Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Forecasting ML Benchmarks in 2023, published by jsteinhardt on July 18, 2022 on LessWrong.
Thanks to Collin Burns, Ruiqi Zhong, Cassidy Laidlaw, Jean-Stanislas Denain, and Erik Jones, who generated most of the considerations discussed in this post.
Previously, I evaluated the accuracy of forecasts about performance on the MATH and MMLU (Massive Multitask) datasets. I argued that most people, including myself, significantly underestimated the rate of progress, and encouraged ML researchers to make forecasts for the next year in order to become more calibrated.
In that spirit, I’ll offer my own forecasts for state-of-the-art performance on MATH and MMLU. Following the corresponding Metaculus questions, I’ll forecast accuracy as of June 30, 2023. My forecasts are based on a one-hour exercise I performed with my research group, where we brainstormed considerations, looked up relevant information, formed initial forecasts, discussed, and then made updated forecasts. It was fairly easy to devote one group meeting to this, and I’d encourage other research groups to do the same.
Below, I’ll describe my reasoning for the MATH and MMLU forecasts in turn. I’ll review relevant background info, describe the key considerations we brainstormed followed, analyze those considerations, and then give my bottom-line forecast.
MATH
Background
Metaculus does a good job of describing the MATH dataset and corresponding forecasting question:
The MATH dataset is a dataset of challenging high school mathematics problems constructed by Hendrycks et al. (2021). Hypermind forecasters were commissioned to predict state-of-the-art performance on June 30, 2022, '23, '24, and '25. The 2022 result of 50.3% was significantly outside forecasters' prediction intervals, so we're seeing what the updated forecasts are for 2023, '24, and '25. What will be state-of-the-art performance on the MATH dataset in the following years? These questions should resolve identically to the Hypermind forecasts: "These questions resolve as the highest performance achieved on MATH by June 30 in the following years by an eligible model. Eligible models may use scratch space before outputting an answer (if desired) and may be trained in any way that does not use the test set (few-shot, fine tuned, etc.).
The model need not be publicly released, as long as the resulting performance itself is reported in a published paper (on arxiv or a major ML conference) or through an official communication channel of an industry lab (e.g. claimed in a research blog post on the OpenAI blog, or a press release). In case of ambiguity, the question will resolve according to Jacob Steinhardt’s expert judgement."
It’s perhaps a bit sketchy for me to be both making and resolving the forecast, but I expect in most cases the answer will be unambiguous.
Key Considerations
Below I list key considerations generated during our brainstorming:
Why did Minerva do well on MATH? Is it easy to scale up those methods? Is there other low-hanging fruit?
What kinds of errors is Minerva making? Do they seem easy or hard to fix?
Minerva was trained on arXiv and other sources of technical writing. How much additional such data could be generated?
Are there other methods that could lead to improvement on mathematical reasoning?
Possibilities: self-supervised learning, verifiers, data retrieval
Base rates: What has been the historical rate of progress on MATH?
Base rates: How does progress typically occur on machine learning datasets (especially NLP datasets)? If there is a sudden large improvement, does that typically continue, or level off?
How much will people work on improving MATH performance?
Analyzing Key Consideratoins
Why did Minerva do well? How much low-hanging fruit is there?
Minerva incorporated several changes that improved performance relative to previou...