# Generative neural networks for characteristic functions

arXiv: https://arxiv.org/abs/2401.04778 · HTML: https://mlsanity.com/paper/2401.04778/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 41 references that are in the map.
- First posted on arXiv 9 Jan 2024.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Statistical Inference for Generative Models with Maximum Mean Discrepancy](https://mlsanity.com/paper/1906.05944/) (2019)
- [On the ability of neural nets to express distributions](https://mlsanity.com/paper/1702.07028/) (2017)
- [A Characteristic Function Approach to Deep Implicit Generative Modeling](https://mlsanity.com/paper/1909.07425/) (2019)
- [On the capacity of deep generative networks for approximating distributions](https://mlsanity.com/paper/2101.12353/) (2021)
- [Controlling Wasserstein Distances by Kernel Norms with Application to Compressive Statistical Learning](https://mlsanity.com/paper/2112.00423/) (2021)
- [Size-Noise Tradeoffs in Generative Networks](https://mlsanity.com/paper/1810.11158/) (2018)
- [Reciprocal Adversarial Learning via Characteristic Functions](https://mlsanity.com/paper/2006.08413/) (2020)
- [Exact simulation of continuous max-id processes with applications to exchangeable max-id sequences](https://mlsanity.com/paper/2107.04630/) (2021)

## Built on by (most cited first, 3 of 3)

- [FAST: Topology-Aware Frequency-Domain Distribution Matching for Coreset Selection](https://mlsanity.com/paper/2511.19476/) (2025)
- [Cloud Model Characteristic Function Auto-Encoder: Integrating Cloud Model Theory with MMD Regularization for Enhanced Generative Modeling](https://mlsanity.com/paper/2508.04447/) (2025)
- [DeepL'evy: Learning Heavy-Tailed Uncertainty in Highly Volatile Time Series](https://mlsanity.com/paper/2605.10364/) (2026)

## Abstract (arXiv)

We provide a simulation algorithm to simulate from a (multivariate) characteristic function, which is only accessible in a black-box format. The method is based on a generative neural network, whose loss function exploits a specific representation of the Maximum-Mean-Discrepancy metric to directly incorporate the targeted characteristic function. The algorithm is universal in the sense that it is independent of the dimension and that it does not require any assumptions on the given characteristic function. Furthermore, finite sample guarantees on the approximation quality in terms of the Maximum-Mean Discrepancy metric are derived. The method is illustrated in a simulation study.