Linear Layer Backward dW

Problem

Gradient of a linear layer with respect to its weight matrix for a single vector input: dW = outer(dout, x), with shape (output_dim, input_dim).

The signature is linear_dw(dout, x). dout is the upstream gradient vector and x is the layer input vector.

Hint

dW[i][j] = dout[i] * x[j]; no summation is needed for a single example.

case 1

in: [[1,2],[3,4,5]]

expected: [[3,4,5],[6,8,10]]

case 2

in: [[2],[1,-1]]

expected: [[2,-2]]

case 3

in: [[-1,0.5],[2]]

expected: [[-2],[1]]

case 4

in: [[1],[0]]

expected: [[0]]

Starter codePython

def linear_dw(dout, x):
    # Your code here
    pass

4 test cases · run your code against them in the editor