Convolutions
121
The Idea
pixel
h
• Translation invariance
+1/−1 • Spatial locality
human?
122
Filter (1D) & Convolution
Image: 0011101000
F1: -1 +1 “left edge detector”
F2: -1+1-1
123
padding
Filters (2D) & Filter banks
124
Layers of Filters
125
Stride
127
Summary – Filter Layer
• Filter layer 𝑙:
• Number of filters 𝑚𝑙
• Size of filters: 𝑘𝑙 × 𝑘𝑙 × 𝑚𝑙−1
• Stride 𝑠𝑙
• Input tensor: 𝑛𝑙−1 × 𝑛𝑙−1 × 𝑚𝑙−1
𝑛𝑙−1 𝑠𝑙
• Generally, an activation function is applied to a convolutional layer, e.g. ReLU 128
• Output tensor: 𝑛𝑙 × 𝑛𝑙 × 𝑚𝑙, where 𝑛𝑙 =
• Weights: 𝑚𝑙 weights of size 𝑘𝑙 × 𝑘𝑙 × 𝑚𝑙−1