mlsanityData to 7 Oct 2026

ELF: Exact-Lipschitz Based Universal Density Approximator Flow

arXiv 2112.06997 ↗First posted 13 Dec 2021cs.LG stat.MLcited by 1

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Abstract (arXiv)

Normalizing flows have grown more popular over the last few years; however, they continue to be computationally expensive, making them difficult to be accepted into the broader machine learning community. In this paper, we introduce a simple one-dimensional one-layer network that has closed form Lipschitz constants; using this, we introduce a new Exact-Lipschitz Flow (ELF) that combines the ease of sampling from residual flows with the strong performance of autoregressive flows. Further, we show that ELF is provably a universal density approximator, more computationally and parameter efficient compared to a multitude of other flows, and achieves state-of-the-art performance on multiple large-scale datasets.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 39 of its 51 references that are in the map. First posted on arXiv 13 Dec 2021.

Builds on

39 of 51 references.

References · 39

  1. 2017Attention Is All You Needcited by 59,932
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2013Intriguing properties of neural networkscited by 5,114
  4. 2018Neural Ordinary Differential Equationscited by 3,733
  5. 2017Improved Training of Wasserstein GANscited by 2,223
  6. 2015Variational Inference with Normalizing Flowscited by 2,161
  7. 2016Density estimation using Real NVPcited by 2,029
  8. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,618
  9. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
  10. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,061
  11. 2014NICE: Non-linear Independent Components Estimationcited by 1,052
  12. 2016HyperNetworkscited by 1,003
27 more
  1. 2016Pixel Recurrent Neural Networkscited by 814
  2. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  3. 2016Improving Variational Inference with Inverse Autoregressive Flowcited by 636
  4. 2019Neural Spline Flowscited by 590
  5. 2017PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modificationscited by 415
  6. 2018Lipschitz regularity of deep neural networks: analysis and efficient estimationcited by 413
  7. 2017A Downsampled Variant of ImageNet as an Alternative to the CIFAR datasetscited by 374
  8. 2018Invertible Residual Networkscited by 364
  9. 2015MADE: Masked Autoencoder for Distribution Estimationcited by 306
  10. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 290
  11. 2019Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Designcited by 258
  12. 2019Residual Flows for Invertible Generative Modelingcited by 256
  13. 2018Sorting out Lipschitz function approximationcited by 211
  14. 2018Neural Autoregressive Flowscited by 207
  15. 2020Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimizationcited by 89
  16. 2020Coupling-based Invertible Neural Networks Are Universal Diffeomorphism Approximatorscited by 85
  17. 2018Sylvester Normalizing Flows for Variational Inferencecited by 71
  18. 2020Augmented Normalizing Flows: Bridging the Gap Between Generative Flows and Latent Variable Modelscited by 66
  19. 2019Block Neural Autoregressive Flowcited by 62
  20. 2019Sum-of-Squares Polynomial Flowcited by 62
  21. 2020Accelerating Feedforward Computation via Parallel Nonlinear Equation Solvingcited by 51
  22. 2018Limitations of the Lipschitz constant as a defense against adversarial examplescited by 48
  23. 2020VFlow: More Expressive Generative Flows with Variational Data Augmentationcited by 38
  24. 2020The Expressive Power of a Class of Normalizing Flow Modelscited by 35
  25. 2019MaCow: Masked Convolutional Generative Flowcited by 32
  26. 2018Transformation Autoregressive Networkscited by 27
  27. 2020Predictive Sampling with Forecasting Autoregressive Modelscited by 10

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