Related papers: Solving Linear Algebra by Program Synthesis

We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…

Can a machine learn Machine Learning? This work trains a machine learning model to solve machine learning problems from a University undergraduate level course. We generate a new training set of questions and answers consisting of course…

This article explores the natural language generation capabilities of large language models with application to the production of two types of learning resources common in programming courses. Using OpenAI Codex as the large language model,…

The ability to think abstractly and reason by analogy is a prerequisite to rapidly adapt to new conditions, tackle newly encountered problems by decomposing them, and synthesize knowledge to solve problems comprehensively. We present…

As soon as a new technology emerges, the education community explores its affordances and the possibilities to apply it in education. In this paper, we analyze sessions with ChatGPT around topics in basic Linear Algebra. We reflect the…

Large language models, such as OpenAI's codex and Deepmind's AlphaCode, can generate code to solve a variety of problems expressed in natural language. This technology has already been commercialised in at least one widely-used programming…

Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…

Large reasoning models (LRMs) like OpenAI-o1 have shown impressive capabilities in natural language reasoning. However, these models frequently demonstrate inefficiencies or inaccuracies when tackling complex mathematical operations. While…

Large language models (LLMs) have made significant strides in code generation, achieving impressive capabilities in synthesizing code snippets from natural language instructions. However, a critical challenge remains in ensuring LLMs…

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…

We present a self-learning approach for synthesizing programs from integer sequences. Our method relies on a tree search guided by a learned policy. Our system is tested on the On-Line Encyclopedia of Integer Sequences. There, it discovers,…

Instructing large language models (LLMs) to solve elementary school math problems has shown great success using Chain of Thought (CoT). However, the CoT approach relies on an LLM to generate a sequence of arithmetic calculations which can…

Assessing student's answers and in particular natural language answers is a crucial challenge in the field of education. Advances in machine learning, including transformer-based models such as Large Language Models(LLMs), have led to…

We argue that reducing nonlinear programming problems to a simple canonical form is an effective way to analyze them, specially when the problem is degenerate and the usual linear independence hypothesis does not hold. To illustrate this…

When giving automated feedback to a student working on a beginner's exercise, many programming tutors run into a completeness problem. On the one hand, we want a student to experiment freely. On the other hand, we want a student to write…

Despite rapid progress in the field, it is still challenging to discover new ways to take advantage of quantum computation: all quantum algorithms need to be designed by hand, and quantum mechanics is notoriously counterintuitive. In this…

We consider feasibility of linear integer programs in the context of verification systems such as SMT solvers or theorem provers. Although satisfiability of linear integer programs is decidable, many state-of-the-art solvers neglect…

Computing students increasingly rely on generative AI tools for programming assistance, often without formal instruction or guidance. This highlights a need to teach students how to effectively interact with AI models, particularly through…