# F22 Q1b

Subject: Deep Learning

Exam: MT2

Reader: https://deep-learning-study-room.vercel.app/#mt2/read/15/mt2-c15-s1

Canonical: https://deep-learning-study-room.vercel.app/read/dl/mt2/section/mt2-c15-s1/

## Question

**Question (4 marks).** Weights are 0.55 and 0.65; their gradients are+0.3 and−0.25. With η = 0.1, compute gradient-descent changes and new weights.

## Answer — step by step

### Given

Old weights = [0.55,0.65].

Corresponding supplied gradients = [0.3,−0.25]; η = 0.1.

### To find

Calculate the signed weight changes and both new weights.

### Formula — which one and why

**Gradient descent.** Evaluate the gradient at the current parameter, multiply by the learning rate and subtract. If the objective is supplied, differentiate it and recompute the gradient after each update.

θ (theta) = trainable parameter; g = derivative of the stated objective J; η = learning rate; t labels the update number.



$$
g_t=J\prime(\theta_{t-1})
$$





$$
\theta_t=\theta_{t-1}-\eta g_t
$$



**Yaad rakhne ka cue:** Naya = purana − learning rate × current gradient.

### Solution — step by step

**Step 1: calculate the change in weight 1.**



$$
\Delta w_1=-0.1(0.3)=-0.03
$$



**Step 2: add that change to old weight 1.**



$$
w_1^{\mathrm{new}}=0.55+(-0.03)=0.52
$$



**Step 3: calculate the change in weight 2.**



$$
\Delta w_2=-0.1(-0.25)=0.025
$$



**Step 4: add that change to old weight 2.**



$$
w_2^{\mathrm{new}}=0.65+0.025=0.675
$$



**Final answer:** changes = [−0.03, +0.025]; new weights = [0.52, 0.675]. A negative gradient increases its weight under descent.