Convolution kernel

As explained in Deep Learning with R, Third Edition

A convolution kernel is a learned weight matrix that transforms each extracted input patch into an output feature vector.

A convolution kernel is a learned weight matrix that transforms each extracted input patch into an output feature vector. Sliding across an image, the same kernel evaluates the same local pattern at every position, producing a response map. Early kernels commonly respond to edges or textures; later kernels can respond to increasingly abstract visual concepts. section 8.1.1 section 10.4

A convolution layer is characterized by:

• Patch size, typically 3 × 3 or 5 × 5, defining the local region examined at each position. section 8.1.1
• Output depth, which determines how many kernels are learned and therefore how many output channels are produced. section 8.1.1
• A response map for each kernel, showing where its learned pattern appears across the input. section 8.1.1
• Window placement controlled by valid locations, padding, and strides, which affect the output dimensions. section 8.1.1

MNIST convolution layer

A first convolution layer can transform a 28 × 28 × 1 grayscale input into a 26 × 26 × 64 feature map. It applies 64 learned kernels over 3 × 3 patches; each output channel is a spatial response map for one kernel. A later stack can increase depth from 64 to 128 to 256, while successive layers represent more complex visual patterns. section 8.1.1

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

Use the response-map figure to see how one kernel records the presence of a learned pattern at different image locations. section 8.1.1

Kernel behavior can be inspected through intermediate activations. Plotting each channel separately reveals which patterns respond to an input; a first-layer channel may behave like a diagonal-edge detector, although learned channels can vary between training runs. section 10.1

How Deep Learning with R, Third Edition covers it

How deep it goes

Explains patches, channels, response maps, padding, and strides, but stops short of formal weight calculations.

Examples

Uses MNIST dimensions, 3 × 3 and 5 × 5 windows, and channel visualizations of a cat image.

What it assumes

Assumes image tensors with height, width, and channels, while introducing filters, feature maps, and response maps.

What you can do after

Evaluate learned patterns by inspecting convolutional activations and their spatial response maps.

How it connects

Connects convolution kernels to feature maps, response maps, intermediate activations, pooling layers, and Grad-CAM.

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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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  Graph Neural Networks in ActionA learnable weighted operation that transforms input data to emphasize particular patterns or features.
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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.

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