Deep Learning · TEE · section

Faculty Assignment2 Q1 · One momentum update with an omitted coefficient

Faculty Assignment 2 · worked practice

Question

Question. For J(w)=½(w−3)²,w₀=5,learning rate0.1,perform one SGD-with-momentum iteration. (Faculty assignment: no marks printed)

Answer — step by step

Given

w₀=5,η=0.1. βandinitialvelocityare not supplied.

To find

One update conditional on zero initial velocity.

Formula: which one and why

g=w-3,\quad v_1=\beta v_0+\eta g,\quad w_1=w_0-v_1LaTeX: g=w-3,\quad v_1=\beta v_0+\eta g,\quad w_1=w_0-v_1

Choose displacement convention and v₀=0; then the first step is independent of β.

Step 1. Differentiate and evaluate

g₀=5−3=2.

Step 2. Calculate momentum displacement

v₁=β×0+0.1×2=0.2.

Step 3. Subtract the displacement

w₁=5−0.2=4.8.

Final answer

w₁=4.8 if v₀=0. For a nonzero initial velocity, w₁=4.8−βv₀; no unique numerical value follows without those givens.

Source / convention note. Authentic faculty Assignment2; no marks printed. β/v₀ omission explicitly identified.