# Faculty Assignment2 Q1 · One momentum update with an omitted coefficient

Subject: Deep Learning

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/#tee/read/22/tee-c22-s0

Canonical: https://deep-learning-study-room.vercel.app/read/dl/tee/section/tee-c22-s0/

## 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



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



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.