Convolution Operation
Five pictures: Convolution solves the translation problem by sliding a single small kernel of weights across the entire input, generating a feature map while sharing parameters.
A fully connected network assigns an independent weight to every pixel. If it learns to recognize an eye in the top-left corner, it must separately relearn the exact same pattern from scratch if the eye moves to the bottom-right.
The Sliding Filter
Convolution solves this by abandoning position-specific weights. Instead, it uses a single, small kernel of weights that slides systematically across the entire image. The same parameters are reused at every position, enforcing the assumption that a feature is the same no matter where it appears.
Element-wise Math
At each stop, the kernel overlaps a small patch of the input. It performs an element-wise multiplication with the underlying pixels and sums the results into a single number. This dot product measures how strongly the local patch matches the kernel's pattern.
The Feature Map
As the kernel scans the input, it produces a new 2D grid called a feature map. Because the scanning preserves the original spatial order, the feature map lights up exactly in the locations where the target pattern was found.
Where It Breaks
A standard convolution is strictly myopic. It can only see what fits inside its small receptive field. If a feature is much larger than the kernel, or if it requires global context to understand, a single convolutional layer will remain entirely blind to it.
The Quick Version
- Fully connected networks must relearn identical features at every new position.
- Convolution slides one small, shared kernel across the whole input.
- Each step multiplies overlapping pixels by the kernel weights and sums them.
- The result is a feature map that highlights where the pattern appeared.
- The failure: a small kernel cannot detect large-scale global structures.