# Leveraging Hyperbolic Embeddings for Coarse-to-Fine Robot Design

arXiv: https://arxiv.org/abs/2311.00462 · HTML: https://mlsanity.com/paper/2311.00462/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 60 references that are in the map.
- First posted on arXiv 1 Nov 2023.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [From Coarse to Fine: Robust Hierarchical Localization at Large Scale](https://mlsanity.com/paper/1812.03506/) (2018)
- [Coarse-to-Fine Volumetric Prediction for Single-Image 3D Human Pose](https://mlsanity.com/paper/1611.07828/) (2016)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Embodied Intelligence via Learning and Evolution](https://mlsanity.com/paper/2102.02202/) (2021)
- [CoFiNet: Reliable Coarse-to-fine Correspondences for Robust Point Cloud Registration](https://mlsanity.com/paper/2110.14076/) (2021)
- [Coarse-to-Fine Q-attention: Efficient Learning for Visual Robotic Manipulation via Discretisation](https://mlsanity.com/paper/2106.12534/) (2021)
- [One Policy to Control Them All: Shared Modular Policies for Agent-Agnostic Control](https://mlsanity.com/paper/2007.04976/) (2020)
- [Multiple Sound Sources Localization from Coarse to Fine](https://mlsanity.com/paper/2007.06355/) (2020)
- [Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoders](https://mlsanity.com/paper/1901.06033/) (2019)
- [Coarse-to-Fine Vision-Language Pre-training with Fusion in the Backbone](https://mlsanity.com/paper/2206.07643/) (2022)
- [Coarse-to-Fine Imitation Learning: Robot Manipulation from a Single Demonstration](https://mlsanity.com/paper/2105.06411/) (2021)
- [MetaMorph: Learning Universal Controllers with Transformers](https://mlsanity.com/paper/2203.11931/) (2022)
- [My Body is a Cage: the Role of Morphology in Graph-Based Incompatible Control](https://mlsanity.com/paper/2010.01856/) (2020)
- [Jointly Learning to Construct and Control Agents using Deep Reinforcement Learning](https://mlsanity.com/paper/1801.01432/) (2018)
- [HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projections](https://mlsanity.com/paper/2106.03306/) (2021)
- [Evolution Gym: A Large-Scale Benchmark for Evolving Soft Robots](https://mlsanity.com/paper/2201.09863/) (2022)
- [Scalable Co-Optimization of Morphology and Control in Embodied Machines](https://mlsanity.com/paper/1706.06133/) (2017)
- [Hyperbolic Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/2202.13852/) (2022)
- [Transform2Act: Learning a Transform-and-Control Policy for Efficient Agent Design](https://mlsanity.com/paper/2110.03659/) (2021)
- [Neural Graph Evolution: Towards Efficient Automatic Robot Design](https://mlsanity.com/paper/1906.05370/) (2019)
- [Hyperbolic Deep Reinforcement Learning](https://mlsanity.com/paper/2210.01542/) (2022)
- [Capturing implicit hierarchical structure in 3D biomedical images with self-supervised hyperbolic representations](https://mlsanity.com/paper/2012.01644/) (2020)
- [Coarse-to-Fine: a Hierarchical Diffusion Model for Molecule Generation in 3D](https://mlsanity.com/paper/2305.13266/) (2023)
- [GLSO: Grammar-guided Latent Space Optimization for Sample-efficient Robot Design Automation](https://mlsanity.com/paper/2209.11748/) (2022)

## Built on by (most cited first, 5 of 5)

- [Bridging Evolutionary Algorithms and Reinforcement Learning: A Comprehensive Survey on Hybrid Algorithms](https://mlsanity.com/paper/2401.11963/) (2024)
- [House of Dextra: Cross-embodied Co-design for Dexterous Hands](https://mlsanity.com/paper/2512.03743/) (2025)
- [Embodied Co-Design for Rapidly Evolving Agents: Taxonomy, Frontiers, and Challenges](https://mlsanity.com/paper/2512.04770/) (2025)
- [On Probabilistic Pullback Metrics for Latent Hyperbolic Manifolds](https://mlsanity.com/paper/2410.20850/) (2024)
- [Generative Evolutionary Design of Voxel-Based Soft Robots with Provable Optimality](https://mlsanity.com/paper/2609.29491/) (2026)

## Abstract (arXiv)

Multi-cellular robot design aims to create robots comprised of numerous cells that can be efficiently controlled to perform diverse tasks. Previous research has demonstrated the ability to generate robots for various tasks, but these approaches often optimize robots directly in the vast design space, resulting in robots with complicated morphologies that are hard to control. In response, this paper presents a novel coarse-to-fine method for designing multi-cellular robots. Initially, this strategy seeks optimal coarse-grained robots and progressively refines them. To mitigate the challenge of determining the precise refinement juncture during the coarse-to-fine transition, we introduce the Hyperbolic Embeddings for Robot Design (HERD) framework. HERD unifies robots of various granularity within a shared hyperbolic space and leverages a refined Cross-Entropy Method for optimization. This framework enables our method to autonomously identify areas of exploration in hyperbolic space and concentrate on regions demonstrating promise. Finally, the extensive empirical studies on various challenging tasks sourced from EvoGym show our approach's superior efficiency and generalization capability.