Related papers: Solving Linear Algebra by Program Synthesis

Synthesizing a program that realizes a logical specification is a classical problem in computer science. We examine a particular type of program synthesis, where the objective is to synthesize a strategy that reacts to a potentially…

Linear algebra is a major field of numerical computation and is widely applied. Most linear algebra libraries (in most programming languages) do not statically guarantee consistency of the dimensions of vectors and matrices, causing runtime…

We suggest that straight-line programs designed for algebraic computations should be accompanied by a comprehensive complexity analysis that takes into account both the number of fundamental algebraic operations needed, as well as memory…

We present a novel approach to the automatic synthesis of recursive programs from mixed-quantifier first-order logic properties. Our approach uses Skolemization to reduce the mixed-quantifier synthesis problem to a $\forall^*$-synthesis…

In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…

Large language models (LLMs) excel at implementing code from functionality descriptions but struggle with algorithmic problems that require not only implementation but also identification of the suitable algorithm. Moreover, LLM-generated…

Open coding, a key inductive step in qualitative research, discovers and constructs concepts from human datasets. However, capturing extensive and nuanced aspects or "coding moments" can be challenging, especially with large discourse…

We study a mixed integer linear program with m integer variables and k non-negative continuous variables in the form of the relaxation of the corner polyhedron that was introduced by Andersen, Louveaux, Weismantel and Wolsey [Inequalities…

Transformers can learn to perform numerical computations from examples only. I study nine problems of linear algebra, from basic matrix operations to eigenvalue decomposition and inversion, and introduce and discuss four encoding schemes to…

A new system of library code is proposed and initiated. It is emphasized that the same terminologies as we find in our textbooks should be used for class names in the library code. The language C# invented by Microsoft is adopted in this…

Flipped classroom pedagogy is widely used in undergraduate mathematics to promote active learning, yet it remains unclear whether students experience it in systematically different ways. In this study, we analyze student perceptions from an…

Linear programming describes the problem of optimising a linear objective function over a set of constraints on its variables. In this paper we present a solver for linear programs implemented in the proof assistant Isabelle/HOL. This…

This paper tackles the challenge of teaching code semantics to Large Language Models (LLMs) for program analysis by incorporating code symmetries into the model architecture. We introduce a group-theoretic framework that defines code…

Writing competitive programming problems is exacting. Authors must: set constraints, input distributions, and edge cases that rule out shortcuts; target specific algorithms (e.g., max-flow, dynamic programming, data structures); and…

There is a growing trend of teaching large language models (LLMs) to solve mathematical problems through coding. Existing studies primarily focus on prompting powerful, closed-source models to generate seed training data followed by…

Program synthesis strives to generate a computer program as a solution to a given problem specification, expressed with input-output examples or natural language descriptions. The prevalence of large language models advances the…

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…

Code generation by Llama 3.1 models, such as Meta's Llama 3.1 405B, represents a significant advancement in the field of artificial intelligence, particularly in natural language processing and programming automation. This paper explores…

We present a finitely convergent cutting-plane algorithm for solving a general mixed-integer convex program given an oracle for solving a general convex program. This method is extended to solve a family of two-stage mixed-integer convex…

Program synthesis with Large Language Models (LLMs) suffers from a "near-miss syndrome": the generated code closely resembles a correct solution but fails unit tests due to minor errors. We address this with a multi-agent framework called…