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Pooling 层一般在网络中是跟在Conv卷积层之后，做采样操作，其实是为了进一步缩小feature map，同时也能增大神经元的视野。在Caffe中，pooling层属于vision_layer的一部分，其相关的定义也在vision_layer.hpp的头文件中。Pooling层的相关操作比较少，在Caffe的自带模式下只有Max pooling和Average poooling两种
下图是一个LeNet的网络结构图，全连接之前主要有2个卷基层，2个池化层，其中sub_sampling layer就是pooling的操作。pooling的范围是给定的一个region。
PoolingLayer
caffe中Pooling的操作相对比较少，结构也简单，首先看它的Forward_cpu函数，在forward的时候根据相应的Pooling_method选择相应的pooling方法
forward_cpu
void PoolingLayer<Dtype>::Forward_cpu(const vector<Blob<Dtype>*>& bottom,
const vector<Blob<Dtype>*>& top) {
const Dtype* bottom_data = bottom[0]->cpu_data();
Dtype* top_data = top[0]->mutable_cpu_data();
const int top_count = top[0]->count();
//将mask信息输出到top[1],如果top大于1
const bool use_top_mask = top.size() > 1;
int* mask = NULL; // suppress warnings about uninitalized variables
Dtype* top_mask = NULL;
switch (this->layer_param_.pooling_param().pool()) {
case PoolingParameter_PoolMethod_MAX://这里的case主要是实现max pooling的方法
// Initialize
if (use_top_mask) {
top_mask = top[1]->mutable_cpu_data();
caffe_set(top_count, Dtype(-1), top_mask);
} else {
mask = max_idx_.mutable_cpu_data();
caffe_set(top_count, -1, mask);
}
caffe_set(top_count, Dtype(-FLT_MAX), top_data);
// The main loop
for (int n = 0; n < bottom[0]->num(); ++n) {
for (int c = 0; c < channels_; ++c) {
for (int ph = 0; ph < pooled_height_; ++ph) {
for (int pw = 0; pw < pooled_width_; ++pw) {
int hstart = ph * stride_h_ - pad_h_;//这里的hstart，wstart,hend,wend指的是pooling窗口在特征图中的坐标，对应左上右下即x1 y1 x2 y2
int wstart = pw * stride_w_ - pad_w_;
int hend = min(hstart + kernel_h_, height_);
int wend = min(wstart + kernel_w_, width_);
hstart = max(hstart, 0);
wstart = max(wstart, 0);
const int pool_index = ph * pooled_width_ + pw;
for (int h = hstart; h < hend; ++h) {
for (int w = wstart; w < wend; ++w) {
const int index = h * width_ + w;//记录index偏差
if (bottom_data[index] > top_data[pool_index]) {//不停迭代
top_data[pool_index] = bottom_data[index];
if (use_top_mask) {
top_mask[pool_index] = static_cast<Dtype>(index);//记录当前最大值的的坐标索引
} else {
mask[pool_index] = index;
}
}
}
}
}
}
// 计算偏移量，进入下一张图的index起始地址
bottom_data += bottom[0]->offset(0, 1);
top_data += top[0]->offset(0, 1);
if (use_top_mask) {
top_mask += top[0]->offset(0, 1);
} else {
mask += top[0]->offset(0, 1);
}
}
}
break;
case PoolingParameter_PoolMethod_AVE://average_pooling
for (int i = 0; i < top_count; ++i) {
top_data[i] = 0;
}
// The main loop
for (int n = 0; n < bottom[0]->num(); ++n) {//同样是主循环
for (int c = 0; c < channels_; ++c) {
for (int ph = 0; ph < pooled_height_; ++ph) {
for (int pw = 0; pw < pooled_width_; ++pw) {
int hstart = ph * stride_h_ - pad_h_;
int wstart = pw * stride_w_ - pad_w_;
int hend = min(hstart + kernel_h_, height_ + pad_h_);
int wend = min(wstart + kernel_w_, width_ + pad_w_);
int pool_size = (hend - hstart) * (wend - wstart);
hstart = max(hstart, 0);
wstart = max(wstart, 0);
hend = min(hend, height_);
wend = min(wend, width_);
for (int h = hstart; h < hend; ++h) {
