Suppose we have an image recognition program to identify objects in an image, such as the example we referred to previously. Now imagine how hard it would be to try and classify an image with a standard feedforward network; each pixel in the image would be a feature that would have to be sent through the network with its own set of parameters. Our parameter space would be quite large, and we could likely run out of computing power! Images, which in technical terms are just high-dimensional vectors, require some special treatment.
What would happen if we were to try and accomplish this task with a basic feedforward network? Let's recall that basic feedforward networks operate on top of vector spaces. We start with an image, which is made up of independent pixels. Let's say our image is 32 pixels by 32 pixels; the input to our convolutional layer...
