Author

Taeyoung Kim

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Preprint Sep 2026

Bipodal optimizers in the upper-tail variational problem for regular subgraph densities

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

Jul 2026

Grokking on the Weight-Decay Clock: A Rate Hierarchy from Softly Broken Symmetries

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