Flow-based generative model: Difference between revisions

Revision as of 19:17, 10 June 2025

Revision as of 19:23, 10 June 2025

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To understand the geometric interpretation of the factor <math>\sqrt{n}</math>, see the example for the 1-simplex in the diagram at right.

The differential volume element at the transformation output, (<math>\mathbf q\in\Delta^{n-1}</math>), is contianed in the parallelotope, <math>V=f(U)=/\mathbf{F_pED}\!/</math>, where <math>\mathbf{F_p}</math> is the <math>n\text{-by-}n</math> Jacobian of <math>f</math> at <math>\mathbf p=e(\tilde\mathbf p)</math>. Its volume is:

:<math>

\operatorname{volume}(V) =