# Quantifying Manifolds: Do the manifolds learned by Generative Adversarial Networks converge to the real data manifold

arXiv: https://arxiv.org/abs/2403.05033 · HTML: https://mlsanity.com/paper/2403.05033/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 11 references that are in the map.
- First posted on arXiv 8 Mar 2024.

## Builds on (most cited first, 4 of 4)

- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [DADApy: Distance-based Analysis of DAta-manifolds in Python](https://mlsanity.com/paper/2205.03373/) (2022)
- [Topology and geometry of data manifold in deep learning](https://mlsanity.com/paper/2204.08624/) (2022)
- [Deep neural networks architectures from the perspective of manifold learning](https://mlsanity.com/paper/2306.03406/) (2023)

## Abstract (arXiv)

This paper presents our experiments to quantify the manifolds learned by ML models (in our experiment, we use a GAN model) as they train. We compare the manifolds learned at each epoch to the real manifolds representing the real data. To quantify a manifold, we study the intrinsic dimensions and topological features of the manifold learned by the ML model, how these metrics change as we continue to train the model, and whether these metrics convergence over the course of training to the metrics of the real data manifold.