More Like this

1. Metastability of Kolmogorov Flows and Inviscid Damping of Shear Flows

   https://doi.org/10.1007/s00205-018-1311-8  

   Lin, Zhiwu; Xu, Ming (March 2019, Archive for Rational Mechanics and Analysis)
2. Semi-Autoregressive Energy Flows: Exploring Likelihood-Free Training of Normalizing Flows

   Si, Phillip; Chen, Zeyi; Sahoo, Subham; Schiff, Yair; Kuleshov, Volodymyr (July 2023, International Conference on Machine Learning)
3. Toda Flows, Gradient Flows, and Total Positivity

   Anthony M. Bloch and Steven N. Karp (January 2022, Proceedings NOLTA 2022)

   We outline various connections between the Toda flows, gradient flows, and the theory of total positivity. 1. 

   more » « less
4. VQ-Flows: Vector Quantized Local Normalizing Flows

   Sidheekh, Sahil; Dock, Chris B.; Jain, Tushar; Balan, Radu; Singh, Maneesh K. (August 2022, Uncertainty in artificial intelligence)

   Normalizing flows provide an elegant approach to generative modeling that allows for efficient sampling and exact density evaluation of unknown data distributions. However, current techniques have significant limitations in their expressivity when the data distribution is supported on a lowdimensional manifold or has a non-trivial topology. We introduce a novel statistical framework for learning a mixture of local normalizing flows as “chart maps” over the data manifold. Our framework augments the expressivity of recent approaches while preserving the signature property of normalizing flows, that they admit exact density evaluation. We learn a suitable atlas of charts for the data manifold via a vector quantized autoencoder (VQ-AE) and the distributions over them using a conditional flow. We validate experimentally that our probabilistic framework enables existing approaches to better model data distributions over complex manifolds. 

   more » « less
5. Gaussianization Flows

   Meng, Chenlin; Song, Yang; Song, Jiaming; Ermon, Stefano (July 2020, International Conference on Artificial Intelligence and Statistics)