Feature extracted by max pooling vs mean pooling In deep learning, and it's application to computer vision, is it possible to tell what kind of features these two types of pooling extract? e.g. is it possible to say that max pool extracts edges? Can we say something similar regarding mean pooling?
P.S. feel free to recommend if stackoverflow is more suitable.
 A: my opinion is that max&mean  pooling is nothing to do with the type of features, but with translation invariance. 
Imagine learning to recognise an 'A' vs 'B' (no variation in A's and in B's pixels).  First in a fixed position in the image. This can be done by a logistic regression (1 neuron): the weights end up being a template of the difference A - B. 
Now what happens if you train to recognise on different locations in the image. You cannot do this with logistic regression, sweeping over the image (ie approximating a convolutional layer with one filter) and labelling all sweeps of the image A or B as appropriate, because learning from the different positions interferes - effectively you try to learn the average of A-B as A/B are passed across your filter - but this is just a blur.
with max pooling learning is only performed on the location of max activation (which is hopefully centred on  the letter). I am not so sure about mean pooling - I would imagine that more learning (ie weight adjustment ) is done at the max activation location and that avoids the blurring)... 
I would encourage you to just implement such a simple network with 2 classes and 1 filter for convolutional layer, then max/mean pooling and 1 output node and inspect the weights/performance.  
A: I wouldn't say the either extract features.  Instead, it is the convolutional layers that construct/extract features, and the pooling layers compress them to a lower fidelity.  The difference is in the way the compression happens, and what type of fidelity is retained:


*

*A max-pool layer compressed by taking the maximum activation in a block.  If you have a block with mostly small activation, but a small bit of large activation, you will loose the information on the low activations.  I think of this as saying "this type of feature was detected in this general area".

*A mean-pool layer compresses by taking the mean activation in a block.  If large activations are balanced by negative activations, the overall compressed activations will look like no activation at all.  On the other hand, you retain some information about low activations in the previous example.

