# Single-level Adversarial Data Synthesis based on Neural Tangent Kernels

arXiv: https://arxiv.org/abs/2204.04090 · HTML: https://mlsanity.com/paper/2204.04090/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 60 of its 80 references that are in the map.
- First posted on arXiv 8 Apr 2022.

## Builds on (most cited first, 30 of 60)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [High-Resolution Image Synthesis and Semantic Manipulation with Conditional GANs](https://mlsanity.com/paper/1711.11585/) (2017)
- [Least Squares Generative Adversarial Networks](https://mlsanity.com/paper/1611.04076/) (2016)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Generating Videos with Scene Dynamics](https://mlsanity.com/paper/1609.02612/) (2016)
- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [NIPS 2016 Tutorial: Generative Adversarial Networks](https://mlsanity.com/paper/1701.00160/) (2016)
- [Are GANs Created Equal? A Large-Scale Study](https://mlsanity.com/paper/1711.10337/) (2017)
- [Improving Unsupervised Defect Segmentation by Applying Structural Similarity to Autoencoders](https://mlsanity.com/paper/1807.02011/) (2018)
- [Exponential expressivity in deep neural networks through transient chaos](https://mlsanity.com/paper/1606.05340/) (2016)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)

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

- [Differentially Private Neural Tangent Kernels for Privacy-Preserving Data Generation](https://mlsanity.com/paper/2303.01687/) (2023)
- [Data Interpolants -- That's What Discriminators in Higher-order Gradient-regularized GANs Are](https://mlsanity.com/paper/2306.00785/) (2023)

## Abstract (arXiv)

Abstract Generative adversarial networks (GANs) have achieved impressive performance in data synthesis and have driven the development of many applications. However, GANs are known to be hard to train due to their bilevel objective, which leads to the problems of convergence, mode collapse, and gradient vanishing. In this paper, we propose a new generative model called the generative adversarial NTK (GA-NTK) that has a single-level objective. The GA-NTK keeps the spirit of adversarial learning (which helps generate plausible data) while avoiding the training difficulties of GANs. This is done by modeling the discriminator as a Gaussian process with a neural tangent kernel (NTK-GP) whose training dynamics can be completely described by a closed-form formula. We analyze the convergence behavior of GA-NTK trained by gradient descent and give some sufficient conditions for convergence. We also conduct extensive experiments to study the advantages and limitations of GA-NTK and propose some techniques that make GA-NTK more practical.