[chpatrick]

I think you're confusing Markov chains and "Markov chain text generators". A Markov chain is a mathematical structure where the probabilities of going to the next state only depend on the current state and not the previous path taken. That's it. It doesn't say anything about whether the probabilities are computed by a transformer or stored in a lookup table, it just exists. How the probabilities are determined in a program doesn't matter mathematically.

[saithound]

Just a heads-up: this is not the first time somebody has to explain Markov chains to famouswaffles on HN, and I'm pretty sure it won't be the last. Engaging further might not be worth it.

[famouswaffles]

I did not even remember you and had to dig to find out what you were on about. Just a heads up, if you've had a previous argument and you want to bring that up later then just speak plainly. Why act like "somebody" is anyone but you?

My response to both of you is the same.

LLMs do depend on previous events, but you say they don't because you've redefined state to include previous events. It's a circular argument. In a Markov chain, state is well defined, not something you can insert any property you want to or redefine as you wish.

It's not my fault neither of you understand what the Markov property is.

[chpatrick]

By that definition n-gram Markov chain text generators also include previous state because you always put the last n grams. :) It's exactly the same situation as LLMs, just with higher, but still fixed n.

[famouswaffles]

We've been through this. The context of a LLM is not fixed. Context windows =/ n gram orders.

They don't because n gram orders are too small and rigid to include the history in the general case.

I think srean's comment up the thread is spot on. This current situation where the state can be anything you want it to be just does not make a productive conversation.

[famouswaffles]

'A Markov chain is a mathematical structure where the probabilities of going to the next state only depend on the current state and not the previous path taken.'

My point, which seems so hard to grasp for whatever reason is that In a Markov chain, state is a well defined thing. It's not a variable you can assign any property to.

LLMs do depend on the previous path taken. That's the entire reason they're so useful! And the only reason you say they don't is because you've redefined 'state' to include that previous path! It's nonsense. Can you not see the circular argument?

The state is required to be a fixed, well-defined element of a structured state space. Redefining the state as an arbitrarily large, continuously valued encoding of the entire history is a redefinition that trivializes the Markov property, which a Markov chain should satisfy. Under your definition, any sequential system can be called Markov, which means the term no longer distinguishes anything.

[chpatrick]

They only have the previous path in as much as n-gram Markov text generators have the previous path.