Author

Song-Tao Mao

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Preprint Sep 2026

Improved polynomial-time algorithms for detecting and recovering planted $\Theta(\sqrt{n})$-cliques

In the planted clique problem, one observes either an Erd\H{o}s--R\'{e}nyi graph on $n$ vertices or such a graph with a clique added to $k = k(n)$ vertices, and seeks to detect or recover the clique. It is widely believed that $k = \Theta(\sqrt{n})$ is the smallest clique size for which polynomial-time algorithms exist...

Dmitriy Kunisky, Song-Tao Mao · 0 citations

Preprint Sep 2026

Abelian Cayley High-Dimensional Expanders with Polylogarithmic Degree

We construct an explicit infinite family of simple two-dimensional Cayley complexes over $\mathbb{F}_2^n$ whose degree is polynomial in $n$ and whose nontrivial vertex-link eigenvalues lie in $[-\lambda,\lambda]$ for every fixed $\lambda>0$. For every fixed $d\ge2$, we also obtain an explicit infinite family of weighte...

Song-Tao Mao · 0 citations

Jul 2026

The Polynomial-Time Low-Degree Conjecture is False

This work disproves the polynomial-time low-degree conjecture and shows that low-degree indistinguishability, a uniform null distribution, permutation invariance, and independent resampling do not by themselves imply polynomial-time hardness, and suggests that a valid general conjecture must impose an additional condit...

Song-Tao Mao · arXiv.org · 1 citation