Convolution kernel

As explained in Graph Neural Networks in Action

A learnable weighted operation that transforms input data to emphasize particular patterns or features.

A convolution kernel, or filter, is a learnable weighted operation that transforms input data to emphasize particular features. Its weights are optimized by an objective or loss function, producing representations that support downstream tasks such as classification or node-feature prediction. section 3.4.1

Use the kernel within a typical convolutional layer pipeline:

• Apply the filter to input data to highlight localized patterns. section 3.4.1
• Pass the filter output through an activation function for nonlinear transformation. section 3.4.1
• Optionally pool the result to reduce its size for later learning tasks. section 3.4.1

Grid and graph inputs

For an image, the kernel passes over a fixed pixel grid to identify visual patterns. In a graph convolutional network, convolution operates over graph nodes to identify patterns in graph structure or predict node features. Graph methods may be spatial, using a sliding window over the graph, or spectral, filtering a graph signal. section 3.4.1

Figure 3.11 A convolution of an input image (left). The kernel (middle) is passed over the image of an animal, resulting in a distinct representation (right) of the input image. In a deep learning process, the parameters of the filter (the numbers in the matrix) are learned parameters.

Inspect how a learned matrix passes over an image and produces a distinct representation. section 3.4.1

How Graph Neural Networks in Action covers it

How deep it goes

Explains the layer pipeline and spatial-versus-spectral distinction without deriving the convolution operator mathematically.

Examples

Uses an animal image, a pixel grid, graph nodes, and graph signals to contrast convolution settings.

What you can do after

Understand how learned filters transform grid or graph data into task-relevant representations.

How it connects

Connects convolution kernels to CNNs, graph convolutional networks, activation functions, pooling, spatial methods, and spectral methods.

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Also explained in

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  Natural Language Processing in Action, Second EditionA convolutional kernel is a parameter matrix or tensor whose sliding weighted operation detects a local pattern in an input sequence.
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  Math and Architectures of Deep LearningA learned kernel applied in a convolution layer to detect local spatial patterns in images.
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  Inside Deep Learning: Math, Algorithms, ModelsA learned array of weights applied over local input regions to compute convolution outputs.
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  Deep Learning with PyTorch, Second EditionA small learned filter window applied over local regions of an input to compute weighted sums.
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  Grokking AI Algorithms, Second EditionA convolutional filter is a small learned grid of weights that detects a particular local pattern in image data.
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  Deep Learning with Python, Third EditionThe learned weight tensor used by a convolution to transform local input patches.
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  Deep Learning with R, Third EditionA convolution kernel is a learned weight matrix that transforms each extracted input patch into an output feature vector.
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  Learn Generative AI with PyTorchA learned convolutional kernel whose weights slide across local input regions to produce feature responses.
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  Sutskever's ListA convolutional kernel is a grid of learned weights applied across local regions of an input to produce spatial responses.
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  Evolutionary Deep Learning: Genetic algorithms and neural networksA convolutional filter is a learned array of weights that is slid across local input regions to produce feature responses.

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Related concepts

• convolutional neural networkused by · A convolutional neural network is a neural-network architecture that applies learned convolutional operations to extract patterns from structured data.
• 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.
• feature mapproduces · A feature map is a spatially organized array of neural-network activations representing the presence or strength of learned features at different locations.
• image processinguses · Image processing is the computational manipulation and analysis of digital image data to transform images or extract information.

This explainer was generated by Manning's knowledge graph from the text of Graph Neural Networks in Action. The section links point to the parts of the book it draws on.