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Computer Science > Machine Learning

arXiv:2112.15594 (cs)
[Submitted on 31 Dec 2021 (v1), last revised 4 Jan 2022 (this
version, v2)]

Title:A Neural Network Solves and Generates Mathematics Problems by
Program Synthesis: Calculus, Differential Equations, Linear Algebra,
and More

Authors:Iddo Drori, Sunny Tran, Roman Wang, Newman Cheng, Kevin Liu,
Leonard Tang, Elizabeth Ke, Nikhil Singh, Taylor L. Patti, Jayson
Lynch, Avi Shporer, Nakul Verma, Eugene Wu, Gilbert Strang
Download PDF

    Abstract: We demonstrate that a neural network pre-trained on
    text and fine-tuned on code solves Mathematics problems by
    program synthesis. We turn questions into programming tasks,
    automatically generate programs, and then execute them, perfectly
    solving university-level problems from MIT's large Mathematics
    courses (Single Variable Calculus 18.01, Multivariable Calculus
    18.02, Differential Equations 18.03, Introduction to Probability
    and Statistics 18.05, Linear Algebra 18.06, and Mathematics for
    Computer Science 6.042), Columbia University's COMS3251
    Computational Linear Algebra course, as well as questions from a
    MATH dataset (on Prealgebra, Algebra, Counting and Probability,
    Number Theory, and Precalculus), the latest benchmark of advanced
    mathematics problems specifically designed to assess mathematical
    reasoning. We explore prompt generation methods that enable
    Transformers to generate question solving programs for these
    subjects, including solutions with plots. We generate correct
    answers for a random sample of questions in each topic. We
    quantify the gap between the original and transformed questions
    and perform a survey to evaluate the quality and difficulty of
    generated questions. This is the first work to automatically
    solve, grade, and generate university-level Mathematics course
    questions at scale. This represents a milestone for higher
    education.

Comments: 128 pages, 250 tables
Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as:  arXiv:2112.15594 [cs.LG]
          (or arXiv:2112.15594v2 [cs.LG] for this version)

Submission history

From: Iddo Drori [view email]
[v1] Fri, 31 Dec 2021 18:57:31 UTC (5,846 KB)
[v2] Tue, 4 Jan 2022 17:35:19 UTC (5,575 KB)
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