As for the fact that it gets things wrong sometimes - sure, this doesn't say it actually learned every algorithm (in whichever model you may be thinking about). But the nice thing is that we now have this proof via category theory, and it allows us to both frame and understand what has occurred, and to consider how to align the systems to learn algorithms better.
Your argument is the equivalent of saying humans can't do math because they rely on calculators.
In the end what matters is whether the problem is solved, not how it is solved.
(assuming that the how has reasonable costs)
What's a token?
Tokens exist because transformers don't work on bytes or words. This is because it would be too slow (bytes), the vocabulary too large (words), and some words would appear too rarely or never. The token system allows a small set of symbols to encode any input. On average you can approximate 1 token = 1 word, or 1 token = 4 chars.
So tokens are the data type of input and output, and the unit of measure for billing and context size for LLMs.
You're using it wrong. If you asked a human to do the same operation in under 2 seconds without paper, would the human be more accurate?
On the other hand if you ask for a step by step execution, the LLM can solve it.
no, it’s the LLMs that are wrong.
ChatGPT needs to do the same process to solve the same problem. It hasn’t memorized the addition table up to 10 digits and neither have you.
A system that can will probably adopt a different acronym (and gosh that will be an exciting development... I look forward to the day when we can dispatch trivial proofs to be formalized by a machine learning algorithm so that we can focus on the interesting parts while still having the entire proof formalized).
1. ChatGPT knows the algorithm for adding two numbers of arbitrary magnitude.
2. It often fails to use the algorithm in point 1 and hallucinates the result.
Knowing something doesn't mean it will get it right all the time. Rather, an LLM is almost guaranteed to mess up some of the time due to the probabilistic nature of its sampling. But this alone doesn't prove that it only brute-forced task X.
