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We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
Large Language Models (LLMs) have grown increasingly expensive to deploy, driving the need for effective model compression techniques. While block pruning offers a straightforward approach to reducing model size, existing methods often…
Integer programming (IP), as the name suggests is an integer-variable-based approach commonly used to formulate real-world optimization problems with constraints. Currently, quantum algorithms reformulate the IP into an unconstrained form…
Large language models (LLMs) have shown increasing competence in solving mathematical reasoning problems. However, many open-source LLMs still struggle with errors in calculation and semantic understanding during intermediate reasoning…
Apache Spark is a popular open-source platform for large-scale data processing that is well-suited for iterative machine learning tasks. In this paper we present MLlib, Spark's open-source distributed machine learning library. MLlib…
An algorithm $M$ is described that solves any well-defined problem $p$ as quickly as the fastest algorithm computing a solution to $p$, save for a factor of 5 and low-order additive terms. $M$ optimally distributes resources between the…
For an easy use of model order reduction techniques in applications, software solutions are needed. In this paper, we describe the MORLAB, Model Order Reduction LABoratory, toolbox as an efficient implementation of model reduction…
Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations.…
This paper presents TIRA, a Matlab library gathering several methods for the computation of interval over-approximations of the reachable sets for both continuous- and discrete-time nonlinear systems. Unlike other existing tools, the main…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
Answer Set Programming (ASP) is a truly-declarative programming paradigm proposed in the area of non-monotonic reasoning and logic programming, that has been recently employed in many applications. The development of efficient ASP systems…
This paper proposes a novel primal heuristic for Mixed Integer Programs, by employing machine learning techniques. Mixed Integer Programming is a general technique for formulating combinatorial optimization problems. Inside a solver, primal…
Leveraging machine learning (ML) to predict an initial solution for mixed-integer linear programming (MILP) has gained considerable popularity in recent years. These methods predict a solution and fix a subset of variables to reduce the…
Nature apparently does a lot of computation constantly. If we can harness some of that computation at an appropriate level, we can potentially perform certain type of computation (much) faster and more efficiently than we can do with a von…
This paper presents a novel approach to the joint optimization of job scheduling and data allocation in grid computing environments. We formulate this joint optimization problem as a mixed integer quadratically constrained program. To…
Speed-robust scheduling is the following two-stage problem of scheduling $n$ jobs on $m$ uniformly related machines. In the first stage, the algorithm receives the value of $m$ and the processing times of $n$ jobs; it has to partition the…
We provide a detailed user guide for SMARTIES, a suite of Matlab codes for the calculation of the optical properties of oblate and prolate spheroidal particles, with comparable capabilities and ease-of-use as Mie theory for spheres.…
Linear algebra expressions, which play a central role in countless scientific computations, are often computed via a sequence of calls to existing libraries of building blocks (such as those provided by BLAS and LAPACK). A sequence…
Neural graphics primitives are faster and achieve higher quality when their neural networks are augmented by spatial data structures that hold trainable features arranged in a grid. However, existing feature grids either come with a large…
Achieving speed and accuracy for math library functions like exp, sin, and log is difficult. This is because low-level implementation languages like C do not help math library developers catch mathematical errors, build implementations…