ECE579 Homework2-Practice of scalar‐based backpropagation Solved

Description

Problem 1 (Practice of scalar‐based backpropagation). You are required to calculate the gradients of 𝑓 𝐱, 𝐰  with respect to x_i

and w_i.

• Use computational graph for calculation
• Based on(a), write a program to implement the computational graph and verify your answer in (a).

Note: You are free to choose the inputs of your computational graph.

Problem 2 (Practice of vector‐based backpropagation). You are required to calculate the gradients of 𝑓 𝑥, 𝑤 ‖𝜎 𝐖𝐱 ‖ with respect to x_i and W_i,j. Here ‖∙‖ is the calculation of L2 loss, W is 3‐by‐3 matrix and x is 3‐by‐1 vector, and 𝜎 ∙ is sigmoid function that performs element‐wise sigmoid operation.

• Use computational graph for calculation
• Based on(a), write a program to implement the computational graph and verify your answer in (a). You can use vectorized approach to simply your codes.

Note: You are free to choose the inputs of your computational graph.