17 CNN Structure 4D Data

Invariance vs. Equivariance:

• Convolutional Layers achieve **shift equivariant (the output shifts as the input shifts).
• Pooling/Fully Connected Layers achieve shift invariance (the classification remains the same regardless of small shifts in input).
• Semantic Segmentation Idea: Using “Fully Convolutional” networks to make prediction for every pixel simultaneously

Understanding 4D Data

Deep learning frameworks typically process data in $4$ dimensions:

1. Batch Index $(N)$: which training example in the batch (the “Archive”).
2. Channel ($C$): which feature map or colour channel (the “Cabinet”).
3. Row $(Y)$: vertical coordinate
4. Column $(X)$: Horizontal coordinate

Weight Initialisation

• Crucial Rule: Never set all weights to $0$ or $1$. If weights are equal, all derivatives will be the same, making neurons “interchangeable” and preventing learning.
• Random Initialisation: Generally centred around 0.
• He/Kaiming Initialisation: Best for ReLU activation functions.
• Xavier/Glorot Initialisation: Best for Sigmoid/Tanh functions.