Year: 2026
Type: preprint
Abstract: There are many types of path between nodes of a Directed acyclic graph (DAG), including the shortest and longest paths. Here, we ask whether the choice of path used in any analysis reflects the geometry of the latent space in which the DAG is embedded. To do this we define L_p-cube spacetimes, a family of continuous ordered spaces in which a single parameter p determines whether the ordered distance satisfies the ordered triangle identity when p>1, or the reverse ordered triangle identity when 01, where the ordered triangle identity holds, the shortest paths provide the closest approximation to the continuum ordered geodesic while for 0
Source: arXiv (Cornell University)
Authors: AlMuhanna, Haya, Evans, Tim S.
Institution: Imperial College London
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223124394