# GeomCA: Geometric Evaluation of Data Representations

arXiv: https://arxiv.org/abs/2105.12486 · HTML: https://mlsanity.com/paper/2105.12486/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 26 May 2021.

## Builds on (most cited first, 18 of 18)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [CURL: Contrastive Unsupervised Representations for Reinforcement Learning](https://mlsanity.com/paper/2004.04136/) (2020)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Keystroke Dynamics as Part of Lifelogging](https://mlsanity.com/paper/2010.10144/) (2020)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [Geometry Score: A Method For Comparing Generative Adversarial Networks](https://mlsanity.com/paper/1802.02664/) (2018)
- [Geometrically Enriched Latent Spaces](https://mlsanity.com/paper/2008.00565/) (2020)
- [Representations for Stable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/2007.05520/) (2020)
- [Disentangling by Subspace Diffusion](https://mlsanity.com/paper/2006.12982/) (2020)
- [Latent Space Roadmap for Visual Action Planning of Deformable and Rigid Object Manipulation](https://mlsanity.com/paper/2003.08974/) (2020)
- [Unsupervised Representation Learning by InvariancePropagation](https://mlsanity.com/paper/2010.11694/) (2020)
- [Data-efficient visuomotor policy training using reinforcement learning and generative models](https://mlsanity.com/paper/2007.13134/) (2020)

## Built on by (most cited first, 9 of 9)

- [Geometric Multimodal Contrastive Representation Learning](https://mlsanity.com/paper/2202.03390/) (2022)
- [Evaluating Latent Space Robustness and Uncertainty of EEG-ML Models under Realistic Distribution Shifts](https://mlsanity.com/paper/2209.11233/) (2022)
- [TopP&R: Robust Support Estimation Approach for Evaluating Fidelity and Diversity in Generative Models](https://mlsanity.com/paper/2306.08013/) (2023)
- [Topological Pooling on Graphs](https://mlsanity.com/paper/2303.14543/) (2023)
- [How to Sense the World: Leveraging Hierarchy in Multimodal Perception for Robust Reinforcement Learning Agents](https://mlsanity.com/paper/2110.03608/) (2021)
- [Delaunay Component Analysis for Evaluation of Data Representations](https://mlsanity.com/paper/2202.06866/) (2022)
- [Hyperbolic Delaunay Geometric Alignment](https://mlsanity.com/paper/2404.08608/) (2024)
- [Training and Evaluation of Deep Policies using Reinforcement Learning and Generative Models](https://mlsanity.com/paper/2204.08573/) (2022)
- [GraphDCA -- a Framework for Node Distribution Comparison in Real and Synthetic Graphs](https://mlsanity.com/paper/2202.03884/) (2022)

## Abstract (arXiv)

Evaluating the quality of learned representations without relying on a downstream task remains one of the challenges in representation learning. In this work, we present Geometric Component Analysis (GeomCA) algorithm that evaluates representation spaces based on their geometric and topological properties. GeomCA can be applied to representations of any dimension, independently of the model that generated them. We demonstrate its applicability by analyzing representations obtained from a variety of scenarios, such as contrastive learning models, generative models and supervised learning models.