# Leverage Score Sampling for Complete Mode Coverage in Generative Adversarial Networks

arXiv: https://arxiv.org/abs/2104.02373 · HTML: https://mlsanity.com/paper/2104.02373/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 28 references that are in the map.
- First posted on arXiv 6 Apr 2021.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Differentiable Augmentation for Data-Efficient GAN Training](https://mlsanity.com/paper/2006.10738/) (2020)
- [Unrolled Generative Adversarial Networks](https://mlsanity.com/paper/1611.02163/) (2016)
- [Sample-Efficient Optimization in the Latent Space of Deep Generative Models via Weighted Retraining](https://mlsanity.com/paper/2006.09191/) (2020)
- [PacGAN: The power of two samples in generative adversarial networks](https://mlsanity.com/paper/1712.04086/) (2017)
- [Inclusive GAN: Improving Data and Minority Coverage in Generative Models](https://mlsanity.com/paper/2004.03355/) (2020)
- [On Fast Leverage Score Sampling and Optimal Learning](https://mlsanity.com/paper/1810.13258/) (2018)
- [Small-GAN: Speeding Up GAN Training Using Core-sets](https://mlsanity.com/paper/1910.13540/) (2019)
- [A Statistical Perspective on Algorithmic Leveraging](https://mlsanity.com/paper/1306.5362/) (2013)
- [Adaptive Sampling for Stochastic Risk-Averse Learning](https://mlsanity.com/paper/1910.12511/) (2019)
- [AdaGAN: Boosting Generative Models](https://mlsanity.com/paper/1701.02386/) (2017)
- [Deep Fried Convnets](https://mlsanity.com/paper/1412.7149/) (2014)
- [Active Mini-Batch Sampling using Repulsive Point Processes](https://mlsanity.com/paper/1804.02772/) (2018)
- [Determinantal Point Processes for Mini-Batch Diversification](https://mlsanity.com/paper/1705.00607/) (2017)
- [Isometric sketching of any set via the Restricted Isometry Property](https://mlsanity.com/paper/1506.03521/) (2015)
- [Importance Weighted Generative Networks](https://mlsanity.com/paper/1806.02512/) (2018)
- [Rethinking Generative Mode Coverage: A Pointwise Guaranteed Approach](https://mlsanity.com/paper/1902.04697/) (2019)

## Built on by (most cited first, 2 of 2)

- [Enhanced Low-Density Region Exploration in Classifier-Guided Diffusion Models Through Modified Reverse Diffusion Sampling](https://mlsanity.com/paper/2606.13347/) (2026)
- [Deep Adaptive Bayesian Screening](https://mlsanity.com/paper/2607.16927/) (2026)

## Abstract (arXiv)

Commonly, machine learning models minimize an empirical expectation. As a result, the trained models typically perform well for the majority of the data but the performance may deteriorate in less dense regions of the dataset. This issue also arises in generative modeling. A generative model may overlook underrepresented modes that are less frequent in the empirical data distribution. This problem is known as complete mode coverage. We propose a sampling procedure based on ridge leverage scores which significantly improves mode coverage when compared to standard methods and can easily be combined with any GAN. Ridge leverage scores are computed by using an explicit feature map, associated with the next-to-last layer of a GAN discriminator or of a pre-trained network, or by using an implicit feature map corresponding to a Gaussian kernel. Multiple evaluations against recent approaches of complete mode coverage show a clear improvement when using the proposed sampling strategy.