CS5720 - Week 4
Slide 72 of 80

Convolutional Layer Details

Convolution Operation

Y[i,j] = Σ Σ X[i+m,j+n] × W[m,n] + b
Where:
• Y[i,j] = Output at position (i,j)
• X = Input feature map
• W = Filter/Kernel weights
• b = Bias term
Core Concepts:

Local Connectivity: Each output connects to small input region
Weight Sharing: Same filter applied across entire input
Translation Equivariance: Shifted input produces shifted output
Hierarchical Features: Build complex from simple patterns

Key Parameters

🔍 Number of Filters
Controls depth of output feature maps and model capacity
📐 Kernel Size
Size of receptive field (1×1, 3×3, 5×5, 7×7)
📏 Stride
Step size for filter movement (1, 2, 3...)
🔲 Padding
Border pixels added to preserve spatial dimensions
Output Size Formula:
Output = ⌊(Input + 2×Padding - Kernel) / Stride⌋ + 1

Interactive Convolution Visualizer

Input Feature Map
5×5×1
*
Filter/Kernel
3×3
=
Output Feature Map
3×3×1

Adjust Parameters

Filter Size:
3×3
Stride:
1
Padding:
0
Filter Type:
Step-by-Step Computation
Prepared by Dr. Gorkem Kar