How to do outer product as a layer with chainer?

Question

How can I include an outer product (of the previous feature vector and itself) as a layer in chainer, especially in a way that's compatible with batching?

Answer 1

F.matmul is also very handy.

Depending on the input shapes, you can combine it with F.expand_dims (of course F.reshape works, too) or use transa/transb arguments.

For details, refer to the official documentation of functions.

Code

import chainer.functions as F
import numpy as np

print("---")
x = np.array([[[1], [2], [3]], [[4], [5], [6]]], 'f')
y = np.array([[[1, 2, 3]], [[4, 5, 6]]], 'f')
print(x.shape)
print(y.shape)
z = F.matmul(x, y)
print(z)


print("---")
x = np.array([[[1], [2], [3]], [[4], [5], [6]]], 'f')
y = np.array([[[1], [2], [3]], [[4], [5], [6]]], 'f')
print(x.shape)
print(y.shape)
z = F.matmul(x, y, transb=True)
print(z)


print("---")
x = np.array([[1, 2, 3], [4, 5, 6]], 'f')
y = np.array([[1, 2, 3], [4, 5, 6]], 'f')
print(x.shape)
print(y.shape)
z = F.matmul(
    F.expand_dims(x, -1),
    F.expand_dims(y, -1),
    transb=True)
print(z)

Output

---
(2, 3, 1)
(2, 1, 3)
variable([[[  1.   2.   3.]
           [  2.   4.   6.]
           [  3.   6.   9.]]

          [[ 16.  20.  24.]
           [ 20.  25.  30.]
           [ 24.  30.  36.]]])
---
(2, 3, 1)
(2, 3, 1)
variable([[[  1.   2.   3.]
           [  2.   4.   6.]
           [  3.   6.   9.]]

          [[ 16.  20.  24.]
           [ 20.  25.  30.]
           [ 24.  30.  36.]]])
---
(2, 3)
(2, 3)
variable([[[  1.   2.   3.]
           [  2.   4.   6.]
           [  3.   6.   9.]]

          [[ 16.  20.  24.]
           [ 20.  25.  30.]
           [ 24.  30.  36.]]])

Answer 2

You can use F.reshape and F.broadcast_to to explicitly handle array.

Assume you have 2-dim array h with shape (minibatch, feature). If you want to calculate outer product of h and h, try below code. Is this what you want to do?

import numpy as np
from chainer import functions as F


def outer_product(h):
    s0, s1 = h.shape
    h1 = F.reshape(h, (s0, s1, 1))
    h1 = F.broadcast_to(h1, (s0, s1, s1))
    h2 = F.reshape(h, (s0, 1, s1))
    h2 = F.broadcast_to(h2, (s0, s1, s1))
    h_outer = h1 * h2
    return h_outer

# test code
h = np.arange(12).reshape(3, 4).astype(np.float32)
h_outer = outer_product(h)
print(h.shape)
print(h_outer.shape, h_outer.data)