# Loss-Sensitive Generative Adversarial Networks on Lipschitz Densities

arXiv: https://arxiv.org/abs/1701.06264 · HTML: https://mlsanity.com/paper/1701.06264/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2017.

## Built on by (most cited first, 29 of 29)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
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- [MutexMatch: Semi-Supervised Learning with Mutex-Based Consistency Regularization](https://mlsanity.com/paper/2203.14316/) (2022)
- [A survey on GANs for computer vision: Recent research, analysis and taxonomy](https://mlsanity.com/paper/2203.11242/) (2022)
- [A Latent Encoder Coupled Generative Adversarial Network (LE-GAN) for Efficient Hyperspectral Image Super-resolution](https://mlsanity.com/paper/2111.08685/) (2021)
- [Generative Adversarial Networks for Image Super-Resolution: A Survey](https://mlsanity.com/paper/2204.13620/) (2022)
- [Training Federated GANs with Theoretical Guarantees: A Universal Aggregation Approach](https://mlsanity.com/paper/2102.04655/) (2021)
- [DuelGAN: A Duel Between Two Discriminators Stabilizes the GAN Training](https://mlsanity.com/paper/2101.07524/) (2021)
- [Imitation from Diverse Behaviors: Wasserstein Quality Diversity Imitation Learning with Single-Step Archive Exploration](https://mlsanity.com/paper/2411.06965/) (2024)
- [Diamond in the rough: Improving image realism by traversing the GAN latent space](https://mlsanity.com/paper/2104.05518/) (2021)
- [MDA GAN: Adversarial-Learning-based 3-D Seismic Data Interpolation and Reconstruction for Complex Missing](https://mlsanity.com/paper/2204.03197/) (2022)
- [Generalization of GANs and overparameterized models under Lipschitz continuity](https://mlsanity.com/paper/2104.02388/) (2021)
- [On the Benefits of Inducing Local Lipschitzness for Robust Generative Adversarial Imitation Learning](https://mlsanity.com/paper/2107.00116/) (2021)
- [Single-level Adversarial Data Synthesis based on Neural Tangent Kernels](https://mlsanity.com/paper/2204.04090/) (2022)
- [Predictions Based on Pixel Data: Insights from PDEs and Finite Differences](https://mlsanity.com/paper/2305.00723/) (2023)
- [UniTTS: An end-to-end TTS system without decoupling of acoustic and semantic information](https://mlsanity.com/paper/2505.17426/) (2025)
- [Signature-Graph Networks](https://mlsanity.com/paper/2110.11551/) (2021)
- [GCCN: Global Context Convolutional Network](https://mlsanity.com/paper/2110.11664/) (2021)
- [UTSGAN: Unseen Transition Suss GAN for Transition-Aware Image-to-image Translation](https://mlsanity.com/paper/2304.11955/) (2023)
- [Unsupervised Adaptive Semantic Segmentation with Local Lipschitz Constraint](https://mlsanity.com/paper/2105.12939/) (2021)
- [Prb-GAN: A Probabilistic Framework for GAN Modelling](https://mlsanity.com/paper/2107.05241/) (2021)
- [Physical Context and Timing Aware Sequence Generating GANs](https://mlsanity.com/paper/2110.04077/) (2021)
- [Conditional Generative Data-free Knowledge Distillation](https://mlsanity.com/paper/2112.15358/) (2021)
- [QS-Craft: Learning to Quantize, Scrabble and Craft for Conditional Human Motion Animation](https://mlsanity.com/paper/2203.11632/) (2022)
- [Accelerated Neural Network Training with Rooted Logistic Objectives](https://mlsanity.com/paper/2310.03890/) (2023)

## Abstract (arXiv)

In this paper, we present the Lipschitz regularization theory and algorithms for a novel Loss-Sensitive Generative Adversarial Network (LS-GAN). Specifically, it trains a loss function to distinguish between real and fake samples by designated margins, while learning a generator alternately to produce realistic samples by minimizing their losses. The LS-GAN further regularizes its loss function with a Lipschitz regularity condition on the density of real data, yielding a regularized model that can better generalize to produce new data from a reasonable number of training examples than the classic GAN. We will further present a Generalized LS-GAN (GLS-GAN) and show it contains a large family of regularized GAN models, including both LS-GAN and Wasserstein GAN, as its special cases. Compared with the other GAN models, we will conduct experiments to show both LS-GAN and GLS-GAN exhibit competitive ability in generating new images in terms of the Minimum Reconstruction Error (MRE) assessed on a separate test set. We further extend the LS-GAN to a conditional form for supervised and semi-supervised learning problems, and demonstrate its outstanding performance on image classification tasks.