Search

We curate a comprehensive dataset of 4,550 questions and solutions from problem sets, midterm exams, and final exams across all MIT Mathematics and Electrical Engineering and Computer Science (EECS) courses required for obtaining a degree. We evaluate the ability of large language models to fulfill the graduation requirements for any MIT major in Mathematics and EECS. Our results demonstrate that GPT-3.5 successfully solves a third of the entire MIT curriculum, while GPT-4, with prompt engineering, achieves a perfect solve rate on a test set excluding questions based on images. We fine-tune an open-source large language model on this dataset. We employ GPT-4 to automatically grade model responses, providing a detailed performance breakdown by course, question, and answer type. By embedding questions in a low-dimensional space, we explore the relationships between questions, topics, and classes and discover which questions and classes are required for solving other questions and classes through few-shot learning. Our analysis offers valuable insights into course prerequisites and curriculum design, highlighting language models' potential for learning and improving Mathematics and EECS education., Comment: Did not receive permission to release the data or model fine-tuned on the data

A final exam in machine learning at a top institution such as MIT, Harvard, or Cornell typically takes faculty days to write, and students hours to solve. We demonstrate that large language models pass machine learning finals at a human level, on finals available online after the models were trained, and automatically generate new human-quality final exam questions in seconds. Previous work has developed program synthesis and few-shot learning methods to solve university-level problem set questions in mathematics and STEM courses. In this work, we develop and compare methods that solve final exams, which differ from problem sets in several ways: the questions are longer, have multiple parts, are more complicated, and span a broader set of topics. We curate a dataset and benchmark of questions from machine learning final exams available online and code for answering these questions and generating new questions. We show how to generate new questions from other questions and course notes. For reproducibility and future research on this final exam benchmark, we use automatic checkers for multiple-choice, numeric, and questions with expression answers. We perform ablation studies comparing zero-shot learning with few-shot learning and chain-of-thought prompting using GPT-3, OPT, Codex, and ChatGPT across machine learning topics and find that few-shot learning methods perform best. We highlight the transformative potential of language models to streamline the writing and solution of large-scale assessments, significantly reducing the workload from human days to mere machine seconds. Our results suggest that rather than banning large language models such as ChatGPT in class, instructors should teach students to harness them by asking students meta-questions about correctness, completeness, and originality of the responses generated, encouraging critical thinking in academic studies., Comment: 9 pages

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., Comment: 181 pages, 8 figures, 280 tables

Pathology is practiced by visual inspection of histochemically stained slides. Most commonly, the hematoxylin and eosin (H&E) stain is used in the diagnostic workflow and it is the gold standard for cancer diagnosis. However, in many cases, especially for non-neoplastic diseases, additional "special stains" are used to provide different levels of contrast and color to tissue components and allow pathologists to get a clearer diagnostic picture. In this study, we demonstrate the utility of supervised learning-based computational stain transformation from H&E to different special stains (Masson's Trichrome, periodic acid-Schiff and Jones silver stain) using tissue sections from kidney needle core biopsies. Based on evaluation by three renal pathologists, followed by adjudication by a fourth renal pathologist, we show that the generation of virtual special stains from existing H&E images improves the diagnosis in several non-neoplastic kidney diseases sampled from 58 unique subjects. A second study performed by three pathologists found that the quality of the special stains generated by the stain transformation network was statistically equivalent to those generated through standard histochemical staining. As the transformation of H&E images into special stains can be achieved within 1 min or less per patient core specimen slide, this stain-to-stain transformation framework can improve the quality of the preliminary diagnosis when additional special stains are needed, along with significant savings in time and cost, reducing the burden on healthcare system and patients., Comment: 27 Pages, 6 Figures