Spatial hierarchy

As explained in Deep Learning with R, Third Edition

A spatial hierarchy is an organization in which increasingly complex visual patterns are composed from simpler patterns across neural-network layers.

A spatial hierarchy organizes visual understanding from small local patterns to increasingly complex patterns across convolutional layers: edges can combine into parts, which can combine into objects. section 8.1.1

Convolutional networks build this hierarchy through:

• Early layers detect small local patterns such as edges or textures. section 8.1.1
• Later layers combine earlier features into larger and more abstract visual concepts. section 8.1.1
• Downsampling makes successive layers view larger portions of the original image while concentrating information increasingly in channels. section 8.1.2

Why pooling matters for digit recognition

A 28 × 28 digit model with three 3 × 3 convolutions but no pooling ends with 22 × 22 feature maps. Its later filters see only 7 × 7 regions of the input, limiting access to the whole digit. Max-pooling with 2 × 2 windows and stride 2 reduces feature-map size and expands the effective visual context. section 8.1.2

Figure 8.2 The visual world forms a spatial hierarchy of visual modules: elementary lines or textures combine into simple objects such as eyes or ears, which combine into high-level concepts such as “cat.”

Visualize how elementary lines and textures combine into parts and then high-level object concepts. section 8.1.1

How Deep Learning with R, Third Edition covers it

How deep it goes

Connects layerwise pattern composition to pooling, receptive-field growth, and feature-map size, without deriving convolution internals.

Examples

Uses edges, textures, object parts, cats, and MNIST digit networks with and without max-pooling.

What it assumes

Assumes convolutional layers and feature maps while defining local patches, channels, filters, and hierarchical composition.

What you can do after

Evaluate convolutional architectures by relating pooling and receptive-field growth to spatial hierarchy.

How it connects

Links convolution, feature maps, filters, pooling, downsampling, receptive fields, and translation invariance.

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Also explained in

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  Deep Learning with Python, Third EditionA layered organization of features in which deeper layers represent patterns over increasingly large spatial extents of the input.

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