HyperbolicRAG: Curved Spaces, Better Answers — AI Innovations and Insights 94

Traditional RAG systems are pretty familiar by now: retrieve a few relevant passages using dense retrieval, then feed them to a language model for answering the question.

GraphRAG builds on this idea by turning documents into graphs, linking entities and passages, then using multi-hop propagation to improve reasoning. It feels more structured.

But here is a deeper problem: while the knowledge in these graphs is hierarchical, the embedding space they live in is flat…

Why Euclidean GraphRAG Isn’t Enough

Nearly all current graph-based RAG methods:

• G-Retriever

• GraphRAG (A Comprehensive Guide to Graph RAG)

• HippoRAG (HippoRAG: Hippocampal Memory of RAG)

• LightRAG (AI Innovations and Trends 03: LightRAG, Docling, DRIFT, and More)

• HippoRAG2 (AI Innovations and Insights 31: olmOCR , HippoRAG 2, and RAG Web UI)

embed nodes in Euclidean space. That works well for capturing “how similar things are,” but this kind of space lacks a geometric notion of hierarchical depth. It can tell you that “chronic stress” and “acute stress” are similar, but it tends not to express that “stress” is a more abstract category that includes both.

This leads to some real issues.

Figure 1: Comparison of Euclidean and hyperbolic embedding effects on retrieval-augmented multi-hop reasoning. (a) In Euclidean space, embeddings reflect surface-level similarity. General concepts (e.g., stress) act as semantic hubs, making top-k retrieval and graph propagation drift toward broad, generic subgraphs. (b) In hyperbolic space, hierarchical depth is radially encoded: abstract nodes lie near the center, while specific facts align near the boundary. Queries are thus aligned to relevant mechanism nodes (e.g., chronic stress, cortisol release), yielding more precise and causally focused reasoning. [Source].

Imagine you’re asking a question like: How does long-term tension (chronic stress) lead to weakened immunity?

A Euclidean-based retriever is likely to pull in general terms like “health” or “illness”, broad concepts that appear in many contexts, because in high-dimensional Euclidean space, these hubs are close to everything. This is a well-known problem called hubness.