# CF-GO-Net: A Universal Distribution Learner via Characteristic Function Networks with Graph Optimizers

arXiv: https://arxiv.org/abs/2409.12610 · HTML: https://mlsanity.com/paper/2409.12610/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 16 references that are in the map.
- First posted on arXiv 19 Sep 2024.

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

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [A Characteristic Function Approach to Deep Implicit Generative Modeling](https://mlsanity.com/paper/1909.07425/) (2019)
- [Fisher GAN](https://mlsanity.com/paper/1705.09675/) (2017)
- [Graph Signal Processing -- Part I: Graphs, Graph Spectra, and Spectral Clustering](https://mlsanity.com/paper/1907.03467/) (2019)
- [Graph Signal Processing -- Part III: Machine Learning on Graphs, from Graph Topology to Applications](https://mlsanity.com/paper/2001.00426/) (2020)
- [Widely Linear Complex-valued Autoencoder: Dealing with Noncircularity in Generative-Discriminative Models](https://mlsanity.com/paper/1903.02014/) (2019)

## Built on by (most cited first, 1 of 1)

- [DeepL'evy: Learning Heavy-Tailed Uncertainty in Highly Volatile Time Series](https://mlsanity.com/paper/2605.10364/) (2026)

## Abstract (arXiv)

Generative models aim to learn the distribution of datasets, such as images, so as to be able to generate samples that statistically resemble real data. However, learning the underlying probability distribution can be very challenging and intractable. To this end, we introduce an approach which employs the characteristic function (CF), a probabilistic descriptor that directly corresponds to the distribution. However, unlike the probability density function (pdf), the characteristic function not only always exists, but also provides an additional degree of freedom, hence enhances flexibility in learning distributions. This removes the critical dependence on pdf-based assumptions, which limit the applicability of traditional methods. While several works have attempted to use CF in generative modeling, they often impose strong constraints on the training process. In contrast, our approach calculates the distance between query points in the CF domain, which is an unconstrained and well defined problem. Next, to deal with the sampling strategy, which is crucial to model performance, we propose a graph neural network (GNN)-based optimizer for the sampling process, which identifies regions where the difference between CFs is most significant. In addition, our method allows the use of a pre-trained model, such as a well-trained autoencoder, and is capable of learning directly in its feature space, without modifying its parameters. This offers a flexible and robust approach to generative modeling, not only provides broader applicability and improved performance, but also equips any latent space world with the ability to become a generative model.