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Sum-of-squares lower bounds for densest k-subgraph
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 …
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 …
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 …
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 …
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 …
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 …
UNIVERSITY OF CHICAGO NONLINEAR RANDOM MATRICES AND APPLICATIONS TO THE …
The Spectrum of the Grigoriev–Laurent Pseudomoments
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 …
hierarchy of semidefinite programs does not exactly represent the hypercube until degree at …