REVIEW 2 cited by
The square root rank of the correlation polytope is exponential
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
The square root rank of a nonnegative matrix $A$ is the minimum rank of a matrix $B$ such that $A=B \circ B$, where $\circ$ denotes entrywise product. We show that the square root rank of the slack matrix of the correlation polytope is exponential. Our main technique is a way to lower bound the rank of certain matrices under arbitrary sign changes of the entries using properties of the roots of polynomials in number fields. The square root rank is an upper bound on the positive semidefinite rank of a matrix, and corresponds the special case where all matrices in the factorization are rank-one.
Forward citations
Cited by 2 Pith papers
-
On the Complexity of Low-Rank Matrix Signing and Entrywise Power Matrix Factorization
Exact low-rank matrix signing is strongly NP-hard in general, polynomial-time for fixed rank and FPT for generic matrices, while Frobenius approximation is already NP-hard at rank 2.
-
Alternating Direction Method of Multipliers for Nonlinear Matrix Decompositions
An ADMM-based framework solves nonlinear matrix factorizations (ReLU, square, MinMax, modulus) under three loss functions with closed-form updates and missing-data support, and outperforms the prior coordinate-descent...
Discussion (0). Continue with ORCID to comment.