• 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×NN\times N
    • Filter: M×MM\times M
    • Stride: SS
    • Output size = (NM)/S+1\lfloor(N-M) / S\rfloor+1
  • Jargon
    • Filters are often called “Kernels
    • The outputs of individual filters are called “channels


  • 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 DD decreases the size of the maps by a factor of DD
  • Filters within a layer must all be the same size, but sizes may vary with layer
    • Similarly for pooling, DD 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

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