Related papers: Generalized ODE reduction algorithm for bounded de…
A wide range of modern science and engineering applications are formulated as optimization problems with a system of partial differential equations (PDEs) as constraints. These PDE-constrained optimization problems are typically solved in a…
In this paper, we develop a simple and fast online algorithm for solving a class of binary integer linear programs (LPs) arisen in general resource allocation problem. The algorithm requires only one single pass through the input data and…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
Learning new tasks by drawing on prior experience gathered from other (related) tasks is a core property of any intelligent system. Gradient-based meta-learning, especially MAML and its variants, has emerged as a viable solution to…
We propose a method to enhance the stability of a neural ordinary differential equation (neural ODE) by reducing the maximum error growth subsequent to a perturbation of the initial value. Since the stability depends on the logarithmic norm…
We propose a novel algorithm for combined unit and layer pruning of deep neural networks that functions during training and without requiring a pre-trained network to apply. Our algorithm optimally trades-off learning accuracy and pruning…
We focus on learning unknown dynamics from data using ODE-nets templated on implicit numerical initial value problem solvers. First, we perform Inverse Modified error analysis of the ODE-nets using unrolled implicit schemes for ease of…
Several problems in magnetically confined fusion, such as the computation of exterior vacuum fields or the decomposition of the total magnetic field into separate contributions from the plasma and the external sources, are best formulated…
We study distributed algorithms for expected loss minimization where the datasets are large and have to be stored on different machines. Often we deal with minimizing the average of a set of convex functions where each function is the…
We propose an efficient algorithm for finding first-order Nash equilibria in min-max problems of the form $\min_{x \in X}\max_{y\in Y} F(x,y)$, where the objective function is smooth in both variables and concave with respect to $y$; the…
We consider the first order autonomous differential equation (ODE) ${\bf x}'={\bf f}({\bf x})$ where ${\bf f}: {\mathbb R}^n\to{\mathbb R}^n$ is locally Lipschitz. For ${\bf x}_0\in{\mathbb R}^n$ and $h>0$, the initial value problem (IVP)…
While obtaining optimal algorithms for the most important problems in the LOCAL model has been one of the central goals in the area of distributed algorithms since its infancy, tight complexity bounds are elusive for many problems even when…
Bayesian Optimization (BO) has shown great promise for the global optimization of functions that are expensive to evaluate, but despite many successes, standard approaches can struggle in high dimensions. To improve the performance of BO,…
We study first-order optimization algorithms under the constraint that the descent direction is quantized using a pre-specified budget of $R$-bits per dimension, where $R \in (0 ,\infty)$. We propose computationally efficient optimization…
Online linear programming (OLP) has gained significant attention from both researchers and practitioners due to its extensive applications, such as online auction, network revenue management, order fulfillment and advertising. Existing OLP…
It was recently shown [7, 9] that "properly built" linear and polyhedral estimates nearly attain minimax accuracy bounds in the problem of recovery of unknown signal from noisy observations of linear images of the signal when the signal set…
We describe a new Maple package for treating boundary problems for linear ordinary differential equations, allowing two-/multipoint as well as Stieltjes boundary conditions. For expressing differential operators, boundary conditions, and…
A central question in mathematics and computer science is the question of determining whether a given ideal $I$ is prime, which geometrically corresponds to the zero set of $I$, denoted $Z(I)$, being irreducible. The case of principal…
We prove that counting the analytic Brouwer degree of rational coefficient polynomial maps in $\operatorname{Map}(\mathbb C^d, \mathbb C^d)$ -- presented in degree-coefficient form -- is hard for the complexity class $\operatorname{\sharp…
Partitioning algorithms play a key role in many scientific and engineering disciplines. A partitioning algorithm divides a set into a number of disjoint subsets or partitions. Often, the quality of the resulted partitions is measured by the…