Digging into convolution

Issues

1) Kaiming Initializtion in Pytorch was in trouble.¹

2) Jeremy started to dig in, in lesson09, but I didn’t know why the size of tensor is ² and even understand this spreadsheet data.³

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Homework

Read Visualizing and Understanding Convolutional Networks paper

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• What is a convolution?
  • Visualization
    • one kernel
    • Matthew D Zeiler & Rob Fergus Paper
  • Convolution can be represented as matmul
  • Padding
  • Kernel has rank 3
  • How can we find a side-edge, a gradient and area of constant weight?

What is a convolution?

A convolutional neural network is that your red, green, and blue pixels go into the simple computation, and something comes out of that, and then the result of that goes into a second layer, and the result of that goes into the third layer and so forth.

Visualization

one kernel

• Refer this site for visualizing CNN filtering

Matthew D Zeiler & Rob Fergus Paper

Lecture01

Nine examples of the actual coefficients from the **first layer**

Convolution can be represented as matmul

CNNs from different viewpoints

{align-items: center;}

• [A B C D E F G H I J] is 3 by 3 image data flatten to vector.

• As a result, convolution is a just matrix just two things happens
  • Some of entries are set to zeros at all the times
  • same color always have the same weight. That called weight time / wegith sharing
• So, we can implement a convolution with matrix multiplication. But, we don’t do that because it’s slow!

Padding

• What most of libraries do is just put zeros asdie of matrix

• fast.ai uses reflection paddings (what is this? Jeremy said he uttered it)

Kernel has rank 3

• As standard picture input would be ^{4 5}, it would be actually 3d, not 2d.
• If we make kernel as a 3x3 size, we pass over same kernel all the different Red, Green, Blue Pixels.
  • This could make problem, because, if we want to detect frog, which is green, we would want more activations on the green(I made a test cell in my colab ⁶)

How can we find a side-edge, a gradient and area of constant weight?

Not top-edge!

• One kernel can find only the top-edge, so we should stack the kernels ⁷
• So, we pass it through bunch of kernels to the input images, and that process gives us height x width x corresponding number of kernels.

• Usually that number of chanel is 16
• And if we want to get the more channels and features, we should repeat that process
  • This process gives rise to memory out of control, we do the stride

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conv-example.xlsx

• 2 convolutional filters
• At a second layer, filter is 3x3x2 tensor, because to add up together the first layer’s channel.

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Reference

1. Problem was math.sqrt(5) was not kaiming initialization formula, Implementation in Pytorch ↩

2. size of tensor, lecture09 ↩

3. conv-example.xlsx ↩

4. Why do computer use red, green and blue instead of primary colors ↩

5. Grayscale is a group of shades without any visible color. … Each of these dots has its own brightness level as well and, therefore, can be converted to grayscale. A grayscale image is one with all color information removed. ↩

6. Testing RGB and grayscale ↩

7. stack kernel and make new rank of tensor at output, Lesson06-2019 ↩