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: Who models the models that model models? An exploration of GPT-3's in-context model fitting ability, published by Lovre on June 7, 2022 on The AI Alignment Forum.
Introduction
Much has been written and much has been observed about the abilities of GPT-3 on many tasks. Most of these capabilities, though not all, pertain to writing convicing text, but, not to undermine GPT-3's impressiveness at performing these tasks, we might call this the predictable part of its oeuvre. It only makes sense that a better language modelling is, well, going to be better at writing text.
Deeper and comparatively much less explored is the unpredictable ability of GPT-3 to learn new tasks by just seeing a few examples, without any training/backpropagation – the so called in-context learning (sometimes called metalearning).
The original paper announcing GPT-3 contained a handful of examples (perhaps mostly notably examples of GPT-3 learning to perform arithmetic, e.g. accurate addition of up to 5-digit numbers), Gwern has also insightfully written about it, Frieda Rong has performed some interesting experiments, and there have been various other experiments one could chance upon. My curiosity being piqued but not sated by these experiments, and also having had the feeling that, as captivating the arithmetic examples were, they weren't the most natural question one could ask about a stochastic model's quantitative capabilities – I decided to investigate whether GPT-3 could fit numerical models in-context.
The Setup
What does it mean to fit a model in-context? Well, recall that GPT-3 has a context window (roughly speaking: text it considers before generating additional text) of length 2048 tokens (roughly speaking: (parts of the) words, punctuation, etc.) so the idea is to put feature vectors inside that context window. Of course, this means you cannot fit any larger or higher-dimensional dataset in there.[1]
In practice this means prompting GPT-3 on input like:
Input: 89, 51, 73, 31, output = 1
[...] Input: 96, 51, 80, 38, output = 2
Input: 90, 37, 76, 27, output =
And then taking its output, i.e. the text it generates, as the prediction.
A couple more technical details: In all the experiments I performed, all the numbers were integers. The GPT-3's outputs were always sampled with temperature 0, i.e. they were deterministic – only the most probable output was considered. I restricted myself that way for simplicity, but hopefully some future work looks at the full distribution over outputs.
(In the rest of this post I share GPT-3's results without too much warning, so if you'd like to make your own predictions about how GPT-3 does at simple classification and regression tasks in-context, now would be the time to pause reading and make your general predictions.)
Iris Dataset
Just as there is the MNIST dataset for visual recognition, so too there is a small low-dimensional classification dataset which every would-be classifier has to solve or else sink – the Iris dataset, composed of 150 observations of septal/petal height/width of three species of iris (50 observations each). Note that classification of the Iris dataset is in some sense trivial, with simple algorithms achieving near-perfect accuracy, but a model still needs to do some meaningful learning, given that it needs to learn to differentiate between three classes based on just a few dozen four-dimensional vectors.
In order to prevent leakage, as the Iris dataset is all over the internet, as well as to get the more-easily-palatable integers out, I transformed every feature with the transformation
xnew=round(14xold+6).
I also split the dataset into 50% train and 50% test folds – so that the model "trained" on, or rather looked at 75 examples.
I hadn't quite been expecting what had followed – I had expected GPT-3 to catch on to some patt...
