Week 2A : CNNs.md

Week 2A : CNNs

Review of convolutions

Why not use FC for images?

• FC 작동 방식

  1. 3232 image data → 10241 Flatten vector

  2. 10개의 class가 있으므로 1024*10 feature 배열 생성

  3. Flatten vector와 feature 배열을 곱해서 Output class 획득하고 이를 통해 Classification

• Issue 1

  • The dimensionality of the number of weights that you need to learn scales really poorly with the size of the image
  • We want neural networks that we use for computer vision to be able to work well with larger images as well

• Issue 2

  • Do we really need this many weights at all?
  • matrix multiplication : learning a weight a separate weight for each input pixel(image)
  • In many images there's maybe a few regions of that image that are particularly important to telling what's inside the image → overkill

• Issue 3

  • FC layer에 image를 넣으면 3차원 → 1차원 변형 과정에서 image의 spatial information을 잃게 됨

Convolutional filters

• entire image를 다루는 대신 flattening 한 후 matrix multiply

• 과정

  1. 5*5 patch를 통해 25 dimensional vector로 추출

  2. dot product를 통해 one-dimensional output으로 get

  3. 전체 image에서 5*5 patch를 slide해서 위 과정 반복

Filter stacks and ConvNets

input과 output이 정확하게 같은 size는 아니지만 3-dimensional tensor는 유지하고 있다.

앞서 본 것은 linear operation. 실제로는 각 layer 뒤에 non-linearity 적용.

Strides & Padding

• Strides
  • Convolutions can subsample the image by jumping across some locations - called ‘stride’

만일 위의 예시와 같이 Stride가 커서 filter가 이동했을 때 image를 벗어나게 되면 어떻게 해야할까? → Padding

• Padding
  • Padding solves the problem of filters running out of image
  • Done by adding extra rows/cols to the input (usually set to 0)
  • ‘SAME’ padding is illustrated here for filter=(3,3) with stride=(2,2)
  • Not padding is called ‘VALID’ padding

Filter Math

• Input: WxHxD volume
• Parameters:
  • K filters, each with size (F, F)
    • commonly set to powers of 2 (e.g. 32, 64, 128)
  • ... moving at stride (S, S)
    • commonly (5,5), (3,3), (2,2), (1,1)
  • ... with padding P
    • ‘SAME’ sets it automatically
• Output
  • W’ = (W - F + 2P) / S + 1
  • H’ = (H - F + 2P) / S + 1
• Each filter has (F * F * D) parameters
• K * (F * F * D) total in the layer

Implementation notes

• X_col (27 * 9)
  • 27 = 3 * 3 * 3 (extracted patch)
  • 9 = each of the positions in the input tensor

• W (32 * 27)
  • 32개의 filter
  • the # of weights (3 * 3 filter, 3-channel input) = 27 (333)
• W @ X = (3227) @ (279) = (32 * 9)
• Reshape (3332)

Other important ConvNet operations

• Increasing the receptive field (dilated convolutions)
• Decreasing the size of the tensor
  • pooling
  • 1*1 - convolutions

Receptive fields