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理解胶囊网络 Understanding Capsule Networks

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《Understanding Capsule Networks — AI’s Alluring New Architecture》by Nick Bourdakos

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NickBourdakos

ComputervisionaddictatIBMWatson

Feb12 · 15minread

UnderstandingCapsuleNetworks—AI’s

AlluringNewArchitecture

Convolutional neural networks have done an amazing job, but are

rooted in problems. It’s time we started thinking about new solutions or

improvements — and now, enter capsules.

Previously, I briey discussed how capsule networks combat some of

these traditional problems. For the past for few months, I’ve been

submerging myself in all things capsules. I think it’s time we all try to

get a deeper understanding of how capsules actually work.

In order to make it easier to follow along, I have built a visualization

tool that allows you to see what is happening at each layer. This is

“Science”byAlexReynolds

paired with a simple implementation of the network. All of it can be

found on GitHub here.

This is the CapsNet architecture. Don’t worry if you don’t understand

what any of it means yet. I’ll be going through it layer by layer, with as

much detail as I can possibly conjure up.

Part0:TheInput

The input into CapsNet is the actual image supplied to the neural net.

In this example the input image is 28 pixels high and 28 pixels wide.

But images are actually 3 dimensions, and the 3rd dimension contains

the color channels.

The image in our example only has one color channel, because it’s black

and white. Most images you are familiar with have 3 or 4 channels, for

Red-Green-Blue and possibly an additional channel for Alpha, or

transparency.

Each one of these pixels is represented as a value from 0 to 255 and

stored in a 28x28x1 matrix [28, 28, 1]. The brighter the pixel, the

larger the value.

Part1a:Convolutions

The rst part of CapsNet is a traditional convolutional layer. What is a

convolutional layer, how does it work, and what is its purpose?

The goal is to extract some extremely basic features from the input

image, like edges or curves.

How can we do this?

Let’s think about an edge:

If we look at a few points on the image, we can start to pick up a

pattern. Focus on the colors to the left and right of the point we are

looking at:

You might notice that they have a larger dierence if the point is an

edge:

255 - 114 = 141

114 - 153 = -39

153 - 153 = 0

255 - 255 = 0

What if we went through each pixel in the image and replaced its value

with the value of the dierence of the pixels to the left and right of it?

In theory, the image should become all black except for the edges.

We could do this by looping through every pixel in the image:

for pixel in image {

result[pixel] = image[pixel - 1] - image[pixel + 1]

}

But this isn’t very ecient. We can instead use something called a

“convolution.” Technically speaking, it’s a “cross-correlation,” but

everyone likes to call them convolutions.

A convolution is essentially doing the same thing as our loop, but it

takes advantage of matrix math.

A convolution is done by lining up a small “window” in the corner of

the image that only lets us see the pixels in that area. We then slide the

window across all the pixels in the image, multiplying each pixel by a

set of weights and then adding up all the values that are in that

window.

This window is a matrix of weights, called a “kernel.”

We only care about 2 pixels, but when we wrap the window around

them it will encapsulate the pixel between them.

Window:

┌─────────────────────────────────────┐

│ left_pixel middle_pixel right_pixel │

└─────────────────────────────────────┘

Can you think of a set of weights that we can multiply these pixels by so

that their sum adds up to the value we are looking for?

Window:

┌─────────────────────────────────────┐

│ left_pixel middle_pixel right_pixel │

└─────────────────────────────────────┘

(w1 * 255) + (w2 * 255) + (w3 * 114) = 141

Spoilers below!

│ │ │

\│/ \│/ \│/

V V V

We can do something like this:

Window:

┌─────────────────────────────────────┐

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