## Key Ideas We can start by thinking of all the ways that we can combine two **lists of numbers** or **functions**.  We can of course add or multiply them:   But we also have access to another type of combination, just as fundamental as addition or multiplication, known as **convolution**. However, unlike the previous two cases, it is not something that you can just inherit from an operation you can do to numbers. It is genuinely new to lists of numbers or functions (put another way, it can be applied to members of a **[vector space](Abstract%20Vector%20Spaces.md)**)  ## Visuals for the discrete case Visually we can see that convolution below producing a moving average of the data:   Vertical Edge detection:    ### Horizontal Edge Detection   ### Kernels  The idea with a [Convolutional Neural Network](Convolutional%20Neural%20Network.md) is that you can use data to learn what the kernel should be in the first place (based on what the neural network wants to detect). ### Flipping the Kernel Note that in the image processing context, flipping our kernel around feels very odd and out of context. However, that is mainly inherited from the pure math context (think of the probability example) where it is a completely natural thing to do. --- Date: 20221203 Links to: [Mathematics MOC](Mathematics%20MOC.md) Tags: #review References: * [But what is a convolution? - YouTube](https://www.youtube.com/watch?v=KuXjwB4LzSA&list=PLwcClAaLqrJyzeqgdc9dJYRh9OYawfkSL&index=4)