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Neural network capable of solving university-level Mathematics problems at scale

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

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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.

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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2 Comments

  1. Not to pour too much cold water on this, but the claim of 100% accuracy has a huge caveat. In the paper (Page 4) they state:

    Interaction. The original question may not be a prompt that synthesizes a program whose execution results in the correct answer. In addition, the answer may require multiple steps with clear plots or other modalities. We therefore may interactively prompt Codex until reaching the correct answer or visualizations, making the minimum necessary changes from the original question

    Which to me basically sounds like they had a human in the loop (that knows how to solve these math problems) that kept changing the question until it gave the correct answer. They do measure the distance (using a sentence embedding model) of the original question to the one that yielded the correct answer, but that feels a bit contrived to me.

    Nevertheless, its still really cool that the correct answer is indeed inside the model.

  2. They rewrite the questions before feeding it into the AI. That makes "100% correct" significantly less impressive.

    For example, they manually rewrote the question:

    > Find the derivative of the function using the definition of a derivative. f(x) = (x2 − 1)/(2x − 3)

    To

    > Use Sympy to find the derivative of f(x)=(x*2-1)/(2*x-3)

    Which completely changes the question, and also their rewrite ensures that the AI doesn't fail to parse any data etc.

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