Kavli Affiliate: Avi Shporer

| First 5 Authors: Iddo Drori, Sarah Zhang, Reece Shuttleworth, Leonard Tang, Albert Lu

| Summary:

We demonstrate that a neural network pre-trained on text and fine-tuned on

code solves mathematics course problems, explains solutions, and generates new

questions at a human level. We automatically synthesize programs using few-shot

learning and OpenAI’s Codex transformer and execute them to solve course

problems at 81% automatic accuracy. We curate a new dataset of questions from

MIT’s largest mathematics courses (Single Variable and Multivariable Calculus,

Differential Equations, Introduction to Probability and Statistics, Linear

Algebra, and Mathematics for Computer Science) and Columbia University’s

Computational Linear Algebra. We solve questions from a MATH dataset (on

Prealgebra, Algebra, Counting and Probability, Intermediate Algebra, Number

Theory, and Precalculus), the latest benchmark of advanced mathematics problems

designed to assess mathematical reasoning. We randomly sample questions and

generate solutions with multiple modalities, including numbers, equations, and

plots. The latest GPT-3 language model pre-trained on text automatically solves

only 18.8% of these university questions using zero-shot learning and 30.8%

using few-shot learning and the most recent chain of thought prompting. In

contrast, program synthesis with few-shot learning using Codex fine-tuned on

code generates programs that automatically solve 81% of these questions. Our

approach improves the previous state-of-the-art automatic solution accuracy on

the benchmark topics from 8.8% to 81.1%. We perform a survey to evaluate the

quality and difficulty of generated questions. This work is the first to

automatically solve university-level mathematics course questions at a human

level and the first work to explain and generate university-level mathematics

course questions at scale, a milestone for higher education.

| Search Query: ArXiv Query: search_query=au:”Avi Shporer”&id_list=&start=0&max_results=10