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l-diffeomorphism

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

Koenen, Niklas, Wright, Marvin N., Maaß, Peter, Behrmann, Jens

arXiv.org Machine LearningJul-9-2021

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.

critical point, generalization, l-diffeomorphism, (14 more...)

arXiv.org Machine Learning

2107.04346

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Technology: Information Technology > Artificial Intelligence > Machine Learning > Neural Networks (0.49)

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