Solving ODE with Universal Flows: Approximation Theory for Flow-Based Models
Normalizing flows are powerful invertible probabilistic models that can be used to translate two probability distributions, in a way that allows us to efficiently track the change of probability density. However, to trade for computational efficiency in sampling and in evaluating the log-density, special parameterization designs have been proposed at the cost of representational expressiveness. In this work, we propose to use ODEs as a framework to establish universal approximation theory for certain families of flow-based models.
Code (0)
등록된 구현이 없습니다.
Tasks
Computational EfficiencySimilar Papers 제목 키워드 기반
Universal Joint Approximation of Manifolds and Densities by Simple Injective Flows
We study approximation of probability measures supported on $n$-dimensional manifolds embedded in $\mathbb{R}^m$ by injective flows -- neural networks composed of invertible flows and injective layers. We show that in ge…
Universal Approximation of Residual Flows in Maximum Mean Discrepancy
Normalizing flows are a class of flexible deep generative models that offer easy likelihood computation. Despite their empirical success, there is little theoretical understanding of their expressiveness. In this work, w…
Universality of parametric Coupling Flows over parametric diffeomorphisms
Invertible neural networks based on Coupling Flows CFlows) have various applications such as image synthesis and data compression. The approximation universality for CFlows is of paramount importance to ensure the model …
Bayesian OptimizationData CompressionImage GenerationConvex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimization
Flow-based models are powerful tools for designing probabilistic models with tractable density. This paper introduces Convex Potential Flows (CP-Flow), a natural and efficient parameterization of invertible models inspir…
Density EstimationVariational InferenceNeural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations
We introduce an abstract neural flow framework for neural networks and neural operators. The framework contains two continuous-depth models, namely neural flows with composition and separation structures, and covers both…