# Multi-Hop Reasoning for Question Answering with Hyperbolic Representations

arXiv: https://arxiv.org/abs/2507.03612 · HTML: https://mlsanity.com/paper/2507.03612/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 28 of its 38 references that are in the map.
- First posted on arXiv 4 Jul 2025.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 28 of 28)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Generating Wikipedia by Summarizing Long Sequences](https://mlsanity.com/paper/1801.10198/) (2018)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Multi-relational Poincar'e Graph Embeddings](https://mlsanity.com/paper/1905.09791/) (2019)
- [Scalable Multi-Hop Relational Reasoning for Knowledge-Aware Question Answering](https://mlsanity.com/paper/2005.00646/) (2020)
- [Hyperbolic Vision Transformers: Combining Improvements in Metric Learning](https://mlsanity.com/paper/2203.10833/) (2022)
- [Multi-Hop Knowledge Graph Reasoning with Reward Shaping](https://mlsanity.com/paper/1808.10568/) (2018)
- [Embedding Text in Hyperbolic Spaces](https://mlsanity.com/paper/1806.04313/) (2018)
- [Generate-then-Ground in Retrieval-Augmented Generation for Multi-hop Question Answering](https://mlsanity.com/paper/2406.14891/) (2024)
- [An Interpretable Reasoning Network for Multi-Relation Question Answering](https://mlsanity.com/paper/1801.04726/) (2018)
- [End-to-End Beam Retrieval for Multi-Hop Question Answering](https://mlsanity.com/paper/2308.08973/) (2023)
- [HyperKG: Hyperbolic Knowledge Graph Embeddings for Knowledge Base Completion](https://mlsanity.com/paper/1908.04895/) (2019)
- [Retrieval-enhanced Knowledge Editing in Language Models for Multi-Hop Question Answering](https://mlsanity.com/paper/2403.19631/) (2024)
- [Exploiting Reasoning Chains for Multi-hop Science Question Answering](https://mlsanity.com/paper/2109.02905/) (2021)
- [HyperMiner: Topic Taxonomy Mining with Hyperbolic Embedding](https://mlsanity.com/paper/2210.10625/) (2022)
- [Hierarchical Retrieval-Augmented Generation Model with Rethink for Multi-hop Question Answering](https://mlsanity.com/paper/2408.11875/) (2024)
- [Hyperbolic Temporal Knowledge Graph Embeddings with Relational and Time Curvatures](https://mlsanity.com/paper/2106.04311/) (2021)
- [Understanding and Improving Zero-shot Multi-hop Reasoning in Generative Question Answering](https://mlsanity.com/paper/2210.04234/) (2022)

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

- [Intrinsic Lorentz Neural Network](https://mlsanity.com/paper/2602.23981/) (2026)

## Abstract (arXiv)

Hyperbolic representations are effective in modeling knowledge graph data which is prevalently used to facilitate multi-hop reasoning. However, a rigorous and detailed comparison of the two spaces for this task is lacking. In this paper, through a simple integration of hyperbolic representations with an encoder-decoder model, we perform a controlled and comprehensive set of experiments to compare the capacity of hyperbolic space versus Euclidean space in multi-hop reasoning. Our results show that the former consistently outperforms the latter across a diverse set of datasets. In addition, through an ablation study, we show that a learnable curvature initialized with the delta hyperbolicity of the utilized data yields superior results to random initializations. Furthermore, our findings suggest that hyperbolic representations can be significantly more advantageous when the datasets exhibit a more hierarchical structure.