TensorFlow matrix rate

Question

I need to calculate the Frobenius norm to get this formula using the TensorFlow framework:

where wis a matrix with 50 rows and 100 columns.

I tried to write something, but I do not understand how to fill in the argument axis.

tf.pow(
    tf.norm(x, ord='fro', axis=?), 2
)

According to the TensorFlow docs, I have to use a 2-tuple (or 2-list) because it defines the axes in the tensor by which to calculate the matrix norm, but I just need a simple Frobenius norm. In SciPy, for example, I can do this without specifying any axis.

So what should I use as a axisfunction to emulate SciPy?

Answer 1

Thus, the Frobenius norm is the sum over the matrix nxm, but tf.normallows you to process several vectors and matrices in batch mode.

To better understand, imagine that you have a rank 3 tensor:

t = [[[2], [4], [6]], [[8], [10], [12]], [[14], [16], [18]]]

This can be seen as several matrices aligned in one direction, but the function cannot determine which one. This may be a batch of the following matrices:

[2, 4, 6], [8 ,10, 12], [14, 16, 18]

or

[2 8 14], [4, 10, 16], [6, 12, 18]

Thus, it axismainly indicates which directions you want to consider when summing in the Frobenius norm.

In your case, either of [1,2]or [-2,-1]will work.

Answer 2

. . , , , = [- 2, -1] = , , .

[-2, -1] .

Answer 3

tf.sqrt(tf.reduce_sum(tf.square(w)))

.

Answer 4

,

tf.reduce_sum(tf.multiply(x, x))

norm, , pow, , , , .