Sum-of-squares lower bounds for densest k-subgraph

C Jones, A Potechin, G Rajendran, J Xu - Proceedings of the 55th …, 2023 - dl.acm.org
Given a graph and an integer k, Densest k-Subgraph is the algorithmic task of finding the
subgraph on k vertices with the maximum number of edges. This is a fundamental problem …

Low coordinate degree algorithms I: Universality of computational thresholds for hypothesis testing

D Kunisky - arxiv preprint arxiv:2403.07862, 2024 - arxiv.org
We study when low coordinate degree functions (LCDF)--linear combinations of functions
depending on small subsets of entries of a vector--can hypothesis test between high …

Cryptographic Hardness of Score Estimation

MJ Song - Advances in Neural Information Processing …, 2025 - proceedings.neurips.cc
We show that L2-accurate score estimation, in the absence of strong assumptions on the
data distribution, is computationally hard even when sample complexity is polynomial in the …

Machinery for proving sum-of-squares lower bounds on certification problems

A Potechin, G Rajendran - arxiv preprint arxiv:2011.04253, 2020 - arxiv.org
In this paper, we construct general machinery for proving Sum-of-Squares lower bounds on
certification problems by generalizing the techniques used by Barak et al.[FOCS 2016] to …

Low coordinate degree algorithms II: Categorical signals and generalized stochastic block models

D Kunisky - arxiv preprint arxiv:2412.21155, 2024 - arxiv.org
We study when low coordinate degree functions (LCDF)--linear combinations of functions
depending on small subsets of entries of a vector--can test for the presence of categorical …

[KNYGA][B] Nonlinear Random Matrices and Applications to the Sum of Squares Hierarchy

G Rajendran - 2022 - search.proquest.com
Nonlinear random matrices and applications to the Sum of Squares hierarchy Page 1 THE
UNIVERSITY OF CHICAGO NONLINEAR RANDOM MATRICES AND APPLICATIONS TO THE …

The Spectrum of the Grigoriev–Laurent Pseudomoments

D Kunisky, C Moore - SIAM Journal on Discrete Mathematics, 2024 - SIAM
Grigoriev (2001) and Laurent (2003) independently showed that the sum-of-squares
hierarchy of semidefinite programs does not exactly represent the hypercube until degree at …