Related papers: Solving Linear Algebra by Program Synthesis
In this paper, we propose a new data synthesis method called \textbf{LogicPro}, which leverages LeetCode-style algorithm \underline{Pro}blems and their corresponding \underline{Pro}gram solutions to synthesize Complex \underline{Logic}al…
We introduce CS1QA, a dataset for code-based question answering in the programming education domain. CS1QA consists of 9,237 question-answer pairs gathered from chat logs in an introductory programming class using Python, and 17,698…
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
Convex polyhedral abstractions of logic programs have been found very useful in deriving numeric relationships between program arguments in order to prove program properties and in other areas such as termination and complexity analysis. We…
The IPARC Challenge, inspired by ARC, provides controlled program synthesis tasks over synthetic images to evaluate automatic program construction, focusing on sequence, selection, and iteration. This set of 600 tasks has resisted automated…
Large language models have demonstrated impressive capabilities across various natural language processing tasks, especially in solving mathematical problems. However, large language models are not good at math theorem proving using formal…
In this paper, we provide an elementary, geometric, and unified framework to analyze conic programs that we call the strict complementarity approach. This framework allows us to establish error bounds and quantify the sensitivity of the…
Nonlinear programming is explicitly analyzed via a novel perspective/method and from a bottom-up manner. The philosophy is based on the recent findings on convex quadratic equation (CQE), which help clarify a geometric interpretation that…
Generative AI (GenAI) models have broad implications for education in general, impacting the foundations of what we teach and how we assess. This is especially true in computing, where LLMs tuned for coding have demonstrated shockingly good…
We analyzed effectiveness of three generative pre-trained transformer (GPT) models in answering multiple-choice question (MCQ) assessments, often involving short snippets of code, from introductory and intermediate programming courses at…
Large language models (LLMs) have shown great potential in automating significant aspects of coding by producing natural code from informal natural language (NL) intent. However, when interacting with LLMs, users have no guarantees that the…
Learning neural program embeddings is key to utilizing deep neural networks in program languages research --- precise and efficient program representations enable the application of deep models to a wide range of program analysis tasks.…
Sparse linear algebra is central to many scientific programs, yet compilers fail to optimize it well. High-performance libraries are available, but adoption costs are significant. Moreover, libraries tie programs into vendor-specific…
Indefinite quadratic programs (QPs) are known to be very difficult to be solved to global optimality, so are linear programs with linear complementarity constraints. Treating the former as a subclass of the latter, this paper presents a…
We consider convex programming problems with integrality constraints that are invariant under a linear symmetry group. To decompose such problems we introduce the new concept of core points, i.e., integral points whose orbit polytopes are…
This work introduces (1) a technique that allows large language models (LLMs) to leverage user-provided code when solving programming tasks and (2) a method to iteratively generate modular sub-functions that can aid future code generation…
We introduce a set of eight universal Rules of Inference by which computer programs with known properties (axioms) are transformed into new programs with known properties (theorems). Axioms are presented to formalize a segment of Number…
Tools for rewriting, refactoring and optimizing code should be fast and correct. Large language models (LLMs), by their nature, possess neither of these qualities. Yet, there remains tremendous opportunity in using LLMs to improve code. We…
This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…
This paper presents an AI-driven approach to enhance math learning in a modern Learning Management System (LMS) by recommending similar math questions. Deep embeddings for math questions are generated using Meta's…