Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometries
Fuente:
arXiv
Saved in:
| Main Authors: | He, Neil, Liu, Jiahong, Zhang, Buze, Bui, Ngoc, Maatouk, Ali, Yang, Menglin, King, Irwin, Weber, Melanie, Ying, Rex |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Similar Items
Towards Non-Euclidean Foundation Models: Advancing AI Beyond Euclidean Frameworks
by: Yang, Menglin, et al.
Published: (2025)
by: Yang, Menglin, et al.
Published: (2025)
Parameter-Efficient Fine-Tuning of LLMs with Mixture of Space Experts
by: Zhang, Buze, et al.
Published: (2026)
by: Zhang, Buze, et al.
Published: (2026)
Hyperbolic Deep Learning for Foundation Models: A Survey
by: He, Neil, et al.
Published: (2025)
by: He, Neil, et al.
Published: (2025)
HyperCore: The Core Framework for Building Hyperbolic Foundation Models with Comprehensive Modules
by: He, Neil, et al.
Published: (2025)
by: He, Neil, et al.
Published: (2025)
Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Space
by: Yang, Menglin, et al.
Published: (2024)
by: Yang, Menglin, et al.
Published: (2024)
Learning Along the Arrow of Time: Hyperbolic Geometry for Backward-Compatible Representation Learning
by: Bui, Ngoc, et al.
Published: (2025)
by: Bui, Ngoc, et al.
Published: (2025)
HELM: Hyperbolic Large Language Models via Mixture-of-Curvature Experts
by: He, Neil, et al.
Published: (2025)
by: He, Neil, et al.
Published: (2025)
Understanding and Mitigating Hyperbolic Dimensional Collapse in Graph Contrastive Learning
by: Zhang, Yifei, et al.
Published: (2023)
by: Zhang, Yifei, et al.
Published: (2023)
Lorentzian Residual Neural Networks
by: He, Neil, et al.
Published: (2024)
by: He, Neil, et al.
Published: (2024)
HypRAG: Hyperbolic Dense Retrieval for Retrieval Augmented Generation
by: Madhu, Hiren, et al.
Published: (2026)
by: Madhu, Hiren, et al.
Published: (2026)
LitFM: A Retrieval Augmented Structure-aware Foundation Model For Citation Graphs
by: Zhang, Jiasheng, et al.
Published: (2024)
by: Zhang, Jiasheng, et al.
Published: (2024)
LitBench: A Graph-Centric Large Language Model Benchmarking Tool For Literature Tasks
by: Varvarigos, Andreas, et al.
Published: (2026)
by: Varvarigos, Andreas, et al.
Published: (2026)
Inscriptions in non-Euclidean Geometries
by: Sadr, Ali Naseri
Published: (2025)
by: Sadr, Ali Naseri
Published: (2025)
Low-Rank Adaptation for Foundation Models: A Comprehensive Review
by: Yang, Menglin, et al.
Published: (2024)
by: Yang, Menglin, et al.
Published: (2024)
Implicit Reasoning in Large Language Models: A Comprehensive Survey
by: Li, Jindong, et al.
Published: (2025)
by: Li, Jindong, et al.
Published: (2025)
Autoformalizing Euclidean Geometry
by: Murphy, Logan, et al.
Published: (2024)
by: Murphy, Logan, et al.
Published: (2024)
Johnson-Lindenstrauss Lemma Beyond Euclidean Geometry
by: Deng, Chengyuan, et al.
Published: (2025)
by: Deng, Chengyuan, et al.
Published: (2025)
Efficient Identity and Position Graph Embedding via Spectral-Based Random Feature Aggregation
by: Qin, Meng, et al.
Published: (2025)
by: Qin, Meng, et al.
Published: (2025)
Bilinear and Fractional Leibniz Rules Beyond Euclidean Spaces: Weighted Besov and Triebel--Lizorkin Estimates
by: Bui, The Anh
Published: (2025)
by: Bui, The Anh
Published: (2025)
Geometry and Mechanics of Non-Euclidean Curved-Crease Origami
by: Wen, Zhixuan, et al.
Published: (2025)
by: Wen, Zhixuan, et al.
Published: (2025)
Tele-LLMs: A Series of Specialized Large Language Models for Telecommunications
by: Maatouk, Ali, et al.
Published: (2024)
by: Maatouk, Ali, et al.
Published: (2024)
Towards Geometry Problem Solving in the Large Model Era: A Survey
by: Zhao, Yurui, et al.
