Bijective Transformation
Affine Coupling
Introduced by Dinh et al. in NICE: Non-linear Independent Components EstimationAffine 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:
$$ \mathbf{x}_{a}, \mathbf{x}_{b} = \text{split}\left(\mathbf{x}\right) $$
The second part stays the same $\mathbf{x}_{b} = \mathbf{y}_{b}$, while the first part $\mathbf{x}_{a}$ undergoes an affine transformation, where the parameters for this transformation are learnt using the second part $\mathbf{x}_{b}$ being put through a neural network. Together we have:
$$ \left(\log{\mathbf{s}, \mathbf{t}}\right) = \text{NN}\left(\mathbf{x}_{b}\right) $$
$$ \mathbf{s} = \exp\left(\log{\mathbf{s}}\right) $$
$$ \mathbf{y}_{a} = \mathbf{s} \odot \mathbf{x}_{a} + \mathbf{t} $$
$$ \mathbf{y}_{b} = \mathbf{x}_{b} $$
$$ \mathbf{y} = \text{concat}\left(\mathbf{y}_{a}, \mathbf{y}_{b}\right) $$
Image: GLOW
Source: NICE: Non-linear Independent Components Estimation
Papers
| Paper | Code | Results | Date | Stars |
|---|
Tasks
| Task | Papers | Share |
|---|---|---|
| Image Dehazing | 2 | 5.56% |
| Image Enhancement | 2 | 5.56% |
| Anomaly Detection | 2 | 5.56% |
| Image Classification | 2 | 5.56% |
| Speech Synthesis | 2 | 5.56% |
| Image Captioning | 2 | 5.56% |
| Management | 1 | 2.78% |
| Pseudo Label | 1 | 2.78% |
| Sign Language Recognition | 1 | 2.78% |
Usage Over Time
Components
| Component | Type |
|
|---|---|---|
| 🤖 No Components Found | You can add them if they exist; e.g. Mask R-CNN uses RoIAlign |