for (int w = wstart; w < wend; ++w) {
top_data[ph * pooled_width_ + pw] +=
bottom_data[h * width_ + w];
}
}
top_data[ph * pooled_width_ + pw] /= pool_size;//获得相应的平均值
}
}
// compute offset同理计算下一个图的起始地址
bottom_data += bottom[0]->offset(0, 1);
top_data += top[0]->offset(0, 1);
}
}
break;
case PoolingParameter_PoolMethod_STOCHASTIC:
NOT_IMPLEMENTED;
break;
default:
LOG(FATAL) << "Unknown pooling method.";
}
backward_cpu
对于误差的反向传导
对于pooling层的误差传到，根据下式
\[\delta^l_j=upsample(\delta^{l+1}_{j})\cdot h(a^l_j)'
\]
\]
这里的Upsample具体可以根据相应的pooling方法来进行上采样，upsample的基本思想也是将误差进行的平摊到各个采样的对应点上。在这里pooling因为是线性的所以h这一项其实是可以省略的。
具体的计算推导过程请结合http://www.cnblogs.com/tornadomeet/p/3468450.html有详细的推导过程，结合代码中主循环中的最里项会更清晰的明白
template <typename Dtype>
void PoolingLayer<Dtype>::Backward_cpu(const vector<Blob<Dtype>*>& top,
const vector<bool>& propagate_down, const vector<Blob<Dtype>*>& bottom) {
if (!propagate_down[0]) {
return;
}
const Dtype* top_diff = top[0]->cpu_diff();//首先获得上层top_blob的diff
Dtype* bottom_diff = bottom[0]->mutable_cpu_diff();
caffe_set(bottom[0]->count(), Dtype(0), bottom_diff);
// We'll output the mask to top[1] if it's of size >1.
const bool use_top_mask = top.size() > 1;
const int* mask = NULL; // suppress warnings about uninitialized variables
const Dtype* top_mask = NULL;
switch (this->layer_param_.pooling_param().pool()) {
case PoolingParameter_PoolMethod_MAX:
// The main loop
if (use_top_mask) {
top_mask = top[1]->cpu_data();
} else {
mask = max_idx_.cpu_data();
}
for (int n = 0; n < top[0]->num(); ++n) {
for (int c = 0; c < channels_; ++c) {
for (int ph = 0; ph < pooled_height_; ++ph) {
for (int pw = 0; pw < pooled_width_; ++pw) {
const int index = ph * pooled_width_ + pw;
const int bottom_index =
use_top_mask ? top_mask[index] : mask[index];//根据max pooling记录的mask位置，进行误差反转
bottom_diff[bottom_index] += top_diff[index];
}
}
bottom_diff += bottom[0]->offset(0, 1);
top_diff += top[0]->offset(0, 1);
if (use_top_mask) {
top_mask += top[0]->offset(0, 1);
} else {
mask += top[0]->offset(0, 1);
}
}
}
break;
case PoolingParameter_PoolMethod_AVE:
// The main loop
for (int n = 0; n < top[0]->num(); ++n) {
for (int c = 0; c < channels_; ++c) {
for (int ph = 0; ph < pooled_height_; ++ph) {
for (int pw = 0; pw < pooled_width_; ++pw) {
int hstart = ph * stride_h_ - pad_h_;
int wstart = pw * stride_w_ - pad_w_;
int hend = min(hstart + kernel_h_, height_ + pad_h_);
int wend = min(wstart + kernel_w_, width_ + pad_w_);
int pool_size = (hend - hstart) * (wend - wstart);
hstart = max(hstart, 0);
wstart = max(wstart, 0);
hend = min(hend, height_);
wend = min(wend, width_);
for (int h = hstart; h < hend; ++h) {
for (int w = wstart; w < wend; ++w) {
bottom_diff[h * width_ + w] +=
top_diff[ph * pooled_width_ + pw] / pool_size;//mean_pooling中，bottom的误差值按pooling窗口中的大小计算，从上一层进行填充后，再除窗口大小
}
}
}
}
// offset
bottom_diff += bottom[0]->offset(0, 1);
top_diff += top[0]->offset(0, 1);
}
}
break;
case PoolingParameter_PoolMethod_STOCHASTIC:
NOT_IMPLEMENTED;
break;
default:
LOG(FATAL) << "Unknown pooling method.";
}
}