Why it is a question
THEORY-566, promoted on 2026-10-19, holds a structural fact about Ganea, Bécigneul and Hofmann’s hyperbolic networks (LIT-879): lifted linear maps and nonlinearities compose to a Euclidean composition read through the chart at the origin, so the curvature acts only through the Möbius bias translations and the distance-based output layer. Until that date THEORY-566’s promote_when asked for an ablation tying the networks’ gains to those two operations, which the title does not claim and the body disclaims. At the owner’s direction, from the promotion audit’s batch 027 (ADR-047), the THEORY was promoted on the structural claim, and the condition moved here unchanged.
It is open because the paper’s comparisons are of whole hyperbolic and Euclidean networks, at dimension 5, with best-of-three runs, on one synthetic task whose tree-likeness is not measured and on embeddings fitted to the hierarchy being classified (NOTE-686). It refines QUESTION-025, which lists encodings of hierarchy.
What would answer it
The condition formerly on THEORY-566, unchanged: an ablation on tree-like data that removes, in turn, the Möbius bias translations and the distance-based hyperbolic output layer from Ganea et al.’s networks, with several seeds and a measure of the data’s tree-likeness. The account that the curvature matters through those operations is supported if the advantage over Euclidean networks goes with them, and refuted if networks without them keep it. More benchmark comparisons of whole hyperbolic and Euclidean networks cannot settle it.