# Reciprocal Adversarial Learning via Characteristic Functions

arXiv: https://arxiv.org/abs/2006.08413 · HTML: https://mlsanity.com/paper/2006.08413/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 7 of 7)

- [Dataset Distillation with Neural Characteristic Function: A Minmax Perspective](https://mlsanity.com/paper/2502.20653/) (2025)
- [PEARL: Data Synthesis via Private Embeddings and Adversarial Reconstruction Learning](https://mlsanity.com/paper/2106.04590/) (2021)
- [PCF-GAN: generating sequential data via the characteristic function of measures on the path space](https://mlsanity.com/paper/2305.12511/) (2023)
- [Generative Modelling of L'evy Area for High Order SDE Simulation](https://mlsanity.com/paper/2308.02452/) (2023)
- [Generative neural networks for characteristic functions](https://mlsanity.com/paper/2401.04778/) (2024)
- [Learning Adaptive Distribution Alignment with Neural Characteristic Function for Graph Domain Adaptation](https://mlsanity.com/paper/2602.10489/) (2026)
- [Towards Principled Dataset Distillation: A Spectral Distribution Perspective](https://mlsanity.com/paper/2603.01698/) (2026)

## Abstract (arXiv)

Generative adversarial nets (GANs) have become a preferred tool for tasks involving complicated distributions. To stabilise the training and reduce the mode collapse of GANs, one of their main variants employs the integral probability metric (IPM) as the loss function. This provides extensive IPM-GANs with theoretical support for basically comparing moments in an embedded domain of the textitcritic. We generalise this by comparing the distributions rather than their moments via a powerful tool, i.e., the characteristic function (CF), which uniquely and universally comprising all the information about a distribution. For rigour, we first establish the physical meaning of the phase and amplitude in CF, and show that this provides a feasible way of balancing the accuracy and diversity of generation. We then develop an efficient sampling strategy to calculate the CFs. Within this framework, we further prove an equivalence between the embedded and data domains when a reciprocal exists, where we naturally develop the GAN in an auto-encoder structure, in a way of comparing everything in the embedded space (a semantically meaningful manifold). This efficient structure uses only two modules, together with a simple training strategy, to achieve bi-directionally generating clear images, which is referred to as the reciprocal CF GAN (RCF-GAN). Experimental results demonstrate the superior performances of the proposed RCF-GAN in terms of both generation and reconstruction.