python - 用于两个 3dim 矩阵的 numpy einsum 的 Theano 版本

Question

我有两个 3dim numpy 矩阵，我想根据一个轴做一个点积，而不用在 theano 中使用循环。带有示例数据的 numpy 解决方案如下:

a=[ [[ 0, 0, 1, 1, 0,  0,  0,  0,  0,  0,  1,  0,  0,  1,  0],
  [ 1,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0,  1,  0],
  [ 0,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  1],
  [ 0,  1,  0,  0,  0,  0,  1,  0,  0,  0,  1,  0,  1,  0,  0]],
    [[ 0,  0,  1,  1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  1,  0],
  [ 1,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0,  1,  0],
  [ 0,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  1],
  [ 0,  1,  0,  0,  0,  0,  1,  0,  0,  0,  1,  0,  1,  0,  0]],
 [ [ 0,  0,  1,  1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  1,  0],
  [ 1,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0,  1,  0],
  [ 0,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  1],
  [ 0,  1,  0,  0,  0,  0,  1,  0,  0,  0,  1,  0,  1,  0,  0]],
 [ [ 0,  0,  1,  1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  1,  0],
  [ 1,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0,  1,  0],
  [ 0,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  1],
  [ 0,  1,  0,  0,  0,  0,  1,  0,  0,  0,  1,  0,  1,  0,  0]],
 [[ 0,  0,  1,  1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  1,  0],
  [ 1,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0,  1,  0],
  [ 0,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  1],
  [ 0,  1,  0,  0,  0,  0,  1,  0,  0,  0,  1,  0,  1,  0,  0]],
 [[ 0,  0,  1,  1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  1,  0],
  [ 1,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0,  1,  0],
  [ 0,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  1],
  [ 0,  1,  0,  0,  0,  0,  1,  0,  0,  0,  1,  0,  1,  0,  0.]],
 [[ 0,  0,  1,  1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  1,  0],
  [ 1,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0,  1,  0],
  [ 0,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  1],
  [ 0,  1,  0,  0,  0,  0,  1,  0,  0,  0,  1,  0,  1,  0,  0]]]

b=[[[ 0,  0,  1,  0,  0.],
  [ 1,  0,  0,  0,  0.],
  [ 0,  0,  0,  0,  0.],
  [ 0,  1,  0,  0,  0.]],
 [[ 0,  0,  1,  0,  0.],
  [ 1,  0,  0,  0,  0.],
  [ 0,  0,  0,  0,  0.],
  [ 0,  1,  0,  0,  0.]],
 [[ 0,  0,  1,  0,  0.],
  [ 1,  0,  0,  0,  0.],
  [ 0,  0,  0,  0,  0.],
  [ 0,  1,  0,  0,  0.]],
 [[ 0,  0,  1,  0,  0.],
  [ 1,  0,  0,  0,  0.],
  [ 0,  0,  0,  0,  0.],
  [ 0,  1,  0,  0,  0.]],
 [[ 0,  0,  1,  0,  0.],
  [ 1,  0,  0,  0,  0.],
  [ 0,  0,  0,  0,  0.],
  [ 0,  1,  0,  0,  0.]],
 [[ 0,  0,  1,  0,  0.],
  [ 1,  0,  0,  0,  0.],
  [ 0,  0,  0,  0,  0.],
  [ 0,  1,  0,  0,  0.]],
 [[ 0,  0,  1,  0,  0.],
  [ 1,  0,  0,  0,  0.],
  [ 0,  0,  0,  0,  0.],
  [ 0,  1,  0,  0,  0.]]]
dt = np.dtype(np.float32)
a=np.asarray(a,dtype=dt)
b=np.asarray(b,dtype=dt)
print(a.shape)
print(b.shape)

其中“a”的形状为 (7, 4, 15)，“b”的形状为 (7, 4, 5)。 “c”，定义为“a”和“b”的点积:

c = np.einsum('ijk,ijl->ilk',a,b)

我正在寻找这个例子的 theano 实现来计算“c”。

有什么想法吗？

Answer 1

完成本题:

import theano as th
import then.Tensor as T

ta = T.tensor3('a')
tb = T.tensor3('b')

tc = T.batched_tensordot(ta, tb, axes=[[1],[1]])

……