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GATE DA 2025 Q42: Backpropagation through a small ReLU network

Question

Consider the neural network shown in the figure with

inputs: u,vu, v

weights: a,b,c,d,e,fa, b, c, d, e, f

output: yy

RR denotes the ReLU function, R(x)=max⁡(0,x)R(x) = \max(0, x).

Neural network: inputs u and v feed two ReLU units. The top unit receives u with weight a and v with weight b; the bottom unit receives u with weight c and v with weight d. The top unit connects to an output ReLU with weight e and the bottom unit with weight f; the output is y.
Tap the figure to enlarge

Given u=2,v=3u = 2, v = 3,

a=1,b=1,c=1,d=−1,e=4,f=−1a = 1, b = 1, c = 1, d = -1, e = 4, f = -1,

which one of the following is correct?

Try it: multiple choice: exactly one correct option

Select one option
Wrong answer costs 2/3 mark in GATE.
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Answer: A (official GATE 2025 final answer key)

Concept used: Forward pass, then chain rule through ReLU units (gradient 1 if active, 0 if not).

First step: Do the forward pass: top unit h1=R(au+bv)=R(5)=5h_1 = R(au + bv) = R(5) = 5, bottom unit h2=R(cu+dv)=R(−1)=0h_2 = R(cu + dv) = R(-1) = 0, output y=R(eh1+fh2)=R(20)=20y = R(e h_1 + f h_2) = R(20) = 20.

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Source: official GATE 2025 DA question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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