Translation Invariance

Translation invariance means a model can recognize a pattern even when its position shifts.

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Definition

Translation invariance means recognizing a pattern even when it moves position.

Example:

pattern appears on the left
pattern appears in the center
pattern appears on the right

The identity of the pattern stays useful even though its position changes.

Translation invariance means position shift does not destroy recognition.

Some patterns can appear in different places.

Example:

a local visual pattern can appear in many image locations
a local signal can appear at different time positions

A model that is too position-specific may fail when the same pattern shifts.

Translation invariance helps models handle shifted patterns.

Convolution reuses the same filter across positions.

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

This lets the model detect the same local pattern in many places.

Shared filters support recognition across positions.

It helps to separate two ideas.

equivariance:
if the input shifts, the feature response shifts too

invariance:
the final decision can stay the same despite the shift

Convolution often creates useful equivariant feature maps.

Pooling and later layers can help produce more invariant decisions.

Equivariance tracks the shift; invariance ignores it when useful.

Translation invariance means recognizing patterns despite position shifts.
It matters when patterns can appear in different places.
Convolution helps by sharing filters across positions.
Equivariance means feature responses shift with the input.
Invariance means the final result can stay stable.
Structured architectures can build position-aware and position-robust representations.

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Feature Map