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Evaluating real-valued expressions to high precision is a key building block in computational mathematics, physics, and numerics. A typical implementation evaluates the whole expression in a uniform precision, doubling that precision until…

Numerical Analysis · Mathematics 2025-04-21 Artem Yadrov , Pavel Panchekha

Evaluating real-valued expressions to high precision is a key building block in computational mathematics, physics, and numerics. A typical implementation evaluates the whole expression in a uniform precision, doubling that precision until…

Mathematical Software · Computer Science 2025-08-13 Artem Yadrov , Pavel Panchekha

Recent research has shown that large language models (LLMs) can utilize low-precision floating point (FP) quantization to deliver high efficiency while maintaining original model accuracy. In particular, recent works have shown the…

Hardware Architecture · Computer Science 2025-06-05 Faraz Tahmasebi , Yian Wang , Benji Y. H. Huang , Hyoukjun Kwon

Parameter-efficient fine-tuning (PEFT) techniques, such as adapter tuning, aim to fine-tune a pre-trained language model (PLM) using a minimal number of parameters for a specific task or profile. Although adapter tuning provides increased…

Machine Learning · Computer Science 2024-01-30 Namju Kwak , Taesup Kim

We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this…

Optimization and Control · Mathematics 2021-03-30 Ben Beach , Robert Hildebrand , Joey Huchette

Test Amplification is a method to extend handwritten tests into a more rigorous test suite covering corner cases in the system under test. Unfortunately, the current state-of-the-art for test amplification heavily relies on program analysis…

Software Engineering · Computer Science 2021-12-22 Ebert Schoofs , Mehrdad Abdi , Serge Demeyer

We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer…

Optimization and Control · Mathematics 2016-06-02 Miles Lubin , Emre Yamangil , Russell Bent , Juan Pablo Vielma

Model predictive control problems for constrained hybrid systems are usually cast as mixed-integer optimization problems (MIP). However, commercial MIP solvers are designed to run on desktop computing platforms and are not suited for…

Optimization and Control · Mathematics 2020-02-05 Damian Frick , Angelos Georghiou , Juan L. Jerez , Alexander Domahidi , Manfred Morari

In recent years fused-multiply-add (FMA) units with lower-precision multiplications and higher-precision accumulation have proven useful in machine learning/artificial intelligence applications, most notably in training deep neural networks…

Mathematical Software · Computer Science 2019-04-16 Greg Henry , Ping Tak Peter Tang , Alexander Heinecke

Scientific machine learning (SciML) has emerged as a versatile approach to address complex computational science and engineering problems. Within this field, physics-informed neural networks (PINNs) and deep operator networks (DeepONets)…

Machine Learning · Computer Science 2024-01-31 Joel Hayford , Jacob Goldman-Wetzler , Eric Wang , Lu Lu

In this paper we use Python to implement two efficient modular exponentiation methods: the adaptive m-ary method and the adaptive sliding-window method of window size k, where both m's are adaptively chosen based on the length of exponent.…

Data Structures and Algorithms · Computer Science 2017-07-10 Shiyu Ji , Kun Wan

The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting of two stages: first, a coarse approximation is obtained by manipulating the bit pattern of the floating point argument using integer…

Numerical Analysis · Mathematics 2023-07-31 Mike Day

Automated paper reproduction has emerged as a promising approach to accelerate scientific research, employing multi-step workflow frameworks to systematically convert academic papers into executable code. However, existing frameworks often…

Artificial Intelligence · Computer Science 2025-12-03 Zijie Lin , Qilin Cai , Liang Shen , Mingjun Xiao

The goal of this paper is to reduce the total complexity of gradient-based methods for two classes of problems: affine-constrained composite convex optimization and bilinear saddle-point structured non-smooth convex optimization. Our…

Optimization and Control · Mathematics 2022-01-05 Qihang Lin , Yangyang Xu

Floating point multiplication is one of the crucial operations in many application domains such as image processing, signal processing etc. But every application requires different working features. Some need high precision, some need low…

Hardware Architecture · Computer Science 2020-12-08 S. Arish , R. K. Sharma

We investigate the use of low-precision first-order methods (FOMs) within a fix-and-propagate (FP) framework for solving mixed-integer programming problems (MIPs). We employ GPU-accelerated PDLP, a variant of the Primal-Dual Hybrid Gradient…

Optimization and Control · Mathematics 2026-03-05 Nils-Christian Kempke , Thorsten Koch

In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform…

Numerical Analysis · Mathematics 2010-01-12 Burak Aksoylu , Stephen Bond , Michael Holst

In this paper, we present a work in progress about a deep learning based approach for automatic code optimization in polyhedral compilers. The proposed technique explores combinations of affine and non-affine loop transformations to find…

Parameter-Efficient Fine-tuning (PEFT) facilitates the fine-tuning of Large Language Models (LLMs) under limited resources. However, the fine-tuning performance with PEFT on complex, knowledge-intensive tasks is limited due to the…

Computation and Language · Computer Science 2024-06-10 Jitai Hao , WeiWei Sun , Xin Xin , Qi Meng , Zhumin Chen , Pengjie Ren , Zhaochun Ren

In this project, we have successfully designed, implemented, deployed and tested a novel FPGA accelerated algorithm for neural network training. The algorithm itself was developed in an independent study option. This training method is…

Machine Learning · Computer Science 2020-09-08 Seyedeh Niusha Alavi Foumani , Ce Guo , Wayne Luk