ensemble multiple deep networks.
1，数据扩增
2.预处理数据
3.初始化网络
4，在训练中的一些tips
5,合理的选择激活函数
6.多种正则化
7，从实验图和结果发现insights
8，如何集合多个网络
依次介绍八种方法：
一、data augmentation
1. th additiarhorizontally
flipping（水平翻转）, random crops(随机切割) and color jittering(颜色抖动). Moreover, you could try combinations of multiple different processing, e.g., doing the rotation and random scaling at the same time. In addition,
you can try to raise saturation and value (S and V components of the HSV color space) of all pixels to a power between 0.25 and 4 (same for all pixels within a patch), multiply these values
by a factor between 0.7 and 1.4, and add to them a value between -0.1 and 0.1. Also, you could add a value between [-0.1, 0.1] to the hue (H component of HSV) of all pixels in the image/patch.
2、Krizhevsky et
al. [1] proposed fancy
PCA。you can firstly perform PCA on the set of RGB pixel values throughout your training images. add
the following quantity to each RGB image pixel (i.e., 
): 
where, 
and 
are
the 
-th
eigenvector and eigenvalue of the 
covariance
matrix of RGB pixel values, respectively, and 
is
a random variable drawn from a Gaussian with mean zero and standard deviation 0.1. 。。
二、Pre-processing
1、The
first and simple pre-processing approach is zero-center the
data, and then normalize them。
code：
>>> X -= np.mean(X, axis = 0) # zero-center >>> X /= np.std(X, axis = 0) # normalize
2、re-processing
approach similar to the first one is PCA Whitening.
>>> X -= np.mean(X, axis = 0) # zero-center >>> cov = np.dot(X.T, X) / X.shape[0] # compute the covariance matrix
>>> U,S,V = np.linalg.svd(cov) # compute the SVD factorization of the data covariance matrix >>> Xrot = np.dot(X, U) # decorrelate the data
>>> Xwhite = Xrot / np.sqrt(S + 1e-5) # divide by the eigenvalues (which are square roots of the singular values)
上面两种方法：these transformations are not used with Convolutional Neural Networks.
However, it is also very important to zero-center the
data, and it is common to see normalization of every pixel
as well.
三、初始化-Initialization
1.All Zero Initialization---假如全部权值都设为0或相同的数，就会计算相同梯度和相同的参数更新，即没有对称性
In the ideal situation, with proper data normalization it is reasonable to assume that approximately half of the weights will
be positive and half of them will be negative. A reasonable-sounding idea then might be to set all the initial weights to zero, which you expect to be
the “best guess” in expectation. But, this turns out to be a mistake, because if every neuron in the network computes the same output, then they will also all compute the same gradients during back-propagation and undergo
the exact same parameter updates. In other words, there is no source of asymmetry between neurons if their weights are initialized to be the same.
2、Initialization with Small Random Numbers
依据：仍然期望各参数接近0，符合对称分布，选取 
来设各个参数，但最后的效果没有实质性提高。
Thus, you still want the weights to be very close to zero, but not identically zero. In this way, you can random these neurons to small numbers which are very close
to zero, and it is treated as symmetry breaking. The idea is that
the neurons are all random and unique in the beginning, so they will compute distinct updates and integrate themselves as diverse parts of the full network. The implementation for weights might simply look like ,
where 
is
a zero mean, unit standard deviation gaussian. It is also possible to use small numbers drawn from a uniform distribution, but this seems to have relatively little impact on the final performance in practice.
3、Calibrating the Variances 调整各个方差，每个细胞源输出的方差归到1，通过除以输入源的个数的平方
One problem with the above suggestion is that the distribution of the outputs from a randomly initialized neuron has a variance that grows with the number of inputs. It turns out thatyou can normalize the variance of each neuron‘s
output to 1 by scaling its weight vector by the square root of its fan-in (i.e., its number of inputs), which is as follows:
>>> w = np.random.randn(n) / sqrt(n) # calibrating the variances with 1/sqrt(n)
4、Current Recommendation 当前流行的方法。是文献[4]神经元方差设定为2/n.n是输入个数。所以对权值w的处理是，正态分布上的采样数乘以sqrt(2.0/n)
As aforementioned, the previous initialization by calibrating the variances of neurons is without considering ReLUs. A more recent paper on this topic by He et al. [4] derives
an initialization specifically for ReLUs, reaching the conclusion that the variance of neurons in the network should be 
as:
>>> w = np.random.randn(n) * sqrt(2.0/n) # current recommendation
- K. He, X. Zhang, S. Ren, and J. Sun. Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification. InICCV, 2015.
