Deep Learning · TEE · section

R24 Q1b

Re examination February 2024 fully solved

Question

Question (5 marks). Draw an animal-classification network with 10 inputs, three hidden layers of 5 neurons each and 4 output classes. Every hidden/output neuron has a bias. Count all trainable parameters.

Answer — step by step

Given

10 input features → 5 hidden → 5 hidden → 5 hidden → 4 output classes.

One bias per hidden/output neuron.

To find

Draw the layer structure and count weights and biases.

Formula — which one and why

Dense-layer parameters. Every output neuron receives every input, so multiply inputs by outputs for weights. Add one bias per receiving neuron. Sum separate layers.

n_in = incoming features; n_out = receiving neurons. The input layer itself has no learned receiving weights or biases.

$P=(n_{\mathrm{in}}+1)n_{\mathrm{out}}$ LaTeX: P=(n_{\mathrm{in}}+1)n_{\mathrm{out}}

Yaad rakhne ka cue: Har output ke liye saare inputs plus ek bias.

Solution — step by step

Architecture: 10 → 5 → 5 → 5 → 4. Each non-input neuron has one bias.

R24 Q1b every layer contains the stated number of neurons Tap the diagram to enlarge.

Layer 10 → 5

Step 1: count connections.

$10(5)=50$ LaTeX: 10(5)=50

Step 2: count receiving-neuron biases.

There are 5 receiving neurons, so 5 biases.

Step 3: add weights and biases.

$50+5=55$ LaTeX: 50+5=55

Layer 5 → 5

Step 1: count connections.

$5(5)=25$ LaTeX: 5(5)=25

Step 2: count receiving-neuron biases.

There are 5 receiving neurons, so 5 biases.

Step 3: add weights and biases.

$25+5=30$ LaTeX: 25+5=30

Layer 5 → 5

Step 1: count connections.

$5(5)=25$ LaTeX: 5(5)=25

Step 2: count receiving-neuron biases.

There are 5 receiving neurons, so 5 biases.

Step 3: add weights and biases.

$25+5=30$ LaTeX: 25+5=30

Layer 5 → 4

Step 1: count connections.

$5(4)=20$ LaTeX: 5(4)=20

Step 2: count receiving-neuron biases.

There are 4 receiving neurons, so 4 biases.

Step 3: add weights and biases.

$20+4=24$ LaTeX: 20+4=24

Total = 139. Input values and activations are not trainable parameters.

Use hidden nonlinearities such as ReLU and a 4-class softmax. Learned parameters are the connections and biases; the number of layers and units are design choices.