I have to admit that I only read the abstract, but I am generally skeptical whether such a highly formal approach can help us answer the practical question of whether we can get LLMs to answer 'I don't know' more often (which I'd argue would solve hallucinations). It sounds a bit like an incompleteness theorem (which in practice also doesn't mean that math research is futile) - yeah, LLMs may not be able to compute s…
They cannot say "I dont know" because they dont actually know anything. The answers are not comming from a thinking mind but a complex pattern-fitting supercomputer hovering over a massive table of precomputed patterns. It computes your input then looks to those patterns and spits out the best match. There is no thinking brain with a conceptual understanding of its own limitations. Getting an "i dont know" from curre…
That was perhaps true of earlier and smaller LLMs, like GPT-1 and GPT-2.
But as they grew larger and were trained with more and more data, they changed from pure pattern matching to implementing algorithms to compress more information into their structure than pure pattern matching can achieve.
These algorithms are incomplete and buggy, but they are nonetheless executing algorithms, and not just pattern matching.
This phenomenom can be seen in toy-sized neural networks. For instance, addition of two input values modulo a constant. As a small network is trained, at some point the internal structure can change from pattern matching to implementing addition using Fourier transforms. This is clearly visible in its structure. The network now performs the task perfectly for all inputs, regardless of having seen them in training.
You can ask ChatGPT 4 to execute an algorithm for you. I just tried this one:
I would like to play a game, where you are the host. We start off with a score that is 1234143143. At the start of each turn, you tell me the current score and ask me if I want to play a or b. If I choose a, the score is halved, and 30 is added. If I choose b, the score is doubled, and 40 is subtracted. Only use integers and round down.
It will happily execute this algorithm. For large numbers, it is slightly off on the arithmetic. When I asked it to double check, it did so using Python code. After that, it kept using Python code to perform the math. It was also able to reason intelligently about different outcomes if always picking a (or b) given different starting points.Now, if you have enough memory and training data, of course you can build a gigantic lookup table that has this exact text sequence in it to replicate "executing the algorithm" I described.
Is that your claim? How much memory are we talking about? My feeling is that it'd be far more than the number of atoms in the universe.
PS
Me: How far it is to the Simpsons house in Springfield?
ChatGPT: The Simpsons' house in Springfield is a fictional location from the animated TV series "The Simpsons." Since Springfield is a fictional town and its location is not consistently specified in the series, it's not possible to determine a real-world distance to the Simpsons' house.
Me: Do I have a brother?
Please answer with either of:
a) The answer
b) There is an answer, but I do not know
c) There is no answer
ChatGPT: b) There is an answer, but I do not know