Ophanimus · Hyperbolic RAG
Embeddings that know your data’s shape.
Most enterprise knowledge is hierarchical. Today’s RAG stacks flatten it into Euclidean vectors and lose it. We rebuild the stack on hyperbolic geometry, so parent–child becomes a geometric primitive — not a feature the model has to relearn from text.
- v0.1 · weeks not months
- 5·Riemannian manifolds
- 8·geodesic algorithms
- fp64 throughout
A CEO’s memo and an intern’s footnote should not be equidistant from “the company strategy.”
Most enterprise knowledge — internal documents, product taxonomies, org charts, codebases — is inherently hierarchical. Today’s RAG stacks flatten that hierarchy into Euclidean vectors and lose it. A module-level contract and a one-off helper end up equidistant from a query about “auth flow.” Adding parent_id metadata filters doesn’t solve this: it preserves explicit edges but loses transitive ancestry distance and breaks the moment the hierarchy is implicit, contested, or missing.
Hyperbolic geometry preserves hierarchy by construction. That hierarchical data embeds with exponentially less distortion in hyperbolic than in Euclidean space has been the established result since Nickel & Kiela, 2017. We are committing to it, not benchmarking against it.
Flat space treats hierarchy as just another semantic feature. A CEO memo and an intern footnote end up equidistant from strategy.
Curve the space and ancestry becomes geometric. Strategy is close to the memo at depth 1 and far from the footnote at depth 4 — by construction, not by hint.
Three stages. One geometry per customer.
Customers connect their data sources. We audit tree-likeness with Gromov δ-hyperbolicity, train a hyperbolic projection head with learnable curvature tuned per customer over a standard sentence-transformer, and serve queries through a geometry-aware index. Parent–child becomes a native distance metric.
- 01
Audit
Gromov δ-hyperbolicity
Before any neural network touches the data we measure tree-likeness directly. δ is computed on the raw distance matrix — geometry is the first thing we look at, not the last hyperparameter we tune.
- 02
Project
per-customer curvature head
A hyperbolic projection head with learnable curvature, trained per customer over a standard sentence-transformer using asymmetric contrastive loss. HypLoRA-style adapter — no base-model retrain.
- 03
Serve
geometry-aware index
Qdrant or FAISS with a custom hyperbolic-distance kernel, fp64 throughout for numerical stability near the Poincaré boundary. Parent–child becomes a native distance metric, not a metadata filter.
The standard objection: “Pinecone will ship a hyperbolic toggle in six months.”
They can’t. Incumbent vector databases like Pinecone, Qdrant, and MongoDB treat embedding space as flat Euclidean by assumption. They optimize resolution but ignore geometry. Solving this requires a full-stack geometry rebuild, not a database feature flag — ¹HNSW, ²encoders, and ³numerics all need to move together.
| vendor | embedding space | HNSW assumption | encoder | numerics | ships? |
|---|---|---|---|---|---|
| Pinecone | Euclidean by assumption | Locked to Euclidean | Cosine-trained | fp32 standard | ✕ |
| Qdrant | Euclidean by assumption | Locked to Euclidean | Cosine-trained | fp32 standard | ✕ |
| MongoDB | Euclidean by assumption | Locked to Euclidean | Cosine-trained | fp32 standard | ✕ |
| Ophanimus | Hyperbolic, per customer | Custom hyperbolic kernel | Geoopt projection head | fp64 throughout | ✓ |
- ¹ HNSW graph construction relies on Euclidean assumptions; swapping the distance formula breaks the index.
- ² Standard encoders are trained for cosine similarity. A dedicated projection head is required to operate in hyperbolic space.
- ³ Standard math libraries suffer floating-point collapse near the Poincaré boundary. fp64 throughout the manifold ops is non-optional.
The library underneath: shipped.
manifold_helpers · v0.1
Five Riemannian manifolds. Eight geodesic algorithms. The closed-loop manifold-selection pipeline picks geometry from the data, not the other way around — Gromov δ plus competitive embedding.
every cell shipped. fp64 throughout. hyperboloid-as-engine, Poincaré-as-dashboard split.
developer wedge
The math is open. The pipeline is paid.
manifold_helpers is the Python library underneath Ophanimus — Riemannian primitives, geodesic algorithms, the manifold-selection pipeline. A pip install to local prototype to hosted contract is the upgrade path.
- · Python · NumPy · SciPy · fp64 throughout
- · JAX or PyTorch for the differentiable projection head
- · Hyperboloid-as-engine, Poincaré-as-dashboard split
solo founder · CEO · 90% reserved
Nicholas Fleischhauer
Building AI systems at Gravity and LexisNexis, I watched flat RAG pipelines fail the same way every time. The retriever returns something semantically near a query but structurally wrong, the LLM produces a confident answer downstream, and an internal SME catches it immediately as belonging to the wrong layer of the org.
My math background let me see this as a geometry problem, not a model-quality problem; my engineering background let me ship the fix. manifold_helpers is the result.
- 1st place, YC AI Coding Agents Hackathon — Operius, an agent swarm that self-heals Kubernetes via chaos engineering. Hosted by YC, Anthropic, Freestyle, Same.new, Morph LLM.
- Founding engineer, Gravity — hybrid SSP-DSP real-time bidding platform. Go + Rust, 8 services, 4–9ms latency at 10K+ req/s.
- Applied math, UC Berkeley · USF. Riemannian geometry and hyperbolic embeddings since well before they were marketable.