Goodman proved a lower bound on triangle counts which, in graphon language, states that every graphon of edge density $p$ has triangle density at least $2p^2-p$. Bennett, Dudek, Lidick\'{y}, and Pikhurko established the corresponding bound for $C_5$, determining its minimum density at every Tur\'an density $p=1-1/k$ wi...
Seonghyuk Im, Taeyoung Kim, Hongseok Yang· 1 citation
We propose a neural exploratory framework for variational problems over graphons, i.e., symmetric measurable functions $[0,1]^2 \to [0,1]$, that arise as limits of dense graph sequences. Such problems are central to two parts of the mathematical literature: extremal graph theory, which studies graph parameter optimisat...
Taeyoung Kim, Jineon Baek, Joonkyung Lee et al.· 1 citation
Let $H$ be a fixed $d$-regular graph with $d\ge2$, and let $t(H,\cdot)$ denote its homomorphism density. We study the upper-tail event $t(H,G(n,p))\ge r^{|E(H)|}$ for fixed $0<p<r<1$ in a dense Erd\H{o}s--R\'enyi random graph $G(n,p)$. Near the Lubetzky--Zhao replica-symmetric phase boundary and away from the exception...
Sang-Ho Lim, Seonghyuk Im, Taeyoung Kim et al.· 0 citations
Delayed generalization, or grokking, remains poorly understood despite extensive empirical study. We identify an exactly solvable late-time relaxation mechanism for grokking in linear models trained with full-batch heavy-ball optimization and weight decay, together with a locally quadratic extension to nonlinear neural...
Taeyoung Kim· arXiv.org· 1 citation
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