相关论文: A priori bounds for certified Krawczyk homotopy tr…

Learned index structures aim to accelerate queries by training machine learning models to approximate the rank function associated with a database attribute. While effective in practice, their theoretical limitations are not fully…

When utilising PAC-Bayes theory for risk certification, it is usually necessary to estimate and bound the Gibbs risk of the PAC-Bayes posterior. Many works in the literature employ a method for this which requires a large number of passes…

Transcorrelated coupled cluster and distinguishable cluster methods are presented. The Hamiltonian is similarity transformed with a Jastrow factor in the first quantisation, which results in up to three-body integrals. The coupled cluster…

Various performance measures based on the ground truth and without ground truth exist to evaluate the quality of a developed tracking algorithm. The existing popular measures - average center location error (ACLE) and average tracking…

We introduce a simple framework for estimating lower bounds on the runtime of a broad class of adiabatic quantum algorithms. The central formula consists of calculating the variance of the final Hamiltonian with respect to the initial…

The model checking problem for various fragments of first-order logic has attracted much attention over the last two decades: in particular, for the primitive positive and the positive Horn fragments, which are better known as the…

We address a specific but recurring problem related to sampled linear systems. In particular, we provide a numerical method for the rigorous verification of constraint satisfaction for linear continuous-time systems between sampling…

This paper studies theoretical lower bounds for estimating the trace of a matrix function, $\text{tr}(f(A))$, focusing on methods that use Hutchinson's method along with Block Krylov techniques. These methods work by approximating…

The paper investigates algorithmic complexity of monadic multimodal predicate logics with equality over finite Kripke frames or classes of finite Kripke frames. Precise complexity bounds for monadic logics of classes of Kripke frames with…

We study the time complexity of the weighted first-order model counting (WFOMC) over the logical language with two variables and counting quantifiers. The problem is known to be solvable in time polynomial in the domain size. However, the…

Many systems of interest in cryptography consist of equations of the same degree. Under the assumption that the degree of regularity is finite, we prove upper bounds on the degree of regularity of a system of equations of the same degree,…

Ollivier-Ricci curvature (ORC), defined via the Wasserstein distance that captures rich geometric information, has received growing attention in both theory and applications. However, the high computational cost of Wasserstein distance…

We consider the problem of sampling a high dimensional multimodal target probability measure. We assume that a good proposal kernel to move only a subset of the degrees of freedoms (also known as collective variables) is known a priori.…

We investigate the initial-boundary value problem for linearized gravitational theory in harmonic coordinates. Rigorous techniques for hyperbolic systems are applied to establish well-posedness for various reductions of the system into a…

Consider the multiple testing problem of testing k null hypotheses, where the unknown family of distributions is assumed to satisfy a certain monotonicity assumption. Attention is restricted to procedures that control the familywise error…

Counting integer solutions of linear constraints has found interesting applications in various fields. It is equivalent to the problem of counting lattice points inside a polytope. However, state-of-the-art algorithms for this problem…

Language model reasoning traces are rarely all-or-nothing; they frequently contain valid intermediate steps before a critical error occurs. Existing uncertainty quantification methods typically certify final answers or entire responses,…

We consider the Helmholtz transmission problem with one penetrable star-shaped Lipschitz obstacle. Under a natural assumption about the ratio of the wavenumbers, we prove bounds on the solution in terms of the data, with these bounds…

A prototypical problem on which techniques for exact enumeration are tested and compared is the enumeration of self-avoiding walks. Here, we show an advance in the methodology of enumeration, making the process thousands or millions of…

Concise complexity analyses are presented for simple trust region algorithms for solving unconstrained optimization problems. In contrast to a traditional trust region algorithm, the algorithms considered in this paper require certain…