Sunny Tran

Iddo Drori, Sarah Zhang, Reece Shuttleworth et al.

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.

Sunny Tran, Pranav Krishna, Ishan Pakuwal et al.

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 exercises, homework, and quiz questions from MIT's 6.036 Introduction to Machine Learning course and train a machine learning model to answer these questions. Our system demonstrates an overall accuracy of 96% for open-response questions and 97% for multiple-choice questions, compared with MIT students' average of 93%, achieving grade A performance in the course, all in real-time. Questions cover all 12 topics taught in the course, excluding coding questions or questions with images. Topics include: (i) basic machine learning principles; (ii) perceptrons; (iii) feature extraction and selection; (iv) logistic regression; (v) regression; (vi) neural networks; (vii) advanced neural networks; (viii) convolutional neural networks; (ix) recurrent neural networks; (x) state machines and MDPs; (xi) reinforcement learning; and (xii) decision trees. Our system uses Transformer models within an encoder-decoder architecture with graph and tree representations. An important aspect of our approach is a data-augmentation scheme for generating new example problems. We also train a machine learning model to generate problem hints. Thus, our system automatically generates new questions across topics, answers both open-response questions and multiple-choice questions, classifies problems, and generates problem hints, pushing the envelope of AI for STEM education.