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Reduced precision computation for deep neural networks is one of the key areas addressing the widening compute gap driven by an exponential growth in model size. In recent years, deep learning training has largely migrated to 16-bit…
Post-training weight quantization is crucial for reducing the memory and inference cost of large language models (LLMs), yet pushing the average precision below 4 bits remains challenging due to highly non-uniform weight sensitivity and the…
Fast numerical libraries have been a cornerstone of scientific computing for decades, but this comes at a price. Programs may be tied to vendor specific software ecosystems resulting in polluted, non-portable code. As we enter an era of…
GlobalBioIm is an open-source MATLAB library for solving inverse problems. The library capitalizes on the strong commonalities between forward models to standardize the resolution of a wide range of imaging inverse problems. Endowed with an…
Floating-point arithmetic performance determines the overall performance of important applications, from graphics to AI. Meeting the IEEE-754 specification for floating-point requires that final results of addition, subtraction,…
We provide a technique to obtain explicit bounds for problems that can be reduced to linear forms in three complex logarithms of algebraic numbers. This technique can produce bounds significantly better than general results on lower bounds…
Floating-point computations are quickly finding their way in the design of safety- and mission-critical systems, despite the fact that designing floating-point algorithms is significantly more difficult than designing integer algorithms.…
Large Language Models (LLMs) are increasingly used for educational support, yet their response quality varies depending on the language of interaction. This paper presents an automated multilingual pipeline for generating, solving, and…
Provably correct software is one of the key challenges in our softwaredriven society. While formal verification establishes the correctness of a given program, the result of program synthesis is a program which is correct by construction.…
Low-precision formats have proven to be an efficient way to reduce not only the memory footprint but also the hardware resources and power consumption of deep learning computations. Under this premise, the posit numerical format appears to…
We present a novel relaxation framework for general mixed-integer nonlinear programming (MINLP) grounded in computational geometry. Our approach constructs polyhedral relaxations by convexifying finite sets of strategically chosen points,…
Finite-precision floating point arithmetic unavoidably introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be…
In this paper, we consider the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network resources to meet diverse…
In this paper, a library-based synthesis methodology for reversible circuits is proposed where a reversible specification is considered as a permutation comprising a set of cycles. To this end, a pre-synthesis optimization step is…
The Lean mathematical library mathlib is developed by a community of users with very different backgrounds and levels of experience. To lower the barrier of entry for contributors and to lessen the burden of reviewing contributions, we have…
Primitive polynomials over finite fields are crucial for various domains of computer science, including classical pseudo-random number generation, coding theory and post-quantum cryptography. Nevertheless, the pursuit of an efficient…
We introduce new rounding methods to improve the accuracy of finite precision quantum arithmetic. These quantum rounding methods are applicable when multiple samples are being taken from a quantum program. We show how to use multiple…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness…
Current methods for compressing neural network weights, such as decomposition, pruning, quantization, and channel simulation, often overlook the inherent symmetries within these networks and thus waste bits on encoding redundant…