Published: (2025)
by: Zhao, Yurui, et al.
Published: (2025)
Hyperbolic Fine-Tuning for Large Language Models
by: Yang, Menglin, et al.
Published: (2024)
by: Yang, Menglin, et al.
Published: (2024)
Methods for Optimization Problems with Markovian Stochasticity and Non-Euclidean Geometry
by: Solodkin, Vladimir, et al.
Published: (2024)
by: Solodkin, Vladimir, et al.
Published: (2024)
Spectral Curvature Duality Across Euclidean and Non-Euclidean Spaces
by: SÉRGIO DE ANDRADE, PAULO
Published: (2025)
by: SÉRGIO DE ANDRADE, PAULO
Published: (2025)
Theoretical Foundations of Principal Manifold Estimation with Non-Euclidean Templates
by: Meng, Kun, et al.
Published: (2026)
by: Meng, Kun, et al.
Published: (2026)
An Observer-Based View of Euclidean Geometry
by: Bahreyni, Newshaw, et al.
Published: (2024)
by: Bahreyni, Newshaw, et al.
Published: (2024)
Grokking Beyond the Euclidean Norm of Model Parameters
by: Notsawo, Pascal Jr Tikeng, et al.
Published: (2025)
by: Notsawo, Pascal Jr Tikeng, et al.
Published: (2025)
A Tale of Two Geometries: Adaptive Optimizers and Non-Euclidean Descent
by: Xie, Shuo, et al.
Published: (2025)
by: Xie, Shuo, et al.
Published: (2025)
Beyond Euclidean Prototypes: Spectral Disentanglement and Geodesic Matching for Few-Shot Medical Image Segmentation
by: Jia, Penghao, et al.
Published: (2026)
by: Jia, Penghao, et al.
Published: (2026)
Private Algorithms for Stochastic Saddle Points and Variational Inequalities: Beyond Euclidean Geometry
by: Bassily, Raef, et al.
Published: (2024)
by: Bassily, Raef, et al.
Published: (2024)
Non-Euclidean Triangle Centers
by: Russell, Robert A.
Published: (2016)
by: Russell, Robert A.
Published: (2016)
Non-Euclidean Crystallographic Rigidity
by: Esson, Jack, et al.
Published: (2025)
by: Esson, Jack, et al.
Published: (2025)
CLIP-Powered Domain Generalization and Domain Adaptation: A Comprehensive Survey
by: Li, Jindong, et al.
Published: (2025)
by: Li, Jindong, et al.
Published: (2025)
Structured Sampling for Robust Euclidean Distance Geometry
by: Kundu, Chandra, et al.
Published: (2024)
by: Kundu, Chandra, et al.
Published: (2024)
Provable Non-Convex Euclidean Distance Matrix Completion: Geometry, Reconstruction, and Robustness
by: Smith, Chandler, et al.
Published: (2025)
by: Smith, Chandler, et al.
Published: (2025)
Riemannian Optimization for Non-convex Euclidean Distance Geometry with Global Recovery Guarantees
by: Smith, Chandler, et al.
Published: (2024)
by: Smith, Chandler, et al.
Published: (2024)
Non-Euclidean Broximal Point Method: A Blueprint for Geometry-Aware Optimization
by: Gruntkowska, Kaja, et al.
Published: (2025)
by: Gruntkowska, Kaja, et al.
Published: (2025)
Multi-Modal Time Series Prediction via Mixture of Modulated Experts
by: Zhang, Lige, et al.
Published: (2026)
by: Zhang, Lige, et al.
Published: (2026)
Non-Euclidean Erdős-Anning Theorems
by: Eppstein, David
Published: (2024)
by: Eppstein, David
Published: (2024)
Similar Items
-
Towards Non-Euclidean Foundation Models: Advancing AI Beyond Euclidean Frameworks
by: Yang, Menglin, et al.
Published: (2025) -
Parameter-Efficient Fine-Tuning of LLMs with Mixture of Space Experts
by: Zhang, Buze, et al.
Published: (2026) -
Hyperbolic Deep Learning for Foundation Models: A Survey
by: He, Neil, et al.
Published: (2025) -
HyperCore: The Core Framework for Building Hyperbolic Foundation Models with Comprehensive Modules
by: He, Neil, et al.
Published: (2025) -
Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Space
by: Yang, Menglin, et al.
Published: (2024)