Related papers: Improvements to Jacobian Arithmetic in Global Func…
This paper presents an efficient method for extracting the second-order sensitivities from a system of implicit nonlinear equations on upcoming graphical processing units (GPU) dominated computer systems. We design a custom automatic…
This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations…
Due to the increasing demand for high performance and cost reduction within the framework of complex system design, numerical optimization of computationally costly problems is an increasingly popular topic in most engineering fields. In…
We present classical and quantum algorithms for approximating partition functions of classical Hamiltonians at a given temperature. Our work has two main contributions: first, we modify the classical algorithm of \v{S}tefankovi\v{c},…
Nonconvex optimization problems are widespread in modern machine learning and data science. We introduce an extrapolation strategy into a class of preconditioned second-order convex splitting algorithms for nonconvex optimization problems.…
Efficient gradient computation of the Jacobian determinant term is a core problem in many machine learning settings, and especially so in the normalizing flow framework. Most proposed flow models therefore either restrict to a function…
We present an algorithm for minimizing a sum of functions that combines the computational efficiency of stochastic gradient descent (SGD) with the second order curvature information leveraged by quasi-Newton methods. We unify these…
Model-based sequential approaches to discrete "black-box" optimization, including Bayesian optimization techniques, often access the same points multiple times for a given objective function in interest, resulting in many steps to find the…
Complex computer codes are often too time expensive to be directly used to perform uncertainty propagation studies, global sensitivity analysis or to solve optimization problems. A well known and widely used method to circumvent this…
In this paper, we study optimization methods consisting of iteratively minimizing surrogates of an objective function. By proposing several algorithmic variants and simple convergence analyses, we make two main contributions. First, we…
Dual quaternion matrices have various applications in robotic research and its spectral theory has been extensively studied in recent years. In this paper, we extend Jacobi method to compute all eigenpairs of dual quaternion Hermitian…
In this paper, we analyze a generic algorithm scheme for sequential global optimization using Gaussian processes. The upper bounds we derive on the cumulative regret for this generic algorithm improve by an exponential factor the previously…
We present two new algorithms for solving norm equations over global function fields with at least one infinite place of degree 1 and no wild ramification. The first of these is a substantial improvement of a method due to Ga\'{a}l and…
In this paper we propose two proximal gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either…
The Jacobian Conjecture states that any locally invertible polynomial system in C^n is globally invertible with polynomial inverse. C. W. Bass et al. (1982) proved a reduction theorem stating that the conjecture is true for any degree of…
Bayesian optimization is a popular formalism for global optimization, but its computational costs limit it to expensive-to-evaluate functions. A competing, computationally more efficient, global optimization framework is optimistic…
Data selection improves computational efficiency by choosing informative subsets of training samples. However, existing methods ignore the compute budget, treating data selection and importance evaluation independently of compute budget…
We derive an explicit formula, as well as an efficient procedure, for constructing a generalized Jacobian for the projector of a given square matrix onto the Birkhoff polytope, i.e., the set of doubly stochastic matrices. To guarantee the…
We describe efficient differentiation methods for computing Jacobians and gradients of a large class of matrix functions including the matrix logarithm $\log(A)$ and $p$-th roots $A^{\frac{1}{p}}$. We exploit contour integrals and conformal…
We use the well-known observation that the solutions of Jacobi's differential equation can be represented via non-oscillatory phase and amplitude functions to develop a fast algorithm for computing multi-dimensional Jacobi polynomial…