Matched Queries for Curvature and Density at Branching Junctions
At a junction, a score field can reveal weighted tangent rays, yet these first-order quantities do not determine how individual branches bend or how their densities change away from the center. Recovering this missing information is necessary for describing local continuation beyond a single point, but finite observations must separate branchwise second-order effects while allowing error in the estimated center. We address this inverse problem using matched score queries at noise scales $σ$ and $λσ$. For a finite union of $C^{2,α}$ half-branches in $\mathbb{R}^D$, the normalized score has the expansion $F_σ=F_0+σG+O(σ^{1+α})$. Matched subtraction cancels the tangent contribution and expos...
| Authors | Ziqi Zhao, Qingjian Ni |
|---|---|
| Primary category | stat.ML |
| Published | 1 September 2026 |
| Last updated at source | 1 September 2026 |
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