相关论文: C++ Codes of Implicit Lu Algorithms for Absdll01
In this paper, we introduce an efficient backpropagation scheme for non-constrained implicit functions. These functions are parametrized by a set of learnable weights and may optionally depend on some input; making them perfectly suitable…
We consider the solution of nonlinear equations in one real variable, the problem usually called by root finding. Although this is an old problem, we believe that some aspects of its solution using interval arithmetic are not well…
Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum…
Large language models (LLMs) have been massively applied to many tasks, often surpassing state-of-the-art approaches. While their effectiveness in code generation has been extensively studied (e.g., AlphaCode), their potential for code…
Verification of numerical accuracy properties in modern software remains an important and challenging task. This paper describes an original framework combining different solutions for numerical accuracy. First, we extend an existing…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
The paper presents AMGCL -- an opensource C++ library implementing the algebraic multigrid method (AMG) for solution of large sparse linear systems of equations, usually arising from discretization of partial differential equations on an…
In this paper, we introduce methods of encoding propositional logic programs in vector spaces. Interpretations are represented by vectors and programs are represented by matrices. The least model of a definite program is computed by…
This paper introduces PolyDiM, an open-source C++ library tailored for the development and implementation of polytopal discretization methods for partial differential equations. The library provides robust and modular tools to support…
Two semi-implicit Euler schemes for differential inclusions are proposed and analyzed in depth. An error analysis shows that both semi-implicit schemes inherit favorable stability properties from the differential inclusion. Their…
Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present…
Large language models (LLMs) are increasingly used for program verification, and yet little is known about \emph{how} they reason about program semantics during this process. In this work, we focus on abstract interpretation based-reasoning…
In an underdetermined system of equations $Ax=y$, where $A$ is an $m\times n$ matrix, only $u$ of the entries of $y$ with $u < m$ are known. Thus $E_jw$, called `measurements', are known for certain $j\in J \subset \{0,1,\ldots,m-1\}$ where…
Assisting LLMs with code generation improved their performance on mathematical reasoning tasks. However, the evaluation of code-assisted LLMs is generally restricted to execution correctness, lacking a rigorous evaluation of their generated…
A visual programming language uses pictorial tools such as diagrams to represent its structural units and control stream. It is useful for enhancing understanding, maintenance, verification, testing, and parallelism. This paper proposes a…
In this paper we present Affine.m - program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. Algorithms are based upon the properties of weights and Weyl symmetry.…
We present an algorithm for the classification of linear codes over finite fields, based on lattice point enumeration. We validate a correct implementation of our algorithm with known classification results from the literature, which we…
The aim of this work is to define and implement an extended C++ language to support the SIMD programming paradigm. The C++ programming language has been extended to express all the potentiality of an abstract SIMD machine consisting of a…
Computational notebooks became indispensable tools for research-related development, offering unprecedented interactivity and flexibility in the development process. However, these benefits come at the cost of reproducibility and an…
In this work, we explore explicit Large Language Model (LLM)-powered support for the iterative design of computer programs. Program design, like other design activity, is characterized by navigating a space of alternative problem…