# F23 Q2a

Subject: Deep Learning

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/#tee/read/13/tee-c13-s4

Canonical: https://deep-learning-study-room.vercel.app/read/dl/tee/section/tee-c13-s4/

## Question

**Question (10 marks).** A feedforward network has inputs 1,2; hidden nodes 3,4; outputs 5,6. Weights: w13 = −2, w23 = 3, w14 = 4, w24 = −1, w35 = 1, w45 = −1, w36 = −1, w46 = 1; all biases 0. All nodes 3–6 use step(z) = 1 if z≥0 else 0. Find(y5, y6) for inputs(0,0), (1,0), (0,1), (1,1).

## Answer — step by step

### Given

A feedforward network has inputs 1,2.

hidden nodes 3,4.

outputs 5,6.

Weights: w13 = −2, w23 = 3, w14 = 4, w24 = −1, w35 = 1, w45 = −1, w36 = −1, w46 = 1.

all biases 0.

All nodes 3–6 use step(z) = 1 if z≥0 else 0.

Find(y5, y6) for inputs(0,0), (1,0), (0,1), (1,1).

### To find

Write every row of the truth table and the requested network output.

### Formula — which one and why

**Threshold logic.** Compute the weighted sum for every binary input combination and apply the threshold rule exactly. Hidden neurons can provide separate threshold decisions before the output combines them.

step(z) returns 1 at or above zero unless the question specifies a strict inequality; otherwise it returns 0.



$$
z=\sum_iw_ix_i+b
$$





$$
\operatorname{step}(z)=\begin{cases}1&z\ge0\\0&z<0\end{cases}
$$



**Yaad rakhne ka cue:** Har input row ka sum nikalo, phir threshold lagao.

### Solution — step by step

Use exactly the printed step: output 1 if z≥0, otherwise 0. In particular, step(0) = 1. The equations are z₃ = −2x₁+3x₂, z₄ = 4x₁−x₂, z₅ = h₃−h₄, z₆ = −h₃+h₄.

**Step 1: Input(0,0).** z₃ = −2 × 0+3 × 0 = 0; h₃ = 1. z₄ = 4 × 0−0 = 0; h₄ = 1. z₅ = 1−1 = 0; y₅ = 1. z₆ = −1+1 = 0; y₆ = 1. Final pair = **(1,1)**.

**Step 2: Input(1,0).** z₃ = −2 × 1+3 × 0 = -2; h₃ = 0. z₄ = 4 × 1−0 = 4; h₄ = 1. z₅ = 0−1 = -1; y₅ = 0. z₆ = −0+1 = 1; y₆ = 1. Final pair = **(0,1)**.

**Step 3: Input(0,1).** z₃ = −2 × 0+3 × 1 = 3; h₃ = 1. z₄ = 4 × 0−1 = -1; h₄ = 0. z₅ = 1−0 = 1; y₅ = 1. z₆ = −1+0 = -1; y₆ = 0. Final pair = **(1,0)**.

**Step 4: Input(1,1).** z₃ = −2 × 1+3 × 1 = 1; h₃ = 1. z₄ = 4 × 1−1 = 3; h₄ = 1. z₅ = 1−1 = 0; y₅ = 1. z₆ = −1+1 = 0; y₆ = 1. Final pair = **(1,1)**.