Ask HN: How are Markov chains so different from tiny LLMs?

A Markov Chain trained by only a single article of text will very likely just regurgitate entire sentences straight from the source material. There just isn't enough variation in sentences.

But then, Markov Chains fall apart when the source material is very large. Try training a chain based on Wikipedia. You'll find that the resulting output becomes incoherent garbage. Increasing the context length may increase coherence, but at the cost of turning into just simple regurgitation.

In addition to the "attention" mechanism that another commenter mentioned, it's important to note that Markov Chains are discrete in their next token prediction while an LLM is more fuzzy. LLMs have latent space where the meaning of a word basically exists as a vector. LLMs will generate token sequences that didn't exist in the source material, whereas Markov Chains will ONLY generate sequences that existed in the source.

This is why it's impossible to create a digital assistant, or really anything useful, via Markov Chain. The fact that they only generate sequences that existed in the source mean that it will never come up with anything creative.

> The fact that they only generate sequences that existed in the source mean that it will never come up with anything creative.

I have seen the argument that LLMs can only give you what its been trained on, i.e. it will not be "creative" or "revolutionary", that it will not output anything "new", but "only what is in its corpus".

I am quite confused right now. Could you please help me with this?

Somewhat related: I like the work of David Hume, and he explains it quite well how we can imagine various creatures, say, a pig with a dragon head, even if we have not seen one ANYWHERE. It is because we can take multiple ideas and combine them together. We know how dragons typically look like, and we know how a pig looks like, and so, we can imagine (through our creativity and combination of these two ideas) how a pig with a dragon head would look like. I wonder how this applies to LLMs, if they even apply.

Edit: to clarify further as to what I want to know: people have been telling me that LLMs cannot solve problems that is not in their training data already. Is this really true or not?

Here's how I see it, but I'm not sure how valid my mental model is.

Imagine a source corpus that consists of:

Cows are big. Big animals are happy. Some other big animals include pigs, horses, and whales.

A Markov chain can only return verbatim combinations. So it might return "Cows are big animals" or "Are big animals happy".

An LLM can get a sense of meaning in these words and can return ideas expressed in the input corpus. So in this case it might say "Pigs and horses are happy". It's not limited to responding with verbatim sequences. It can be seen as a bit more creative.

However, LLMs will not be able to represent ideas that it has not encountered before. It won't be able to come up with truly novel concepts, or even ask questions about them. Humans (some at least) have that unbounded creativity that LLMs do not.

> However, LLMs will not be able to represent ideas that it has not encountered before. It won't be able to come up with truly novel concepts, or even ask questions about them. Humans (some at least) have that unbounded creativity that LLMs do not.

There's absolutely no evidence to support this claim. It'd require humans to exceed the Turing computable, and we have no evidence that is possible.

Turing computability is tangential to his claim, as LLMs are obviously not carrying out the breadth of all computable concepts. His claim can be trivially proven by considering the history of humanity. We went from a starting point of having literally no language whatsoever, and technology that would not have expanded much beyond an understanding of 'poke him with the pointy side'. And from there we would go on to discover the secrets of the atom, put a man on the Moon, and more. To say nothing of inventing language itself.

An LLM trained on this starting state of humanity is never going to do anything except remix basically nothing. It's never going to discover the secrets of the atom, or how to put a man on the Moon. Now whether any artificial device could achieve what humans did is where the question of computability comes into play, and that's a much more interesting one. But if we limit ourselves to LLMs, then this is very straight forward to answer.

> Turing computability is tangential to his claim, as LLMs are obviously not carrying out the breadth of all computable concepts

They don't need to. To be Turing complete a system including an LLM need to be able to simulate a 2-state 3-symbol Turing machine (or the inverse). Any LLM with a loop can satisfy that.

If you think Turing computability is tangential to this claim, you don't understand the implications of Turing computability.

> His claim can be trivially proven by considering the history of humanity.

Then show me a single example where humans demonstrably exceeding the Turing computable.

We don't even know any way for that to be possible.