RealNVP Triangular Density Coupling
An invertible triangular warp makes a flexible density while keeping its inverse and volume correction explicit.
Free theory articleAn invertible triangular warp makes a flexible density while keeping its inverse and volume correction explicit.
Concept & interpretation
In RealNVP, an affine coupling layer partitions dimensions to keep the Jacobian determinant triangular, ensuring fast, analytical inversion and exact density evaluation while allowing expressive scale and shift warps driven by arbitrary neural functions.
Experiment
In the interactive module, you can alter the observed values for x_1 and x_2 as well as the geometric warp parameters s and t. The interactive view visualizes how a regular grid in the latent standard normal space transforms into the warped grid of the observed space.
- Select Observed x1 and Observed x2 to set the target point.
- Modify the Scale slope and Shift slope controls to see how shear (s=0, t ≠ 0) preserves density volume (0 log-determinant) but warps geometry, whereas a non-zero Scale slope fundamentally stretches or squashes the area element.
- Observe the recomputed Observed density and Latent coordinates in the results pane.