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.

翻译：流动的正常化利用变数公式的变化来定义灵活的密度模型。然而,对变数公式的平稳转换要求对构建这些模型提出了重大挑战。为了扩大流量的设计空间,我们引入了美元=mathcal{L}$-difforticisms,作为可能违反零 Lebesgue-度量组要求的普遍转换。这种放松允许使用非移动的激活功能,例如ReLU。 最后,我们将所获得的结果应用于平流、半径和紧凑剩余流。