Clarification about flatten function in Theano

Question

in [http://deeplearning.net/tutorial/lenet.html#lenet] it says:

This will generate a matrix of shape (batch_size, nkerns[1] * 4 * 4),
# or (500, 50 * 4 * 4) = (500, 800) with the default values.
layer2_input = layer1.output.flatten(2)

when I use flatten function on a numpy 3d array I get a 1D array. but here it says I get a matrix. How does flatten(2) work in theano?

A similar example on numpy produces 1D array:

     a= array([[[ 1,  2,  3],
    [ 4,  5,  6],
    [ 7,  8,  9]],

   [[10, 11, 12],
    [13, 14, 15],
    [16, 17, 18]],

   [[19, 20, 21],
    [22, 23, 24],
    [25, 26, 27]]])

   a.flatten(2)=array([ 1, 10, 19,  4, 13, 22,  7, 16, 25,  2, 11, 20,  5, 14, 23,  8, 17,
   26,  3, 12, 21,  6, 15, 24,  9, 18, 27])

Answer 1

numpy doesn't support flattening only some dimensions but Theano does.

So if a is a numpy array, a.flatten(2) doesn't make any sense. It runs without error but only because the 2 is passed as the order parameter which seems to cause numpy to stick with the default order of C.

Theano's flatten does support axis specification. The documentation explains how it works.

Parameters:
    x (any TensorVariable (or compatible)) – variable to be flattened
    outdim (int) – the number of dimensions in the returned variable

Return type:
    variable with same dtype as x and outdim dimensions

Returns:
    variable with the same shape as x in the leading outdim-1 dimensions,
    but with all remaining dimensions of x collapsed into the last dimension.

For example, if we flatten a tensor of shape (2, 3, 4, 5) with flatten(x, outdim=2), then we’ll have the same (2-1=1) leading dimensions (2,), and the remaining dimensions are collapsed. So the output in this example would have shape (2, 60).

A simple Theano demonstration:

import numpy
import theano
import theano.tensor as tt


def compile():
    x = tt.tensor3()
    return theano.function([x], x.flatten(2))


def main():
    a = numpy.arange(2 * 3 * 4).reshape((2, 3, 4))
    f = compile()
    print a.shape, f(a).shape


main()

prints

(2L, 3L, 4L) (2L, 12L)