Architecture

• A convolutional neural network comprises “convolutional” and “downsampling ” layers
  • Convolutional layers comprise neurons that scan their input for patterns
  • Downsampling layers perform max operations on groups of outputs from the convolutional layers
    • Perform on individual map
    • For reduce the number of parameters
• The two may occur in any sequence, but typically they alternate
• Followed by an MLP with one or more layers

A convolutional layer

• Each activation map has two components
  • An affine map, obtained by convolution over maps in the previous layer
    • Each affine map has, associated with it, a learnable filter
  • An activation that operates on the output of the convolution
• What is a convolution
  • Scanning an image with a “filter”
  • Equivalent to scanning with an MLP
• Weights
  • size of the filter $\times$ no. of maps in previous layer
• Size
  • Image size: $N\times N$
  • Filter: $M\times M$
  • Stride: $S$
  • Output size = $\lfloor(N-M) / S\rfloor+1$
• Jargon
  • Filters are often called “Kernels”
  • The outputs of individual filters are called “channels”

Notion

• Each convolution layer maintains the size of the image
  • With appropriate zero padding
  • If performed without zero padding it will decrease the size of the input
• Each convolution layer may increase the number of maps from the previous layer
  • Depends on the number of filters
• Each pooling layer with hop $D$ decreases the size of the maps by a factor of $D$
• Filters within a layer must all be the same size, but sizes may vary with layer
  • Similarly for pooling, $D$ may vary with layer
• In general the number of convolutional filters increases with layers
  • Because the patterns gets more complex, hence larger combinations of patterns to capture
• Training is as in the case of the regular MLP
  • The only difference is in the structure of the network