# BourGAN: Generative Networks with Metric Embeddings

arXiv: https://arxiv.org/abs/1805.07674 · HTML: https://mlsanity.com/paper/1805.07674/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2018.

## Built on by (most cited first, 22 of 22)

- [A Fast Optimization View: Reformulating Single Layer Attention in LLM Based on Tensor and SVM Trick, and Solving It in Matrix Multiplication Time](https://mlsanity.com/paper/2309.07418/) (2023)
- [Sketching for First Order Method: Efficient Algorithm for Low-Bandwidth Channel and Vulnerability](https://mlsanity.com/paper/2210.08371/) (2022)
- [Complexity Matters: Rethinking the Latent Space for Generative Modeling](https://mlsanity.com/paper/2307.08283/) (2023)
- [Dynamic Tensor Product Regression](https://mlsanity.com/paper/2210.03961/) (2022)
- [Efficient SGD Neural Network Training via Sublinear Activated Neuron Identification](https://mlsanity.com/paper/2307.06565/) (2023)
- [Partition-Guided GANs](https://mlsanity.com/paper/2104.00816/) (2021)
- [Self-Supervised GANs with Label Augmentation](https://mlsanity.com/paper/2106.08601/) (2021)
- [Federated Empirical Risk Minimization via Second-Order Method](https://mlsanity.com/paper/2305.17482/) (2023)
- [Is Solving Graph Neural Tangent Kernel Equivalent to Training Graph Neural Network?](https://mlsanity.com/paper/2309.07452/) (2023)
- [Generative Trees: Adversarial and Copycat](https://mlsanity.com/paper/2201.11205/) (2022)
- [DigGAN: Discriminator gradIent Gap Regularization for GAN Training with Limited Data](https://mlsanity.com/paper/2211.14694/) (2022)
- [Fast John Ellipsoid Computation with Differential Privacy Optimization](https://mlsanity.com/paper/2408.06395/) (2024)
- [Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution](https://mlsanity.com/paper/2307.16422/) (2023)
- [Quantum latent distributions in deep generative models](https://mlsanity.com/paper/2508.19857/) (2025)
- [Fast Graph Neural Tangent Kernel via Kronecker Sketching](https://mlsanity.com/paper/2112.02446/) (2021)
- [Manifold embedding data-driven mechanics](https://mlsanity.com/paper/2112.09842/) (2021)
- [Robust training of implicit generative models for multivariate and heavy-tailed distributions with an invariant statistical loss](https://mlsanity.com/paper/2410.22381/) (2024)
- [StegOT: Trade-offs in Steganography via Optimal Transport](https://mlsanity.com/paper/2509.11178/) (2025)
- [Alleviating Mode Collapse in GAN via Diversity Penalty Module](https://mlsanity.com/paper/2108.02353/) (2021)
- [Online Adaptive Mahalanobis Distance Estimation](https://mlsanity.com/paper/2309.01030/) (2023)
- [Fast Heavy Inner Product Identification Between Weights and Inputs in Neural Network Training](https://mlsanity.com/paper/2311.11429/) (2023)
- [Backdoor Attack with Mode Mixture Latent Modification](https://mlsanity.com/paper/2403.07463/) (2024)

## Abstract (arXiv)

This paper addresses the mode collapse for generative adversarial networks (GANs). We view modes as a geometric structure of data distribution in a metric space. Under this geometric lens, we embed subsamples of the dataset from an arbitrary metric space into the l2 space, while preserving their pairwise distance distribution. Not only does this metric embedding determine the dimensionality of the latent space automatically, it also enables us to construct a mixture of Gaussians to draw latent space random vectors. We use the Gaussian mixture model in tandem with a simple augmentation of the objective function to train GANs. Every major step of our method is supported by theoretical analysis, and our experiments on real and synthetic data confirm that the generator is able to produce samples spreading over most of the modes while avoiding unwanted samples, outperforming several recent GAN variants on a number of metrics and offering new features.