相关论文: A sharper Magnus expansion bound woven in binary b…

We conclude our work [arXiv:2403.07628, arXiv:2503.12644] on asymptotic expansions at the soft edge for the classical $n$-dimensional Gaussian and Laguerre ensembles, now studying the gap-probability generating functions. We show that the…

A compact and accurate solution method is provided for problems whose infinite power series solution diverges and/or whose series coefficients are only known up to a finite order. The method only requires that either the power series…

Let $A$ be an isotropic, sub-gaussian $m \times n$ matrix. We prove that the process $Z_x := \|Ax\|_2 - \sqrt m \|x\|_2$ has sub-gaussian increments. Using this, we show that for any bounded set $T \subseteq \mathbb{R}^n$, the deviation of…

Gaussian graphical models (GGMs) are widely used for statistical modeling, because of ease of inference and the ubiquitous use of the normal distribution in practical approximations. However, they are also known for their limited modeling…

Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the…

Automated mathematical reasoning is a challenging problem that requires an agent to learn algebraic patterns that contain long-range dependencies. Two particular tasks that test this type of reasoning are (1) mathematical equation…

We prove the existence of a 1/N expansion in unitary multimatrix models which are Gibbs perturbations of the Haar measure, and express the expansion coefficients recursively in terms of the unique solution of a noncommutative initial value…

The tree based representation described in this paper, hereditarily binary numbers, applies recursively a run-length compression mechanism that enables computations limited by the structural complexity of their operands rather than by their…

We deal with the efficient parallelization of Bayesian global optimization algorithms, and more specifically of those based on the expected improvement criterion and its variants. A closed form formula relying on multivariate Gaussian…

Infinite-activity completely random measures (CRMs) have become important building blocks of complex Bayesian nonparametric models. They have been successfully used in various applications such as clustering, density estimation, latent…

We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our…

For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…

This paper investigates the a-posteriori analysis of Branch-and-Bound~(BB) trees to extract structural information about the feasible region of mixed-binary linear programs. We introduce three novel outer approximations of the feasible…

We introduce templates for exponential asymptotic expansions that, in contrast to matched asymptotic approaches, enable the simultaneous satisfaction of both boundary values in classes of linear and nonlinear equations that are singularly…

Decision trees are important both as interpretable models amenable to high-stakes decision-making, and as building blocks of ensemble methods such as random forests and gradient boosting. Their statistical properties, however, are not well…

The truncation operation facilitates the articulation and analysis of several aspects of the structure of archimedean vector lattices; we investigate two such aspects in this article. We refer to archimedean vector lattices equipped with a…

If the numerical range of a matrix is contained in the right half of the complex plane, the GMRES algorithm for solving linear systems will reduce the norm of the residual at every iteration. In his Ph.D. dissertation, Howard Elman derived…

We prove non-asymptotic stretched exponential tail bounds on the height of a randomly sampled node in a random combinatorial tree, which we use to prove bounds on the heights and widths of random trees from a variety of models. Our results…

Rationalization is to employ a generator and a predictor to construct a self-explaining NLP model in which the generator selects a subset of human-intelligible pieces of the input text to the following predictor. However, rationalization…

We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error…