Methods › General › Bijective Transformation › Affine Coupling

Affine Coupling

230 papers tagged archive 2025-07-28

archive 2025-07-28 Description, source and code snippet are the archive's method entry.

Affine Coupling is a method for implementing a normalizing flow (where we stack a sequence of invertible bijective transformation functions). Affine coupling is one of these bijective transformation functions. Specifically, it is an example of a reversible transformation where the forward function, the reverse function and the log-determinant are computationally efficient. For the forward function, we split the input dimension into two parts:

𝐱ₐ, 𝐱_b = split(𝐱)

The second part stays the same 𝐱_b = 𝐲_b, while the first part 𝐱ₐ undergoes an affine transformation, where the parameters for this transformation are learnt using the second part 𝐱_b being put through a neural network. Together we have:

(log𝐬, 𝐭) = NN(𝐱_b)

𝐬 = exp(log𝐬)

𝐲ₐ = 𝐬 ⊙𝐱ₐ + 𝐭

𝐲_b = 𝐱_b

𝐲 = concat(𝐲ₐ, 𝐲_b)

Image: GLOW

Source: NICE: Non-linear Independent Components EstimationSee Code · paultsw/nice_pytorch

Papers archive 2025-07-28

30 shown of 230, newest first. Repository counts are the archive's code-links table. A Syntology line states what Syntology ran from that paper's harvested code; it is per sample and not a correctness claim.

Tasks archive 2025-07-28

20 shown of 200 tasks the archive attaches to papers tagged with this method, by distinct papers. A task without a page in the catalog is plain text.

TaskPapers
Text to Speech16
text-to-speech16
Image Generation15
Density Estimation11
Speech Synthesis11
Anomaly Detection8
regression8
Decoder7
BIG-bench Machine Learning6
General Classification6
Attribute5
Image Classification5
Retrieval5
Zero-Shot Learning5
valid5
Classification4
Data Augmentation4
Denoising4
GPU4
Image Enhancement4

Usage over time archive 2025-07-28

Papers per year tagged with Affine Coupling: 2014 to 2025, peak 43 43 0 2014: 2 papers 2014 2015: 8 papers 2015 2016: 10 papers 2016 2017: 24 papers 2017 2018: 25 papers 2018 2019: 43 papers 2019 2020: 28 papers 2020 2021: 24 papers 2021 2022: 18 papers 2022 2023: 22 papers 2023 2024: 21 papers 2024 2025: 5 papers 2025
Papers per year the archive tags with this method, by the paper's archive date (230 dated). Bars are counts, not a trend claim.

Components: the archive holds no method-to-method composition, so PwC's Components table cannot be rebuilt; the Papers list carries no Results column for the same reason (the archive does not join its leaderboard rows to method tags).

Categories archive 2025-07-28

Bijective Transformation

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