Reproduce “Low-Degree Hardness of Recovery Below the Kesten–Stigum Threshold in Planted 3-SAT” on OpenResearch
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About this paper
Yan Ru Pei
The authors bound low-degree estimation of the planted assignment’s pairwise feature, showing vanishing squared correlation below the Kesten–Stigum threshold. For fixed density, p0<1/4, resampling noise η<1, and coordinate degree D≤nδ, the bound applies to functions of at most D clause-slots. At density 4.3, a separate first-moment condition guarantees vector recovery for p0∈(0.13799,1/4); the low-degree result does not rule out other algorithms.
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