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Ultrametric OGP - parametric RDT \emph{symmetric} binary perceptron connection
arXiv CS.LG
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ArXi:2604.19712v1 Announce Type: new In [97,99,100], an fl-RDT framework is In this paper, we further connect parametric RDT to overlap gap properties (OGPs), another key geometric feature of the solution space. Specifically, for any positive integer $s$, we consider $s$-level ultrametric OGPs ($ult_s$-OGPs) and rigorously upper-bound the associated constraint densities $\alpha_{ult_s}$. To achieve this, we develop an analytical union-bounding program consisting of combinatorial and probabilistic components.