四、训练过程
1、Filters and pooling size. 滤波子大小和尺化大小的设定
the size of input images prefers to be power-of-2, such as32 (e.g., CIFAR-10),
64, 224 (e.g., common used ImageNet), 384 or 512, etc. Moreover, it is important to employ a
small filter (e.g., )
and small strides (e.g., 1) with zeros-padding, which not only reduces the number of parameters, but improves the accuracy rates of the whole deep network. Meanwhile, a special case mentioned above, i.e., filters
with stride 1, could preserve the spatial size of images/feature maps. For the pooling layers, the common usedpooling size is of 
.
2、Learning rate.
建议学习率，gradients除以batch size 。在没有改变mini batch时，最好别改变lr.
开始lr设定为0.1~~利用validation set来确定Lr,再每次除以2或5
In addition, as described in a blog by Ilya Sutskever [2],
he recommended to divide the gradients by mini batch size. Thus, you should not always change the learning rates (LR), if you change the mini batch size. For obtaining an appropriate LR, utilizing the validation set is an effective way. Usually, a typical
value of LR in the beginning of your training is 0.1. In practice, if you see that you stopped making progress on the validation set, divide the LR by 2 (or by 5), and keep going, which might give you a surprise.
3、Fine-tune
on pre-trained models，微调和预训练，直接利用已经公布的一些模型：Caffe
Model Zoo and VGG
Group。
结合这些模型用于新的数据集上，需要fine-tune，需要考虑两个重要因子：数据集大小和与原数据的相似度。
For further improving the classification
performance on your data set, a very simple yet effective approach is to fine-tune the pre-trained models on your own data. As shown in following table, the two most important factors are the size
of the new data set (small or big), and its similarity to the original data set. Different strategies of fine-tuning can be utilized in different situations. For instance, a good case is that your new data set is very
similar to the data used for training pre-trained models. In that case, if you have very little data, you can just train a linear classifier on the features extracted from the top layers of pre-trained models. 微调分两种情况：第一种：如果新数据集少，且分布类似预训练的库（现实是残酷的，不太可能），只需要调整最后一层的线性分类器。
If your have quite a lot of data at
hand, please fine-tune a few top layers of pre-trained models with a small learning rate.
如果有很多数据，就用小的LR调整模块的最后几层
However, if your own data set is
quite different from the data used in pre-trained models but with enough training images, a large number of layers should be fine-tuned on your data also with a small learning rate for improving performance.
如果你的数据与预模型不同，但数量充足，用一个小的Lr对很多层进行调整
However, if your data set not only
contains little data, but is very different from the data used in pre-trained models, you will be in trouble. Since the data is limited, it seems better to only train a linear classifier. Since the data set is very different, it might not be best to train
the classifier from the top of the network, which contains more dataset-specific features. Instead, it might work better to train the SVM classifier on activations/features from somewhere earlier in the network.
假如，数据少且不同与源数据模型，这就会很复杂。仅仅靠训练分类器肯定不行。也许可以对网络中前几层的激活层和特征层做SVM分类器训练。
五、 selections
of activation functions;合理选择激活函数
One of the crucial factors in deep networks
is activation function, which brings the non-linearity into
networks. Here we will introduce the details and characters of some popular activation functions and give advices later in this section.
本图取之：http://cs231n.stanford.edu/index.html
几种激活函数：
Sigmoid：
The sigmoid non-linearity has the mathematical form 
.
It takes a real-valued number and “squashes” it into range between 0 and 1. In particular, large negative numbers become 0 and large positive numbers become 1. The sigmoid function has seen frequent use historically since it has a nice interpretation as the
firing rate of a neuron: from not firing at all (0) to fully-saturated firing at an assumed maximum frequency (1).在最大阈值1时，就达到饱和--Saturated.
sigmoid已经失宠，因为他的两个缺点：
（1）.Sigmoids saturate and kill gradients.
