Components of Convolutional Network

Fully connected Layers

• 32 x 32 x 3 image → stretch to 4072 x 1
• Multiply Weight with dimension 10 x 3072 to output 10 values

Convolution Layers

• Instead of stretching the data, the input image preserves spacial structure: 32 x 32 x 3
• Weight matrix also has such dimension. i.e. 5 x 5 x 3 filter
  • The weight matrix needs the same weight
  • 1 output number = result of dot product between filter and small chunk in input data
• Output would be a 1 x 28 x 28 matrix (called Activation Map)
• Usually there are multiple filters of size 5 x 5 x 3, so the Convolution layer would be sth like. 6 x 5 x 5 x 3, and out put would be 6 activation maps, with each size 1 x 28 x 28
  • Each layer filters would also have a bias vector
  • Also, the input will usually be a batch of images

Convolutional Layer Dimensions

Input: $N\times C_{in}\times H\times W$

• N, H, W: Number of images in the mini-batch, Height, Width
• $C_{in}$ : number of channels for each image (3 for RGB)

filters: $C_{out}\times C_{in}\times K_w \times K_h$

Output: $N\times C_{out}\times H'\times W'$

When doing convolution, the size shrinks based on size of filter

• So we need to use padding
• Input: W
• Filter: K