# F22 Q6b

Subject: Deep Learning

Exam: MT2

Reader: https://deep-learning-study-room.vercel.app/#mt2/read/15/mt2-c15-s9

Canonical: https://deep-learning-study-room.vercel.app/read/dl/mt2/section/mt2-c15-s9/

## Question

**Question (10 marks).** Design a clothes classifier for 250,000 six-dimensional samples,6 classes and 2 hidden layers. Give train/validation/test split, activations/loss, actions for 15% training 20% validation error, interpret improvement to 1%/1.5%, then address 15% test error.

## Answer — step by step

**One explicit design:** 6 → 16 → 8 → 6, ReLU hidden layers,6-unit softmax output, categorical cross-entropy. The hidden widths are chosen assumptions, not supplied numerical requirements.

Architecture: 6 → 16 → 8 → 6. Each non-input neuron has one bias.

### Layer 6 → 16

**Step 1: count connections.**



$$
6(16)=96
$$



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

There are 16 receiving neurons, so 16 biases.

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



$$
96+16=112
$$



### Layer 16 → 8

**Step 1: count connections.**



$$
16(8)=128
$$



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

There are 8 receiving neurons, so 8 biases.

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



$$
128+8=136
$$



### Layer 8 → 6

**Step 1: count connections.**



$$
8(6)=48
$$



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

There are 6 receiving neurons, so 6 biases.

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



$$
48+6=54
$$



**Total = 302**. Input values and activations are not trainable parameters.

**Split:**  a stratified 70/15/15 split gives 175,000 training,37,500 validation,37,500 test samples. Fit preprocessing on training data only and keep related duplicates within a single split.

**15%/20%:**  inspect learning curves and baseline difficulty. Substantial training error suggests capacity/optimization or data-quality issues; the 5 point gap also suggests a generalization issue. Improve training fit, tune regularization and collect useful representative data instead of blindly increasing capacity.

**1%/1.5%:**  good comparable-set results with a small gap are encouraging; verify that validation has not leaked into training.

**15% test:**  inspect distribution shift, preprocessing differences, label quality, leakage or repeated validation overfitting. Compare per-class errors and collection conditions. Address the actual cause and collect representative data if necessary. If test results guide retuning, use a fresh untouched final test set.