Receptive Field

综述

• 感受野

  除了卷积和池化，其他层并不影响感受野大小

  感受野与卷积核尺寸kernel_size和步长stride有关

  递归计算：

  $$N\_RF = kernel\_size + (cur\_RF-1)*stride$$

  其中$cur_RF$是当前层（start from 1），$kernel_size$、$stride$是当前层参数，$N_RF$是上一层的感受野。

• 感受野计算器

  https://fomoro.com/research/article/receptive-field-calculator

Understanding the Effective Receptive Field in Deep Convolutional Neural Networks

1. 动机

   • effective receptive field

   • the effect of nonlinear activations, dropout, sub-sampling and skip connections on it

2. 论点

   • it is critical for each output pixel to have a big receptive field, such that no important information is left out when making the prediction
   • deeper network：increase the receptive field size linearly
   • Sub-sampling：increases the receptive field size multiplicatively
   • it is easy to see that pixels at the center of a receptive field have a much larger impact on an output：前向传播的时候，中间位置的像素点有更多条path通向output

3. 方法看不懂直接看结论

   • dropout does not change the Gaussian ERF shape

   • Subsampling and dilated convolutions turn out to be effective ways to increase receptive field size quickly

   • Skip-connections make ERFs smaller

   • ERFs are Gaussian distributed

     • uniformly和随机初始化都是perfect Gaus- sian shapes

     • 加上非线性激活函数以后是near Gaussian shapes

       

     • with different nonlinearities

       

   • $\sqrt n$ absolute growth and $1/\sqrt n$ relative shrinkage：RF是随着layer线性增长的，ERF在log上0.56的斜率，约等于$\sqrt n$

     

   • Subsampling & dilated convolution increases receptive field

     • The reference baseline is a convnet with 15 dense convolution layers
     • Subsampling：replace 3 of the 15 convolutional layers with stride-2 convolution

     • dilated：replace them with dilated convolution with factor 2,4 and 8，rectangular ERF shape

       

   • evolves during training

     • as the networks learns, the ERF gets bigger, and at the end of training is significantly larger than the initial ERF
     • classification
       • 32*32 cifar 10
       • theoretical receptive field of our network is actually 74 × 74
     • segmentation
       • CamVid dataset
       • the theoretical receptive field of the top convolutional layer units is quite big at 505 × 505

     • 实际的ERF都很小，都没到原图大小

       

   • increase the effective receptive field

     • New Initialization：
       • makes the weights at the center of the convolution kernel to have a smaller scale, and the weights on the outside to be larger
       • 30% speed-up of training
       • 其他效果不明显
     • Architecturalchanges
       • sparsely connect each unit to a larger area
       • dilated convolution or even not grid-like

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