We define a class of divergences to measure differences between probability
density functions in one-dimensional sample space. The construction is based on
the convex function with the Jacobi operator of mapping function that
pushforwards one density to the other. We call these information measures
transport f-divergences. We present several properties of transport
$f$-divergences, including invariances, convexities, variational formulations,
and Taylor expansions in terms of mapping functions. Examples of transport
f-divergences in generative models are provided.

Cet article explore les excursions dans le temps et leurs implications.

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