Make Theano's max_pool_2d support strides and support padding with 0 (to support size preserving version)

[carriepl]

Allow max_pool_2d (in theano.tensor.signal.downsample) to work with strides that differ from the size of the pooling region.

• support stride
• support pad

[benanne]

This would be awesome, it seems like strided pooling is an essential component of many state of the art network architectures lately.

One more addition that would be interesting is the support of implicit zero padding around the input. For example, in the GoogLeNet architecture, a component of the 'inception module' is a 3x3 pooling layer with stride 1, that has the same output dimensions as the input. This is only possible if the input is first padded with a border of zeros with width 1. Explicitly doing this padding would require a copy operation, which slows things down unnecessarily. I guess it comes down to substituting a zero whenever an index is out of bounds, so this should be straightforward to implement.

[ebattenberg]

The pooling routines from Caffe support these options if you can convince @f0k to pull them in. http://caffe.berkeleyvision.org/tutorial/layers.html

[nouiz]

Update, the support for stride on the CPU (with only python code) is merged.

[lamblin]

Padding was added in #2543.