Imagine the gap between GPT-2 and GPT-3. Imagine the gap between GPT-3 and GPT-4. Let's suppose GPT-5 has the same gap with GPT-4, and GPT-6 has the same gap with GPT-5, and so on till GPT-8.

It is still entirely possible that GPT-8 is not better than the best of humanity at all possible tasks. There can still exist multiple tasks at which the best humans beat GPT-8.

One way to build this intuition is the following thought experiment: Try imagining a GPT-5 that makes headway in GPT4's weaknesses, but has its own weaknesses. Try imagining a GPT-6 that makes headway in GPT-5's weaknesses, but has its own weaknesses. Iterate till you get GPT-8.

Here's one run of this thought experiment:

My thought experiments focusses on mathematics, but you could also pick a natural language example and run your own thought experiment instead.

GPT4 has high error rate per reasoning step, and sequentially chaining many such reasoning steps blows up error to 1. GPT4 cannot accurately answer square root of 1234.

Let's suppose GPT-5 can look at sequentially chained reasoning steps that are likely to occur in training, and for those chains it is able to perform the entire chain with low error. But if it needs to join separate reasoning steps in a novel manner, it again has high error. GPT5 answers square root of 1234 correctly because it has seen previous square root examples and internalises all the steps of the square root algorithm (in a way that doesn't add up error with each step). But it cannot answer (1234 + 5678^(1/2))^(1/3).

Let's suppose GPT-6 can do the same thing that GPT-5 does, but first it can transform the input space into a variety of other spaces. For instance it can transform numbers into a space that naturally does binomial expansions (including of fractional exponents) and it can transform symbols into a space that naturally does arithmetic using a FIFO stack and it can transform symbols into a space that does first-order logic. Let's suppose however that GPT-6 now requires a lot of data to get this to work though. For instance to make it solve all possible arithmetic expressions of length 50 symbols, it needs 1 trillion examples of length 50 symbols. So it can answer (1234 + 5678^(1/2))^(1/3) but it can't prove a statement as complicated as the fundamental theorem of algebra, assuming the proof does not exist verbatim in its training data.

Let's suppose GP...

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