Reece Shuttleworth

Iddo Drori, Sarah J. Zhang, Reece Shuttleworth et al. · harvard

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.

Reece Shuttleworth, Jacob Andreas, Antonio Torralba et al. · mit

Fine-tuning is a crucial paradigm for adapting pre-trained large language models to downstream tasks. Recently, methods like Low-Rank Adaptation (LoRA) have been shown to effectively fine-tune LLMs with an extreme reduction in trainable parameters. But, \emph{are their learned solutions really equivalent?} We study how LoRA and full-finetuning change pre-trained models by analyzing the model's weight matrices through the lens of their spectral properties. We find that LoRA and full fine-tuning yield weight matrices whose singular value decompositions exhibit very different structure: weight matrices trained with LoRA have new, high-ranking singular vectors, which we call \emph{intruder dimensions}, while those trained with full fine-tuning do not. Further, we extend the finding that LoRA forgets less than full fine-tuning and find its forgetting is vastly localized to the intruder dimension -- by causally intervening on the intruder dimensions by changing their associated singular values post-fine-tuning, we show that they cause forgetting. Moreover, scaling them down significantly improves modeling of the pre-training distribution with a minimal drop in downstream task performance. Given this, we should expect accumulating intruder dimensions to be harmful and lead to more forgetting. This will be amplified during continual learning because of sequentially fine-tuning, and we show that LoRA models do accumulate intruder dimensions here tend to perform worse in this setting, emphasizing the practicality of our findings.

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.