# R24 Q1b

Subject: Deep Learning

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/#tee/read/14/tee-c14-s1

Canonical: https://deep-learning-study-room.vercel.app/read/dl/tee/section/tee-c14-s1/

## 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.



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



**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](https://deep-learning-study-room.vercel.app/assets/figures/dense_10_5_5_5_4.svg)

Diagram: R24 Q1b every layer contains the stated number of neurons. Labels: Input | 10 neurons | Hidden 1 | 5 neurons | Hidden 2 | 5 neurons | Hidden 3 | 5 neurons | Output | 4 neurons | Every receiving neuron has one bias. All adjacent layers are fully connected.

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

### Layer 10 → 5

**Step 1: count connections.**



$$
10(5)=50
$$



**Step 2: count receiving-neuron biases.**

There are 5 receiving neurons, so 5 biases.

**Step 3: add weights and biases.**



$$
50+5=55
$$



### Layer 5 → 5

**Step 1: count connections.**



$$
5(5)=25
$$



**Step 2: count receiving-neuron biases.**

There are 5 receiving neurons, so 5 biases.

**Step 3: add weights and biases.**



$$
25+5=30
$$



### Layer 5 → 5

**Step 1: count connections.**



$$
5(5)=25
$$



**Step 2: count receiving-neuron biases.**

There are 5 receiving neurons, so 5 biases.

**Step 3: add weights and biases.**



$$
25+5=30
$$



### Layer 5 → 4

**Step 1: count connections.**



$$
5(4)=20
$$



**Step 2: count receiving-neuron biases.**

There are 4 receiving neurons, so 4 biases.

**Step 3: add weights and biases.**



$$
20+4=24
$$



**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.