March 30, 2024Open Access

Convergence of Continuous Normalizing Flows for Learning Probability Distributions

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Authors

YGYuan GaoBeijing University of Posts and Telecommunications JHJian HuangShandong University of Traditional Chinese Medicine YJYuling JiaoWuhan University

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Implication

Theoretical analysis reveals non-asymptotic error bounds for continuous normalizing flows, highlighting formal guarantees for generative models trained on finite samples.

Key Points

Continuous normalizing flows achieve non-asymptotic error bounds under the Wasserstein-2 distance when learning probability distributions with bounded support or log-concavity.
Theoretical model establishes velocity field regularity with linear interpolation and derives uniform error bounds for deep ReLU networks approximating Lipschitz functions.
Convergence analysis offers theoretical guarantees for generative modeling from finite random samples, addressing early stopping and velocity discretization errors.

Cite This Study

Gao et al. (2024) studied this question.

synapsesocial.com/papers/68e71abfb6db64358769493e https://doi.org/10.48550/arxiv.2404.00551

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Implication

Theoretical analysis reveals non-asymptotic error bounds for continuous normalizing flows, highlighting formal guarantees for generative models trained on finite samples.

Convergence of Continuous Normalizing Flows for Learning Probability Distributions

Discussion

Member takes

Implication

Key Points

Cite This Study

Convergence of Continuous Normalizing Flows for Learning Probability Distributions

Discussion

Member takes

Implication

Key Points

Cite This Study

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