Related papers: Lower Bounds for CSP Hierarchies Through Ideal Red…
Due to their importance in both data analysis and numerical algorithms, low rank approximations have recently been widely studied. They enable the handling of very large matrices. Tight error bounds for the computationally efficient…
We propose a non-iterative method to optimize pseudo-labeling thresholds for learning object detection from a collection of low-cost datasets, each of which is annotated for only a subset of all the object classes. A popular approach to…
A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing…
This work is concerned with approximating constraint satisfaction problems (CSPs) with an additional global cardinality constraints. For example, \maxcut is a boolean CSP where the input is a graph $G = (V,E)$ and the goal is to find a cut…
Following the success of the so-called algebraic approach to the study of decision constraint satisfaction problems (CSPs), exact optimization of valued CSPs, and most recently promise CSPs, we propose an algebraic framework for valued…
This paper analyzes to what extent it is possible to efficiently reduce the number of clauses in NP-hard satisfiability problems, without changing the answer. Upper and lower bounds are established using the concept of kernelization.…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
We introduce a new framework for unifying and systematizing the performance analysis of first-order black-box optimization algorithms for unconstrained convex minimization. The low-cost iteration complexity enjoyed by first-order algorithms…
We present a hierarchy of tractable relaxations to obtain lower bounds on the minimum value of a polynomial over a constraint set defined by polynomial equations. In contrast to previous convex relaxation techniques for this problem, our…
Locally Decodable Codes (LDCs) are error-correcting codes $C\colon\Sigma^n\rightarrow \Sigma^m,$ encoding \emph{messages} in $\Sigma^n$ to \emph{codewords} in $\Sigma^m$, with super-fast decoding algorithms. They are important mathematical…
The Sum-of-Squares (SoS) hierarchy of semidefinite programs is a powerful algorithmic paradigm which captures state-of-the-art algorithmic guarantees for a wide array of problems. In the average case setting, SoS lower bounds provide strong…
In this paper we introduce a general framework for proving lower bounds for various Ramsey type problems within random settings. The main idea is to view the problem from an algorithmic perspective: we aim at providing an algorithm that…
We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and turns out to be ``liftable'' under finite morphisms, paving…
The present work concerns spherical spin glass models with disorder satisfying a uniform logarithmic Sobolev inequality. We show that the Hessian descent algorithm introduced by Subag can be extended to this setting, thanks to the abundance…
A unital $C^*$-algebra is called $N$-subhomogeneous if its irreducible representations are finite dimensional with dimension at most $N$. We extend this notion to operator systems, replacing irreducible representations by boundary…
It has long been known, since the classical work of (Arora, Karger, Karpinski, JCSS~99), that \MC\ admits a PTAS on dense graphs, and more generally, \kCSP\ admits a PTAS on "dense" instances with $\Omega(n^k)$ constraints. In this paper we…
Constraint satisfaction problems (CSPs) are about finding values of variables that satisfy the given constraints. We show that Transformer extended with recurrence is a viable approach to learning to solve CSPs in an end-to-end manner,…
For $\nu\in[0, 1]$ let $D^\nu$ be the distinguished self-adjoint realisation of the three-dimensional Coulomb-Dirac operator $-\mathrm i\boldsymbol\alpha\cdot\nabla -\nu|\cdot|^{-1}$. For $\nu\in[0, 1)$ we prove the lower bound of the form…
We initiate a study of when the value of mathematical relaxations such as linear and semidefinite programs for constraint satisfaction problems (CSPs) is approximately preserved when restricting the instance to a sub-instance induced by a…
Strong refutation of random CSPs is a fundamental question in theoretical computer science that has received particular attention due to the long-standing gap between the information-theoretic limit and the computational limit. This gap is…