T-wise independence is the necessary and sufficient hardness condition for sum-of-squares refutation of general random k-CSPs, generalizing the optimal density-degree-strength tradeoff beyond Boolean domains and random literals.
Machinery for proving sum-of-squares lower bounds on certification problems
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
years
2026 2representative citing papers
The minimax rate for estimating d-th order moment tensors is sqrt(p/n) wedge 1, while low-degree evidence shows detection of vanishing cumulants is hard for n much less than p to the d/2, creating a reverse detection-estimation gap.
citing papers explorer
-
Strongly Refuting Random CSP without Literals
T-wise independence is the necessary and sufficient hardness condition for sum-of-squares refutation of general random k-CSPs, generalizing the optimal density-degree-strength tradeoff beyond Boolean domains and random literals.
-
Detection Is Harder Than Estimation in Certain Regimes: Inference for Moment and Cumulant Tensors
The minimax rate for estimating d-th order moment tensors is sqrt(p/n) wedge 1, while low-degree evidence shows detection of vanishing cumulants is hard for n much less than p to the d/2, creating a reverse detection-estimation gap.