Convolution

Definition

Convolution is an operation that applies a small learned pattern across different positions of an input.

Basic idea:

small pattern -> slide across input -> produce responses

The same pattern is reused at multiple positions.

Convolution detects local patterns using shared weights.

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Why Local Patterns Matter

Some data has local structure.

Examples:

nearby pixels in an image
nearby values in a signal
nearby tokens in a short window

Convolution focuses on local neighborhoods instead of connecting everything to everything.

Convolution assumes nearby values can form meaningful patterns.

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Shared Weights

In a fully connected layer, different positions can have different weights.

In convolution, the same weights are reused across positions.

Example:

same filter at position 1
same filter at position 2
same filter at position 3

This makes convolution efficient and gives it a useful bias.

Shared weights let one learned pattern be recognized in many places.

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Convolution Output

As the pattern moves across the input, it produces values.

These values form a feature map.

input -> convolution -> feature map

High response means the learned pattern matched strongly at that position.

Low response means it matched weakly.

Convolution produces a map of where a pattern appears.

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Final Summary

• Convolution applies a small learned pattern across positions.
• It focuses on local structure.
• It reuses the same weights in different locations.
• This creates a bias toward repeated local patterns.
• The output is a feature map.
• Convolution is useful when position and neighborhood structure matter.