How deeply does Math and Architectures of Deep Learning cover local pattern?

Defines local connectivity and relates it to kernels, stride, padding, and dimensionality without deriving convolution algebra.

Local pattern

As explained in Math and Architectures of Deep Learning

A pattern that is confined to a small neighborhood of the input and can be captured by a local operator such as convolution.

A local pattern is a structure confined to a small neighborhood of an input. Convolutional layers capture it by connecting a small set of adjacent input values to each output, unlike fully connected layers, which connect every input to every output. section 10.8

A kernel slides across an input array and detects or transforms nearby structure. Kernel size, stride, and padding determine how much of the input each step examines and the resulting output size. section 10.8

Convolution applies the same local-neighborhood idea across different input dimensions:

1D convolution slides a kernel along an array, supporting smoothing and edge detection in curves. section 10.8
2D convolution slides a kernel across an image, supporting smoothing and edge detection. section 10.8
3D convolution slides a kernel through a volume, supporting motion detection in image sequences. section 10.8

Geometric intuition

Picture a 2D kernel as a tile sliding over a wall-like input array. At each position, it examines only the values beneath the tile, producing an output that reflects that local neighborhood. section 10.8

How Math and Architectures of Deep Learning covers it

Cover of Math and Architectures of Deep Learning

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Also explained in

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Deep Learning with Python, Third EditionA pattern that occurs within a limited neighborhood of the input rather than across the whole input space.

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Related concepts

long-range dependencycontrasts with · A long-range dependency is a relationship between elements separated by substantial distance in a sequence or other structured representation that are jointly relevant.
convolutional layerused by · A convolutional layer is a neural-network layer that applies shared learned filters to local regions of structured input to produce feature representations.
convolutional neural networkproduced by · A convolutional neural network is a neural-network architecture that applies learned convolutional operations to extract patterns from structured data.

This explainer was generated by Manning's knowledge graph from the text of Math and Architectures of Deep Learning. The section links point to the parts of the book it draws on.