Tensor multiplication in Tensorflow

Question

I am trying to carry out tensor multiplication in NumPy/Tensorflow.

I have 3 tensors- A (M X h), B (h X N X s), C (s X T).

I believe that A X B X C should produce a tensor D (M X N X T).

Here's the code (using both numpy and tensorflow).

M = 5
N = 2
T = 3
h = 2
s = 3
A_np = np.random.randn(M, h)
C_np = np.random.randn(s, T)
B_np = np.random.randn(h, N, s)

A_tf = tf.Variable(A_np)
C_tf = tf.Variable(C_np)
B_tf = tf.Variable(B_np)

# Tensorflow
with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    print sess.run(A_tf)
    p = tf.matmul(A_tf, B_tf)
    sess.run(p)

This returns the following error:

ValueError: Shape must be rank 2 but is rank 3 for 'MatMul_2' (op: 'MatMul') with input shapes: [5,2], [2,2,3].

If we try the multiplication only with numpy matrices, we get the following errors:

np.multiply(A_np, B_np)

ValueError: operands could not be broadcast together with shapes (5,2) (2,2,3)

However, we can use np.tensordot as follows:

np.tensordot(np.tensordot(A_np, B_np, axes=1), C_np, axes=1)

Is there an equivalent operation in TensorFlow?

Answer

In numpy, we would do as follows:

ABC_np = np.tensordot(np.tensordot(A_np, B_np, axes=1), C_np, axes=1)

In tensorflow, we would do as follows:

AB_tf = tf.tensordot(A_tf, B_tf,axes = [[1], [0]])
AB_tf_C_tf = tf.tensordot(AB_tf, C_tf, axes=[[2], [0]])

with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    ABC_tf = sess.run(AB_tf_C_tf)

np.allclose(ABC_np, ABC_tf) return True.

Solution

Try

tf.tensordot(A_tf, B_tf,axes = [[1], [0]])

For example:

x=tf.tensordot(A_tf, B_tf,axes = [[1], [0]])
x.get_shape()
TensorShape([Dimension(5), Dimension(2), Dimension(3)])

Here is tensordot documentation, and here is the relevant github repository.