Polytopes with Bounded Integral Slack Matrices Have Sub-Exponential Extension Complexity

07/30/2023
by   Sally Dong, et al.
University of Washington
0

We show that any bounded integral function f : A × B ↦{0,1, …, Δ} with rank r has deterministic communication complexity Δ^O(Δ)·√(r)·log^2 r, where the rank of f is defined to be the rank of the A × B matrix whose entries are the function values. As a corollary, we show that any n-dimensional polytope that admits a slack matrix with entries from {0,1,…,Δ} has extension complexity at most exp(Δ^O(Δ)·√(n)·log^2 n).

READ FULL TEXT

page 1

page 2

page 3

page 4

07/22/2022

Ladder Matrix Recovery from Permutations

We give unique recovery guarantees for matrices of bounded rank that hav...
07/10/2023

Randomized Communication and Implicit Representations for Matrices and Graphs of Small Sign-Rank

We prove a characterization of the structural conditions on matrices of ...
02/26/2023

Fast Attention Requires Bounded Entries

In modern machine learning, inner product attention computation is a fun...
07/15/2023

Bulk Johnson-Lindenstrauss Lemmas

For a set X of N points in ℝ^D, the Johnson-Lindenstrauss lemma provides...
01/28/2018

Adaptive Estimation of Noise Variance and Matrix Estimation via USVT Algorithm

Consider the problem of denoising a large m× n matrix. This problem has ...
05/09/2022

Tensor rank bounds and explicit QTT representations for the inverses of circulant matrices

In this paper, we are concerned with the inversion of circulant matrices...

Please sign up or login with your details

Forgot password? Click here to reset