有效感受野--Understanding the Effective Receptive Field in Deep Convolutional Neural Networks

Understanding the Effective Receptive Field in Deep Convolutional Neural Networks
NIPS 2016

本文主要分析了 CNN 网络中的 Receptive Field，发现实际有效的感受野和理论上的感受野差距比较大，实际有效的感受野是一个高斯分布。

We introduce the notion of an effective receptive field, and show that it both has a Gaussian distribution and only occupies a fraction of the full theoretical receptive field.

2.1 The simplest case: a stack of convolutional layers of weights all equal to one
先分析了一种特殊情况，所有滤波器的权值全部等于 1 。2D 变成两个 1D 相乘，所以可以首先分析 1D 的情况
首先我们从数学上证明了 Effective Receptive Fields 在 1D 是一个高斯分布，随后推出 2D ，大于2D的情况都是高斯分布

2.2 Random weights
接着证明了当滤波器权值是随机值时， effective receptive field 的分布仍然是高斯分布

2.3 Non-uniform kernels
还是高斯分布

上图理论感受野尺寸分别是 11*11， 21*21， 41*41， 81*81
有效感受野对应正方形中额白色区域，符合高斯分布

不同激活函数得到的有效感受野略有不同

Subsampling 和 dilated convolution 都可以增加有效感受野范围

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