MeSH terms sit in a tree of broader and narrower concepts. Ranking can use that structure as extra evidence. A gradient-boosted model, which combines many small decision rules, can read plain tree facts. Poincaré coordinates, a way of placing a tree in curved space so deep branches have room, capture the same parent-child structure as measured positions.
tree depthancestor overlapGBMPoincaré disk
Geometry: Hierarchies expand faster than Euclidean space
| Space | Representation | Boundary |
|---|---|---|
| Euclidean | Equal physical distance represents equal vector distance. | Deep branches compete for finite area. |
| Poincaré | Space grows toward the disk boundary. | Distance represents structure, not word meaning. |
Explicit hierarchy features: Auditable ranker inputs
| Feature | Question answered |
|---|---|
| Depth | How specific is the candidate? |
| Ancestor overlap | Do candidates share a branch? |
| Path distance | How far apart are the concepts? |
| Sibling density | Does a crowded branch require stronger separation? |
Model sequence: Add structural evidence in measured stages
Inference: The deterministic index defines the candidate pool
ordinary query → normalized words, phrases, and identifiers → associated MeSH candidates → hierarchy features → GBM scores → current descriptors
Controlled comparison: One evidence layer changes at a time
| Model | Evidence | Excluded evidence |
|---|---|---|
| Frequency formula | Pair frequency, lift, phrase weight, cross-source bonus | Learned ranking and hierarchy |
| GBM plus hierarchy | Frequency, depth, ancestors, branch, relatives, positions | Learned graph coordinates |
| GBM plus Poincaré | All explicit features, coordinates, centroid distance, radial depth, separation | No additional evidence layer |
Poincaré signals: Coordinates supplement explicit tree facts
- Candidate coordinates represent location in the learned graph.
- Token-associated centroid distance compares a candidate with query-linked terms.
- Nearest-candidate distance represents local structural density.
- Radial position approximates depth.
- Cross-branch separation distinguishes distant subtrees.