# Exploring the Precise Dynamics of Single-Layer GAN Models: Leveraging Multi-Feature Discriminators for High-Dimensional Subspace Learning

arXiv: https://arxiv.org/abs/2411.00498 · HTML: https://mlsanity.com/paper/2411.00498/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 22 references that are in the map.
- First posted on arXiv 1 Nov 2024.

## Builds on (most cited first, 11 of 11)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [StyleCLIP: Text-Driven Manipulation of StyleGAN Imagery](https://mlsanity.com/paper/2103.17249/) (2021)
- [Phase diagram of Stochastic Gradient Descent in high-dimensional two-layer neural networks](https://mlsanity.com/paper/2202.00293/) (2022)
- [From high-dimensional & mean-field dynamics to dimensionless ODEs: A unifying approach to SGD in two-layers networks](https://mlsanity.com/paper/2302.05882/) (2023)
- [On Finding Local Nash Equilibria (and Only Local Nash Equilibria) in Zero-Sum Games](https://mlsanity.com/paper/1901.00838/) (2019)
- [The dynamics of representation learning in shallow, non-linear autoencoders](https://mlsanity.com/paper/2201.02115/) (2022)
- [Streaming PCA and Subspace Tracking: The Missing Data Case](https://mlsanity.com/paper/1806.04609/) (2018)
- [A Solvable High-Dimensional Model of GAN](https://mlsanity.com/paper/1805.08349/) (2018)
- [Learning Dynamics in Linear VAE: Posterior Collapse Threshold, Superfluous Latent Space Pitfalls, and Speedup with KL Annealing](https://mlsanity.com/paper/2310.15440/) (2023)
- [Subspace Estimation from Incomplete Observations: A High-Dimensional Analysis](https://mlsanity.com/paper/1805.06834/) (2018)

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

- [Implicitly Normalized Online PCA: A Regularized Algorithm with Exact High-Dimensional Dynamics](https://mlsanity.com/paper/2512.01231/) (2025)
- [Effective Covariance Dynamics in Solvable High-Dimensional GANs](https://mlsanity.com/paper/2606.27246/) (2026)

## Abstract (arXiv)

Subspace learning is a critical endeavor in contemporary machine learning, particularly given the vast dimensions of modern datasets. In this study, we delve into the training dynamics of a single-layer GAN model from the perspective of subspace learning, framing these GANs as a novel approach to this fundamental task. Through a rigorous scaling limit analysis, we offer insights into the behavior of this model. Extending beyond prior research that primarily focused on sequential feature learning, we investigate the non-sequential scenario, emphasizing the pivotal role of inter-feature interactions in expediting training and enhancing performance, particularly with an uninformed initialization strategy. Our investigation encompasses both synthetic and real-world datasets, such as MNIST and Olivetti Faces, demonstrating the robustness and applicability of our findings to practical scenarios. By bridging our analysis to the realm of subspace learning, we systematically compare the efficacy of GAN-based methods against conventional approaches, both theoretically and empirically. Notably, our results unveil that while all methodologies successfully capture the underlying subspace, GANs exhibit a remarkable capability to acquire a more informative basis, owing to their intrinsic ability to generate new data samples. This elucidates the unique advantage of GAN-based approaches in subspace learning tasks.