What a Convolution Is - Convolution, Exactly

A convolution slides a given kernel across an exact integer image. This lesson fixes the visible image, kernel, padding, and stride before any output value appears.

highlighted = computed this step

The image and the kernel

A convolution starts with a grid of input values and a smaller kernel. Here the image is 4 by 4, and the kernel is 3 by 3. Every entry is a pinned integer, so the source values are visible before any sum is made.

\text{image }4\times4,\quad \text{kernel }3\times3

Valid padding and stride

The policy is valid padding and stride 1. That means the kernel only lands where the whole patch is inside the image. No hidden border values are invented.

\text{valid padding},\quad \text{stride }1

Summary

This setup fixes the exact data for the whole book. The kernel is given as part of the forward pass, not fitted inside this surface.

\text{given integer kernel; exact integer image}