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arXiv · 2107.04346

Generalization of the Change of Variables Formula with Applications to Residual Flows

Niklas Koenen·Marvin N. Wright·Peter Maaß·Jens Behrmann
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Abstract

Normalizing flows leverage the Change of Variables Formula (CVF) to define flexible density models. Yet, the requirement of smooth transformations (diffeomorphisms) in the CVF poses a significant challenge in the construction of these models. To enlarge the design space of flows, we introduce $\mathcal{L}$-diffeomorphisms as generalized transformations which may violate these requirements on zero Lebesgue-measure sets. This relaxation allows e.g. the use of non-smooth activation functions such as ReLU. Finally, we apply the obtained results to planar, radial, and contractive residual flows.

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Niklas Koenen, Marvin N. Wright, Peter Maaß, Jens Behrmann. 2021-07-09. Generalization of the Change of Variables Formula with Applications to Residual Flows. https://arxiv.org/abs/2107.04346

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