avatarMatt Kleinsmith

Summary

The web content provides an in-depth explanation of Convolutional Neural Networks (CNNs), illustrating how filters apply to images, the role of biases, and the concept of shared weights within the network's architecture.

Abstract

The article titled "CNNs from different viewpoints" is designed for readers with a basic understanding of neural networks. It delves into the mechanics of CNNs, showcasing how a filter convolves with an image to produce multiple results. The text explains the significance of the bias term, which remains constant across different sections of an image, akin to the weights within the filter. It further elaborates on the compact equation view, the neural network view, and the matrix multiplication view, emphasizing the unique properties of CNN weight matrices, such as untrainable zeros and shared weights. The dense neural network view is presented to draw parallels with traditional neural networks, highlighting the untrainable connections. The article also touches on zero-padding and the use of a 3x3 filter to maintain image size, and it concludes by acknowledging concepts not covered, such as activation functions, pooling, and the optimization process.

Opinions

  • The author emphasizes the importance of understanding CNNs through various representations, including equations, neural network diagrams, and matrix multiplications.
  • Zero-padding is highlighted as a technique to preserve the dimensions of the output image when using filters.
  • The author credits learning resources such as Jeremy Howard's deep learning course and Michael Nielsen's deep learning book for aiding their understanding of CNNs.
  • The article suggests that the connection between traditional neural networks and CNNs becomes more apparent when visualizing the dense neural network with untrainable zeros.
  • The author points out that the explanation is not exhaustive, listing important aspects of CNNs that are not discussed, such as multiple filters, convolutional layers, and the optimization process.
  • Interactive learning tools and realistic image examples are recommended for a more comprehensive understanding of CNNs.

CNNs from different viewpoints

Prerequisite: Basic neural networks

The theme of this post

The image

The filter

Since the filter fits in the image four times, we have four results

Here’s how we applied the filter to each section of the image to yield each result

The equation view

Notice that the bias term, b, is the same for each section of the image. You can consider the bias as part of the filter, just like the weights (α, β, γ, δ) are part of the filter.

The compact equation view

The neural network view

The matrix multiplication view

The matrix above is a weight matrix, just like the ones from traditional neural networks. However, this weight matrix has two special properties:

  1. The zeros shown in gray are untrainable. This means that they’ll stay zero throughout the optimization process.
  2. Some of the weights are equal, and while they are trainable (i.e. changeable), they must remain equal. These are called “shared weights”.

The zeros correspond to the pixels that the filter didn’t touch. Each row of the weight matrix corresponds to one application of the filter.

The dense neural network view

The gray connections correspond to the untrainable zeros. This graph is the same as the previous graph, except that it shows the untrainable zeros. This view helped me see the connection between traditional neural networks and CNNs.

A familiar diagram

How did I learn this?

  1. Jeremy Howard’s deep learning course, especially his CNN spreadsheet and the corresponding video (0:00 to 14:00)
  2. Michael Nielsen’s deep learning book, especially chapter 1 (NNs) and chapter 6 (CNNs)

I found out about Michael Nielsen’s book from Jeremy’s suggested readings for NNs and readings for CNNs.

Bonus: Preserving the image size with zero-padding and a 3x3 filter

Notice that we went from a 3x3 image to a 2x2 image.

With zero-padding and a 3x3 filter, we can preserve the image size.

Here’s what zero-padding with a 3x3 filter looks like:

The 3x3 filter allows us to center the filter on each pixel, so that each original pixel corresponds to a pixel in the result. Although, without zero-padding, our filter would get stuck in the corners, unable to center on any pixel except pixel E, and the result would be a 1x1 image.

Important things that I didn’t talk about or diagram

  • Activation functions
  • Pooling
  • Multiple filters
  • Multiple convolutional layers
  • Dense layers (without shared weights or untrainable zeros)
  • The output layer
  • The optimization process (i.e. gradient descent via backpropagation)
  • How to do useful things with CNNs

Important views I didn’t show

Machine Learning
Artificial Intelligence
Neural Networks
Deep Learning
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