由于饱和而失去了梯度
因为在when the neuron‘s activation saturates at either tail of 0 or 1, the
gradient at these regions is almost zero。看图就知道，整个曲线的倾斜角度，在两端倾斜角都是平的。
关键的问题在于this
(local) gradient will be multiplied to the gradient of this gate‘s output for the whole objective。这样就会因为local gradient 太小，而it will effectively “kill”
the gradient and almost no signal will flow through the neuron to its weights
and
recursively to its data. 影响到梯度，导致没有信号能通过神经元传递给权值。而且还需要小心关注初始权值，one must pay extra caution when initializing
the weights of sigmoid neurons to prevent saturation. For example, if the initial weights are too large then most neurons would become saturated and the network will barely learn.因为初始的权值太大，就会让神经元直接饱和，整个网络难以学习。
(2)
.Sigmoid outputs are not zero-centered. 不是以0为中心
This
is undesirable since neurons in later layers of processing in a Neural Network (more on this soon) would be receiving data that isnot zero-centered. This has implications on the dynamics duringgradient
descent, because if the data coming into a neuron is always positive(e.g., 
element
wise in 
),
then the gradient on the weights 
will
during back-propagation become either all be positive, or all negative(depending on the gradient of the whole expression 
).
这样在后几层网络中接受的值也不是0中心，这样在动态梯度下降法中，如果进入nueron中的数据都是正的，那么整个权值梯度w要不全为正，或者全为负（取决于f的表达形式）。
This
could introduce undesirable zig-zagging dynamics in the gradient updates for the weights. However, notice that once these gradients are added up across a batch of data the final update for the weights can have variable signs, somewhat mitigating this issue.
Therefore, this is an inconvenience but it has less severe consequences compared to the saturated activation problem above.
这回导致锯齿状的动态梯度，但如果在一个batch数据中将梯度求和来更新权值，有可能会相互抵消，从而缓解上诉的影响。这笔饱和激活带来的影响要轻太多了！
Tanh(x)
The
tanh non-linearity squashes a real-valued number to the range [-1, 1]. Like the sigmoid neuron, its activations saturate, but unlike the sigmoid neuron its output is zero-centered. Therefore, in practice the tanh non-linearity is always preferred to the sigmoid
nonlinearity.
tanh的作用是将真个实数数据放到了[-1,1]之间，他的激活依旧是饱和状态，但他的输出是0中心。
Rectified Linear Unit
The
Rectified Linear Unit (ReLU) has become very popular in the last few years. It computes the function 
,
which is simply thresholded at zero.
Relu 有一些优点和缺点：
There are several pros and cons to using the ReLUs:
- (Pros) Compared to sigmoid/tanh neurons that involve expensive operations (exponentials, etc.), the ReLU can be implemented by simply thresholding a matrix of activations at zero. Meanwhile, ReLUs does not suffer from saturating.
运算简单，非指数形式，切不会饱和
- (Pros) It was found to greatly accelerate (e.g., a factor of 6 in [1])
the convergence of stochastic gradient descent compared to the sigmoid/tanh functions. It is argued that this is due to its linear, non-saturating form.已被证明可以加速随机梯度收敛，被认为是由于其线性和非饱和形式（有待考证）
- (Cons) Unfortunately, ReLU units can be fragile during training and can “die”. For example, a large gradient flowing through a ReLU neuron could cause the weights to update in such a way that the neuron will never activate on any datapoint again. If
this happens, then the gradient flowing through the unit will forever be zero from that point on. That is, the ReLU units can irreversibly die during training since they can get knocked off the data manifold.
For example, you may find that as much as 40% of your network can be “dead” (i.e., neurons that never activate across the entire training dataset) if the learning rate is set too high. With a proper setting of the learning rate this is less frequently an issue.
缺点：Relu Unit在训练中容易die，例如一个大的梯度流过nueron，会导致部分unit一直为0，例如，lr设置很高时，你的网络又40%的neuro未被激活。