# Towards Non-Euclidean Foundation Models: Advancing AI Beyond Euclidean Frameworks

arXiv: https://arxiv.org/abs/2505.14417 · HTML: https://mlsanity.com/paper/2505.14417/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 45 references that are in the map.
- First posted on arXiv 20 May 2025.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Hyperbolic Entailment Cones for Learning Hierarchical Embeddings](https://mlsanity.com/paper/1804.01882/) (2018)
- [Equivariant Subgraph Aggregation Networks](https://mlsanity.com/paper/2110.02910/) (2021)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Constant Curvature Graph Convolutional Networks](https://mlsanity.com/paper/1911.05076/) (2019)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [Discrete-time Temporal Network Embedding via Implicit Hierarchical Learning in Hyperbolic Space](https://mlsanity.com/paper/2107.03767/) (2021)
- [Graph Geometry Interaction Learning](https://mlsanity.com/paper/2010.12135/) (2020)
- [Spherical Text Embedding](https://mlsanity.com/paper/1911.01196/) (2019)
- [The Numerical Stability of Hyperbolic Representation Learning](https://mlsanity.com/paper/2211.00181/) (2022)
- [Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Space](https://mlsanity.com/paper/2407.01290/) (2024)
- [Modeling Scale-free Graphs with Hyperbolic Geometry for Knowledge-aware Recommendation](https://mlsanity.com/paper/2108.06468/) (2021)
- [RiemannGFM: Learning a Graph Foundation Model from Riemannian Geometry](https://mlsanity.com/paper/2502.03251/) (2025)
- [HRCF: Enhancing Collaborative Filtering via Hyperbolic Geometric Regularization](https://mlsanity.com/paper/2204.08176/) (2022)
- [Deep Metric Learning with Spherical Embedding](https://mlsanity.com/paper/2011.02785/) (2020)
- [Where are we in embedding spaces? A Comprehensive Analysis on Network Embedding Approaches for Recommender Systems](https://mlsanity.com/paper/2105.08908/) (2021)
- [Hyperbolic Representation Learning for Fast and Efficient Neural Question Answering](https://mlsanity.com/paper/1707.07847/) (2017)
- [Robust Large-Margin Learning in Hyperbolic Space](https://mlsanity.com/paper/2004.05465/) (2020)
- [Hardness of Learning Neural Networks under the Manifold Hypothesis](https://mlsanity.com/paper/2406.01461/) (2024)
- [Ultrahyperbolic Representation Learning](https://mlsanity.com/paper/2007.00211/) (2020)
- [On the hardness of learning under symmetries](https://mlsanity.com/paper/2401.01869/) (2024)
- [Generalization Error Bound for Hyperbolic Ordinal Embedding](https://mlsanity.com/paper/2105.10475/) (2021)
- [Directed Graph Embeddings in Pseudo-Riemannian Manifolds](https://mlsanity.com/paper/2106.08678/) (2021)

## Built on by (most cited first, 1 of 1)

- [Intrinsic Associative Memory on Riemannian Manifolds: Curvature, Capacity, and Emergent Modes](https://mlsanity.com/paper/2609.35948/) (2026)

## Abstract (arXiv)

In the era of foundation models and Large Language Models (LLMs), Euclidean space is the de facto geometric setting of our machine learning architectures. However, recent literature has demonstrated that this choice comes with fundamental limitations. To that end, non-Euclidean learning is quickly gaining traction, particularly in web-related applications where complex relationships and structures are prevalent. Non-Euclidean spaces, such as hyperbolic, spherical, and mixed-curvature spaces, have been shown to provide more efficient and effective representations for data with intrinsic geometric properties, including web-related data like social network topology, query-document relationships, and user-item interactions. Integrating foundation models with non-Euclidean geometries has great potential to enhance their ability to capture and model the underlying structures, leading to better performance in search, recommendations, and content understanding. This workshop focuses on the intersection of Non-Euclidean Foundation Models and Geometric Learning (NEGEL), exploring its potential benefits, including the potential benefits for advancing web-related technologies, challenges, and future directions. Workshop page: [https://hyperboliclearning.github.io/events/www2025workshop](https://hyperboliclearning.github.io/events/www2025workshop)