# Faculty Assignment2 Q2 · Specified momentum update

Subject: Deep Learning

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/#tee/read/22/tee-c22-s1

Canonical: https://deep-learning-study-room.vercel.app/read/dl/tee/section/tee-c22-s1/

## Question

**Question. For J(w)=½(w+2)²,η=0.2,β=0.8,w₀=4,v₀=0,perform one momentum step.** (Faculty assignment: no marks printed)

## Answer — step by step

### Given

All givens above.

### To find

v₁andw₁.

### Formula: which one and why



$$
g=w+2,\quad v_1=\beta v_0+\eta g,\quad w_1=w_0-v_1
$$



### Step 1. Gradient

g₀=4+2=6.

### Step 2. Momentum displacement

v₁=0.8×0+0.2×6=1.2.

### Step 3. Weight

w₁=4−1.2=2.8.

### Final answer

**v₁=1.2,w₁=2.8.** A signed-velocity convention givesv₁=−1.2andw₁=w₀+v₁; the final weight is the same.