# Geometry Score: A Method For Comparing Generative Adversarial Networks

arXiv: https://arxiv.org/abs/1802.02664 · HTML: https://mlsanity.com/paper/1802.02664/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2018.

## Built on by (most cited first, 30 of 57)

- [Similarity of Neural Network Models: A Survey of Functional and Representational Measures](https://mlsanity.com/paper/2305.06329/) (2023)
- [Pros and Cons of GAN Evaluation Measures: New Developments](https://mlsanity.com/paper/2103.09396/) (2021)
- [Universal Neurons in GPT2 Language Models](https://mlsanity.com/paper/2401.12181/) (2024)
- [Representation Topology Divergence: A Method for Comparing Neural Network Representations](https://mlsanity.com/paper/2201.00058/) (2021)
- [Conditional Text Image Generation with Diffusion Models](https://mlsanity.com/paper/2306.10804/) (2023)
- [TextStyleBrush: Transfer of Text Aesthetics from a Single Example](https://mlsanity.com/paper/2106.08385/) (2021)
- [PyTorch Image Quality: Metrics for Image Quality Assessment](https://mlsanity.com/paper/2208.14818/) (2022)
- [Handwritten Text Generation from Visual Archetypes](https://mlsanity.com/paper/2303.15269/) (2023)
- [Manifold Topology Divergence: a Framework for Comparing Data Manifolds](https://mlsanity.com/paper/2106.04024/) (2021)
- [Towards Universality: Studying Mechanistic Similarity Across Language Model Architectures](https://mlsanity.com/paper/2410.06672/) (2024)
- [SLOGAN: Handwriting Style Synthesis for Arbitrary-Length and Out-of-Vocabulary Text](https://mlsanity.com/paper/2202.11456/) (2022)
- [Diffusion models for Handwriting Generation](https://mlsanity.com/paper/2011.06704/) (2020)
- [One-Shot Diffusion Mimicker for Handwritten Text Generation](https://mlsanity.com/paper/2409.04004/) (2024)
- [HWD: A Novel Evaluation Score for Styled Handwritten Text Generation](https://mlsanity.com/paper/2310.20316/) (2023)
- [VATr++: Choose Your Words Wisely for Handwritten Text Generation](https://mlsanity.com/paper/2402.10798/) (2024)
- [TopoDiffusionNet: A Topology-aware Diffusion Model](https://mlsanity.com/paper/2410.16646/) (2024)
- [Beyond Isolated Words: Diffusion Brush for Handwritten Text-Line Generation](https://mlsanity.com/paper/2508.03256/) (2025)
- [GeomCA: Geometric Evaluation of Data Representations](https://mlsanity.com/paper/2105.12486/) (2021)
- [Predicting the generalization gap in neural networks using topological data analysis](https://mlsanity.com/paper/2203.12330/) (2022)
- [Neural Lineage](https://mlsanity.com/paper/2406.11129/) (2024)
- [Freehand Sketch Generation from Mechanical Components](https://mlsanity.com/paper/2408.05966/) (2024)
- [TexTile: A Differentiable Metric for Texture Tileability](https://mlsanity.com/paper/2403.12961/) (2024)
- [Delaunay Component Analysis for Evaluation of Data Representations](https://mlsanity.com/paper/2202.06866/) (2022)
- [Rethinking HTG Evaluation: Bridging Generation and Recognition](https://mlsanity.com/paper/2409.02683/) (2024)
- [Double Descent and Other Interpolation Phenomena in GANs](https://mlsanity.com/paper/2106.04003/) (2021)
- [Log-Euclidean Signatures for Intrinsic Distances Between Unaligned Datasets](https://mlsanity.com/paper/2202.01671/) (2022)
- [A Realism Metric for Generated LiDAR Point Clouds](https://mlsanity.com/paper/2208.14958/) (2022)
- [FONDUE: an algorithm to find the optimal dimensionality of the latent representations of variational autoencoders](https://mlsanity.com/paper/2209.12806/) (2022)
- [Graph-Regularized Manifold-Aware Conditional Wasserstein GAN for Brain Functional Connectivity Generation](https://mlsanity.com/paper/2212.05316/) (2022)
- [Approximating Latent Manifolds in Neural Networks via Vanishing Ideals](https://mlsanity.com/paper/2502.15051/) (2025)

## Abstract (arXiv)

One of the biggest challenges in the research of generative adversarial networks (GANs) is assessing the quality of generated samples and detecting various levels of mode collapse. In this work, we construct a novel measure of performance of a GAN by comparing geometrical properties of the underlying data manifold and the generated one, which provides both qualitative and quantitative means for evaluation. Our algorithm can be applied to datasets of an arbitrary nature and is not limited to visual data. We test the obtained metric on various real-life models and datasets and demonstrate that our method provides new insights into properties of GANs.