CF-GO-Net: A Universal Distribution Learner via Characteristic Function Networks with Graph Optimizers
Zeyang Yu, Shengxi Li, Danilo Mandic
TL;DR
This work tackles the challenge of distribution learning by moving beyond pdf-based divergences to a characteristic-function (CF) distance between distributions, operationalized via the Empirical Characteristic Function (ECF). It defines a CF loss $\, ext{C}_{\mathcal{T}}$ that can be decomposed into amplitude and phase terms, and uses a Graph Neural Network (GNN) as a worst-case sampler to dynamically identify CF-discrepant regions in the sampling domain $F_{\,\mathcal{T}}(\mathbf{t})$. A key feature is the ability to leverage pre-trained, non-generative models by training only the generator in their latent spaces, enabling conversion of models like autoencoders into generative ones. Empirical validation on CelebA autoencoder feature spaces shows the CF-GO-Net approach achieves higher fidelity and diversity than Gaussian sampling or fully-connected optimizers, illustrating scalable, flexible distribution matching with broad applicability to high-dimensional latent spaces.
Abstract
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.