澄清 Theano 中的 flatten 函数

Question

在 [http://deeplearning.net/tutorial/lenet.html#lenet] 中说：

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)

当我在 numpy 3d 数组上使用 flatten 函数时，我得到了一个 1D 数组。但在这里它说我得到了一个矩阵。 flatten(2) 在 theano 中如何工作？

numpy 上的类似示例生成一维数组：

     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 不支持仅展平某些维度，但 Theano 支持。

所以如果 a 是一个 numpy 数组，a.flatten(2) 没有任何意义。它运行没有错误，但只是因为 2 作为 order 参数传递，这似乎导致 numpy 坚持默认顺序 C.

Theano 的 flatten 支持轴规范。 The documentation 解释它是如何工作的。

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).

一个简单的 Theano 演示：

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()

打印

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

澄清 Theano 中的 flatten 函数

Clarification about flatten function in Theano

numpy

flatten

theano

conv-neural-network