Deep Learning · MT2 · section

F22 Q6b

F22 selected MT2 practice

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.

$6(16)=96$ LaTeX: 6(16)=96

Step 2: count receiving-neuron biases.

There are 16 receiving neurons, so 16 biases.

Step 3: add weights and biases.

$96+16=112$ LaTeX: 96+16=112

Layer 16 → 8

Step 1: count connections.

$16(8)=128$ LaTeX: 16(8)=128

Step 2: count receiving-neuron biases.

There are 8 receiving neurons, so 8 biases.

Step 3: add weights and biases.

$128+8=136$ LaTeX: 128+8=136

Layer 8 → 6

Step 1: count connections.

$8(6)=48$ LaTeX: 8(6)=48

Step 2: count receiving-neuron biases.

There are 6 receiving neurons, so 6 biases.

Step 3: add weights and biases.

$48+6=54$ LaTeX: 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.