🖼️ Convolutional Neural Networks

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# 🖼️ Convolutional Neural Networks ## 1. 🎯 Learning Objectives - Compute convolution output dimensions: $(n+2p-f)/s + 1$ - Explain the purpose of padding and stride - Compare pooling types: max vs average - Identify key architectural innovations in LeNet, AlexNet, VGG ## 2.

🖼️ Convolutional Neural Networks

1. 🎯 Learning Objectives

Compute convolution output dimensions: $(n+2p-f)/s + 1$
Explain the purpose of padding and stride
Compare pooling types: max vs average
Identify key architectural innovations in LeNet, AlexNet, VGG

2. 📖 Core Content

3.1 Convolution Operation

A convolution applies a kernel (filter) across the input:

(I * K)(i,j) = \sum_m \sum_n I(i+m, j+n) \cdot K(m,n)

3.2 Output Size Formula

H_{out} = \left\lfloor \frac{H_{in} + 2p - f}{s} + 1 \right\rfloor

Where:

$H_{in}$ : Input height
$f$ : Filter/kernel size
$p$ : Padding
$s$ : Stride Example: Input 32×32, filter 5×5, padding 0, stride 1: (32+0-5)/1+1 = 28. Output: 28×28.

3.3 Padding

Valid padding (p=0): No padding. Output smaller than input.
Same padding: $p = (f-1)/2$ . Output same size as input.
Only possible with odd filter sizes (3, 5, 7...).

3.4 Stride

Stride s > 1 downsamples the input. Higher stride = smaller output.

3.5 Pooling

Max pooling: Take maximum value in each window. Average pooling: Take average value in each window. Typically 2×2 with stride 2: halves spatial dimensions.

3.6 CNN Architectures

Architecture	Year	Key Innovation	Parameters
LeNet-5	1998	First successful CNN	60K
AlexNet	2012	Deep CNN + ReLU + Dropout + GPU	60M
VGG-16	2014	Very deep (16 layers), 3×3 conv only	138M
GoogLeNet	2014	Inception modules, efficient	4M
ResNet	2015	Skip connections (residual blocks)	25M

4. 📝 Practice Questions

Q1: Input 224×224×3, filters 64 of size 7×7, padding 3, stride 2. Output size?

Answer: H_out = (224 + 2×3 - 7)/2 + 1 = (224+6-7)/2 + 1 = 223/2 + 1 = 111.5 + 1 = 112 (assuming integer division). Actually: (224+6-7)/2 + 1 = 223/2 + 1 = 111.5 + 1 = 112.5 → floor 112. Output: 112×112×64. Join Discord PreviousCNN OperationsNextCNN Architectures