Translation invariance

As explained in Deep Learning with Python, Third Edition

The property that a learned pattern can be recognized at different spatial locations without relearning it from scratch.

Translation invariance lets a learned pattern be recognized at different locations without relearning it. Convolutional networks achieve this by applying the same transformation to local patches across an input, producing a response map of pattern presence. section 8.1.1

A pattern moves across an image

Suppose a convolutional network learns an edge or small texture in the lower-right corner of an image. It can recognize the same pattern in the upper-left because the convolution scans equivalent local windows with shared transformations. A densely connected model would need to learn the pattern again at the new location. section 8.1.1

Use translation invariance as a practical modeling assumption:

• Choose convolution when the same local structure should retain similar meaning wherever it appears. section 8.1.1
• Expect the assumption to support data efficiency because one learned representation can generalize across locations. section 8.1.1
• Check the data before applying it to sequences: time-of-day effects or strong recency can make locations behave differently. section 13.2.4

Figure 8.3 The concept of a response map: a 2D map of the presence of a pattern at different locations in an input

A response map makes the idea concrete by showing where a learned pattern appears across an input. section 8.1.1

How Deep Learning with Python, Third Edition covers it

How deep it goes

Explains shared local transformations and practical limits, but stops short of a mathematical derivation of convolution.

Examples

Uses moving image edges and textures, plus a Conv1D temperature-forecasting model that achieves about 2.9 degrees validation MAE.

What it assumes

Assumes basic familiarity with convolutional and densely connected layers while explaining local windows and shared transformations concretely.

What you can do after

Evaluate whether convolutional models suit data whose local patterns behave consistently across locations.

How it connects

Connects translation invariance with convolution, feature maps, response maps, spatial hierarchies, and pooling.

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Also explained in

• 

  liveBookmanning.com
  Deep Learning with PyTorch, Second EditionThe property of a model or representation whose output is unchanged, or changes minimally, when an input object shifts position.
• 

  liveBookmanning.com
  Inside Deep Learning: Math, Algorithms, ModelsA property of a model whose output is unchanged, or less changed, when the input is shifted in position.
• 

  liveBookmanning.com
  Natural Language Processing in Action, Second EditionTranslation invariance is the property of recognizing a pattern despite changes in its position within an input.
• 

  liveBookmanning.com
  Sutskever's ListThe property of recognizing a pattern similarly despite changes in its spatial location.

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Related concepts

• inductive biaskind of · Inductive bias is the set of assumptions a learning method uses to favor some hypotheses or generalizations over others when learning from data.
• scale invariancecontrasts with · Scale invariance is the property that a relationship or recognized pattern retains its form when the system’s scale or dimensions change.
• poolingaddressed by · Pooling is an operation that aggregates values or representations across regions or axes to produce a reduced or summarized representation.
• convolutional layeraddressed by · A convolutional layer is a neural-network layer that applies shared learned filters to local regions of structured input to produce feature representations.

This explainer was generated by Manning's knowledge graph from the text of Deep Learning with Python, Third Edition. The section links point to the parts of the book it draws on.