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Core ML
Visual explainer

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 hardcodes positions, meaning a feature learned in one corner is invisible if it appears in another.
A fully connected network hardcodes positions, meaning a feature learned in one corner is invisible if it appears in another.

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

A convolution uses a small, shared filter that slides across the entire image, using the same weights everywhere.
A convolution uses a small, shared filter that slides across the entire image, using the same weights everywhere.

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 position, the overlapping pixels are multiplied by the filter weights and summed into a single feature map value.
At each position, the overlapping pixels are multiplied by the filter weights and summed into a single feature map value.

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

The output feature map preserves the spatial arrangement of the input, lighting up exactly where the pattern was found.
The output feature map preserves the spatial arrangement of the input, lighting up exactly where the pattern was found.

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 convolution only sees inside its small window, so it remains blind to large-scale context and misses features that exceed its receptive field.
A convolution only sees inside its small window, so it remains blind to large-scale context and misses features that exceed its receptive field.

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.

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