Note: this post was cross-posted to Metaculus over a week ago as part of their new Metaculus journal.

Here, I describe a way of measuring the performance of language models, and extrapolate this measure using publicly available data on benchmarks. The result is a (surprisingly) short timeline to "human-level"—within one decade from now. Since posting to Metaculus, I have realized the need to clarify a few things first,

I am not saying that this model represents my inside view. I merely used linear regression to extrapolate performance metrics, and I think there is credible reason to doubt these results, not least of which because I may have made a mistake. Check out the comment section on Metaculus for more discussion.
That said, it may still be interesting to consider what might be true about the world if we just take these results literally. Predicting that a trend will soon inexplicably slow down is easy. What's harder is proposing an alternative model.
There are probably errors in the Jupyter notebook, my graphs, and my equations. Just let me know in the comments if you see any.

Language models have received a lot of attention recently, especially OpenAI’s GPT-3 and Codex. While the possibility of a human-level language model remains out of reach, when might one arrive? To help answer this question, I turn to some basic concepts in information theory, as pioneered by Claude Shannon.

Shannon was interested in understanding how much information is conveyed by English text. His key insight was that when a text is more predictable, less information is conveyed per symbol compared to unpredictable texts. He made this statement more precise by introducing the concept of entropy. Roughly speaking, entropy measures the predictability of a sequence of text, in the limit of perfect prediction abilities.

Since Shannon’s work, a popular hobby of computational linguists has been to invent new ways of measuring the entropy of the English language. By comparing these estimates with the actual performance of language models at the task of predicting English text, it is possible to chart the progress we have made toward the goal of human-level language modeling. Furthermore, there are strong reasons to believe that entropy is a more useful metric for tracking general language modeling performance when compared to performance metrics on extrinsic tasks, such as those...

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