arXiv:2605.21945v1 Announce Type: new
Abstract: We give a Hasse-diagram characterization of when a clustering system $mathcal C$ on a finite taxa set $X$ is the hardwired clustering system $C_N$ of a rooted level-$k$ network. For each non-trivial block $B$ of $H=mathcal H[mathcal C]$, we define a parameter $mu(B)$ using minimum families of clusters that generate all overlap-intersections inside $B$. The main theorem proves that there exists a rooted level-$k$ network $N$ with $C_N=mathcal C$ if and only if $mu(B)le k$ for every non-trivial block $B$ of $H$. The necessity proof shows that overlap-intersection pieces must be represented by non-root hybrid vertices in any realizing block. The sufficiency proof is constructive: starting from the Hasse diagram, it iteratively splits selected hybrid vertices, preserves the hardwired clustering system, and terminates with a realization whose level is bounded by the block-wise values of $mu$.
Semantic Robustness Probing via Inpainting: An Interactive Tool for Safety-Critical Object Detection
arXiv:2605.27155v1 Announce Type: cross Abstract: Testing object detectors in safety-critical domains requires semantically meaningful probes beyond pixel-level corruptions. We present SemProbe, a tool for semantic