Transposed convolution

As explained in Grokking AI Algorithms, Second Edition

A transposed convolution is a learnable convolutional operation that projects a lower-resolution representation into a higher-resolution output space.

A transposed convolution is a learnable layer that projects a low-resolution feature map into a larger one. Unlike nearest-neighbor interpolation, which duplicates pixels, it uses trainable filters to reconstruct useful detail. section 12.19

The upsampling process works like this:

• Take one pixel at a time from the small feature map. section 12.19
• Use a learnable filter to paint a larger patch on the output map rather than producing only one output pixel. section 12.19
• Repeat the operation for every input pixel and add values where painted patches overlap. section 12.19
• Learn the filter weights during training so the layer can reconstruct cleaner, more coherent detail. section 12.19

From 4×4 to 8×8

A decoder receives sixteen 4×4 feature maps from a compressed bridge. A transposed-convolution layer enlarges them to sixteen 8×8 maps, carrying image data together with text-label and timestep embeddings. In a simple implementation, a filter size of 4, stride of 2, and padding of 1 produce the doubled spatial dimensions. section 12.19

Figure 12.41 The upsampling layer in our U-Net

View the U-Net upsampling layer alongside the feature-map transition from compressed representations to larger maps. section 12.19

How Grokking AI Algorithms, Second Edition covers it

How deep it goes

Explains filter-based patch painting, overlap accumulation, learned weights, and a small implementation while stopping short of deeper theory.

Examples

Uses nearest-neighbor duplication, an artist reconstruction analogy, and a 4×4-to-8×8 U-Net feature-map example.

What it assumes

Assumes familiarity with feature maps and convolutional layers while introducing the upsampling intuition from pixel duplication.

What you can do after

Builds a basic upsampling layer using filters, stride, padding, output dimensions, and accumulated overlapping contributions.

How it connects

Connects transposed convolution to convolution, nearest-neighbor interpolation, U-Net decoders, skip connections, and diffusion models.

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Also explained in

• 

  liveBookmanning.com
  Learn Generative AI with PyTorchThe 2D computation performed by a transposed convolutional layer to expand an image or feature map.
• 

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  Inside Deep Learning: Math, Algorithms, ModelsA convolution-like operation used to increase spatial resolution in a tensor, often to undo downsampling from pooling in dense prediction models.
• 

  liveBookmanning.com
  Build a Text-to-Image Generator (from Scratch)A transposed convolutional layer increases spatial resolution by applying a learned convolution-like operation that can expand spatial dimensions.
• 

  liveBookmanning.com
  Math and Architectures of Deep LearningA convolution-like operation often described via the transpose of the convolution matrix, used here as a motivation for understanding the matrix form of convolution.

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Related concepts

• up blockused by · An up block is a U-Net component that increases spatial resolution through operations such as transposed convolution.
• upsamplingimplements · Upsampling is a process that increases the number, density, or spatial or temporal resolution of samples or values in a dataset or representation by adding, duplicating, or estimating them.
• convolution kerneluses · A convolution kernel is a small array or tensor of weights applied across local input regions to compute weighted responses and detect or transform patterns.
• convolutional layercontrasts with · A convolutional layer is a neural-network layer that applies shared learned filters to local regions of structured input to produce feature representations.
• decodeused by · Decoding is the process of transforming an encoded or internal representation into an interpretable or target-form output.

This explainer was generated by Manning's knowledge graph from the text of Grokking AI Algorithms, Second Edition. The section links point to the parts of the book it draws on.