Related papers: Lower Bounds against the Ideal Proof System in Fin…
In this paper, we prove super-polynomial lower bounds for the model of \emph{sum of ordered set-multilinear algebraic branching programs}, each with a possibly different ordering ($\sum \mathsf{smABP}$). Specifically, we give an explicit…
We revisit the Raz-Safra plane-vs.-plane test and study the closely related cube vs. cube test. In this test the tester has access to a "cubes table" which assigns to every cube a low degree polynomial. The tester randomly selects two cubes…
We consider the top tree compression scheme introduced by Bille et al. [ICALP 2013] and construct an infinite family of trees on $n$ nodes labeled from an alphabet of size $\sigma$, for which the size of the top DAG is…
We prove that the most natural low-degree test for polynomials over finite fields is ``robust'' in the high-error regime for linear-sized fields. Specifically we consider the ``local'' agreement of a function $f: \mathbb{F}_q^m \to…
Gordeev and Haeusler [GH19] claim that each tautology $\rho$ of minimal propositional logic can be proved with a natural deduction of size polynomial in $|\rho|$. This builds on work from Hudelmaier [Hud93] that found a similar result for…
We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…
Existing few-shot segmentation (FSS) methods mainly focus on designing novel support-query matching and self-matching mechanisms to exploit implicit knowledge in pre-trained backbones. However, the performance of these methods is often…
The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain infinitely many…
Fine-grained visual categorization (FGVC) is a challenging task due to similar visual appearances between various species. Previous studies always implicitly assume that the training and test data have the same underlying distributions, and…
In this work, we improve upon the guarantees for sparse random embeddings, as they were recently provided and analyzed by Freksen at al. (NIPS'18) and Jagadeesan (NIPS'19). Specifically, we show that (a) our bounds are explicit as opposed…
During design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A levelset description of…
We prove the #P-hardness of the counting problems associated with various satisfiability, graph and combinatorial problems, when restricted to planar instances. These problems include \begin{romannum} \item[{}] {\sc 3Sat, 1-3Sat, 1-Ex3Sat,…
We present and discuss general techniques for proving inapproximability results for truthful mechanisms. We make use of these techniques to prove lower bounds on the approximability of several non-utilitarian multi-parameter problems. In…
Recent Leibniz scholarship has sought to gauge which foundational framework provides the most successful account of the procedures of the Leibnizian calculus (LC). While many scholars (e.g., Ishiguro, Levey) opt for a default Weierstrassian…
Recently, Balliu, Brandt, and Olivetti [FOCS '20] showed the first $\omega(\log^* n)$ lower bound for the maximal independent set (MIS) problem in trees. In this work we prove lower bounds for a much more relaxed family of distributed…
We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…
Recent advances in large language models (LLMs) have demonstrated impressive capabilities in formal theorem proving, particularly on contest-based mathematical benchmarks like the IMO. However, these contests do not reflect the depth,…
Large-scale subset selection asks for a small useful set of examples, features, sensors, seed users, or context passages from an enormous ground set. Submodular maximization is a canonical model for such diminishing-returns problems, but…
In conic linear programming -- in contrast to linear programming -- the Lagrange dual is not an exact dual: it may not attain its optimal value, or there may be a positive duality gap. The corresponding Farkas' lemma is also not exact (it…
We develop an automated framework for proving lower bounds on the bilinear complexity of matrix multiplication over finite fields. Our approach systematically combines orbit classification of the restricted first matrix and dynamic…