# Analytic Manifold Learning: Unifying and Evaluating Representations for Continuous Control

arXiv: https://arxiv.org/abs/2006.08718 · HTML: https://mlsanity.com/paper/2006.08718/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 6 of 6)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Learning to Compute Gr"obner Bases](https://mlsanity.com/paper/2311.12904/) (2023)
- [Border basis computation with gradient-weighted normalization](https://mlsanity.com/paper/2101.00401/) (2021)
- [Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces](https://mlsanity.com/paper/2507.20853/) (2025)
- [Vanishing Component Analysis with Contrastive Normalization](https://mlsanity.com/paper/2210.16171/) (2022)
- [On the Geometry of Reinforcement Learning in Continuous State and Action Spaces](https://mlsanity.com/paper/2301.00009/) (2022)

## Abstract (arXiv)

We address the problem of learning reusable state representations from streaming high-dimensional observations. This is important for areas like Reinforcement Learning (RL), which yields non-stationary data distributions during training. We make two key contributions. First, we propose an evaluation suite that measures alignment between latent and true low-dimensional states. We benchmark several widely used unsupervised learning approaches. This uncovers the strengths and limitations of existing approaches that impose additional constraints/objectives on the latent space. Our second contribution is a unifying mathematical formulation for learning latent relations. We learn analytic relations on source domains, then use these relations to help structure the latent space when learning on target domains. This formulation enables a more general, flexible and principled way of shaping the latent space. It formalizes the notion of learning independent relations, without imposing restrictive simplifying assumptions or requiring domain-specific information. We present mathematical properties, concrete algorithms for implementation and experimental validation of successful learning and transfer of latent relations.