cs231n-notes-Lecture-4/5/6: 反向传播/**函数/数据预处理/权重初始化/batch norm

Lecture-4 Backpropagation and Neural Networks

Computational Graphs

• Node gradient = [local gradient] x [upstream gradient]
• add gate: gradient distributor
• max gate: gradient router (choose only a way)
• mul gate: gradient switcher
  
  

Lecture-5 Convolutional Neural Networks

image N*N, fliter F*F, stride S, then the feature map: (N-F)/S + 1.
common setting: F=2/3, S=2.

ConvNetJS demo:http://cs.stanford.edu/people/karpathy/convnetjs/demo/cifar10.html

Lecture-6 Training Neural Networks

Activation function

Sigmoid

• Pros：
  • squashes numbers into range [0,1].
  • nice interpretation as a saturating “firing rate” of a neuron
• Cons:
  • Saturated neurons kill the gardients
  • not zero-centered
  • exp() is a bit compute expensive

tanh

• squashes numbers into range [0,1].
• zero-centered
• Saturated neurons kill the gardients

Relu

• Pros：
  • Does not Saturate
  • Computationally efficient
  • Converges much faser that tanh and sigmoid.(eg. 6x)
  • Actually more biologically plausible than sigmoid.
• Cons:
  • not zero-centered
  • kill the half gradient. dead relu will never update the weights

Leaky Relu

$f(x) = max(0.01x, x)$f(x)=max(0.01x,x)

• Pros：
  • Does not Saturate
  • Computationally efficient
  • Converges much faser that tanh and sigmoid.(eg. 6x)
  • will not “die”
• parametric Relu : $f(x) = max(\alpha x, x)$f(x)=max(αx,x)

Exponential Linear Units(ELU)

Maxout

$f(x) = max(W^T_1x+b_1, W^T_2x+b_2)$f(x)=max(W1T​x+b1​,W2T​x+b2​)

Data Preprocessing

Preprocess Data

• Normalization
  • For images, e.g. consider CIFAR-10 example with [32,32,3] images.
    • Subtract the mean image (e.g. AlexNet)(mean image = [32,32,3] array)
    • Subtract per-channel mean (e.g. VGGNet)(mean along each channel = 3 numbers)

Weight Initialization

• pre-training or fine-tuning
• Small random numbers.
  • eg.N(0,1e-2), but it has problems in deep neural Networks. The weights of deep layers become zeroes because the gradients are too small.
• large random numbers: it’s easy for the neurons to Saturate.
• Xavier Initialization : $ W_{a*b} = \frac{N(0,1)}{\sqrt{a}}$
  • performs well using tanh but breaks using relu. Hence, it’s Initialized by $W_{a*b} = \frac{N(0,1)}{\sqrt{a/2}}$Wa∗b​=a/2​N(0,1)​

ref: https://www.leiphone.com/news/201703/3qMp45aQtbxTdzmK.html

Batch Normalization

W : N*D (N: sample numbers; D: the dimension of features)

1. compute the mean and variance for each dimension
2. normlize

• usually after fc and conv layers and before nonlinearity.

Tip:

Before training a large number of data, you can test if the model can overfit a small amount of data.