MediumCalculusca-294

Chain Rule Through Two Linear Maps

Problem

For the composition y = W2 @ (W1 @ x) with constant matrices, the Jacobian with respect to x is the product W2 @ W1.

Given W1 as a list of rows (m x n) and W2 as a list of rows (k x m), return the k x n Jacobian as a nested list.

Hint

Compose the linear maps by multiplying the matrices in order.

case 1

in: [[[1,2],[3,4]],[[1,0]]]

expected: [[1,2]]

case 2

in: [[[1,0],[0,1]],[[2,3],[4,5]]]

expected: [[2,3],[4,5]]

case 3

in: [[[2]],[[3]]]

expected: [[6]]

Starter codePython

def chain_rule_linear_jacobian(w1, w2):
    # Your code here
    pass

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