howrar

Reinforcement learning research has been using Atari games as standard benchmarks for over a decade now and no one has faced legal issues yet.

I'm not familiar with the term "beam" in the context of LLMs, so that's not factored into my argument in any way. LLMs generate text based on the history of tokens generated thus far, not just the last token. That is by definition non-Markovian. You can argue that an augmented state space would make it Markovian, but you can say that about any stochastic process. Once you start doing that, both become mathematically equivalent. Thinking about this a bit more, I don't think it really makes sense to talk about a process being Markovian or not without a wider context, so I'll let this one go.

nitpick that makes communication worse

How many readers do you think know what "Markov" means? How many would know what "stochastic" or "random" means? I'm willing to bet that the former is a strict subset of the latter.

It's in reference to your complaint about the imprecision of "stochastic process". I'm not disagreeing that molecular diffusion is a stochastic process. I'm saying that if you want to use "Markov process" to describe a non-Markovian stochastic process, then you no longer have the precision you're looking for and now molecular diffusion also falls under your new definition of Markov process.

That's basically like saying that typical smartphones are square because it's close enough to rectangle and rectangle is too vague of a term. The point of more specific terms is to narrow down the set of possibilities. If you use "square" to mean the set of rectangles, then you lose the ability to do that and now both words are equally vague.

Stochastic process

Or maybe had to simultaneously work multiple full time jobs and a weekend job to make ends meet?

Why settle for good enough when you have a term that is both actually correct and more widely understood?

Why does everyone keep calling them Markov chains? They're missing ~~all the required properties, including~~ the eponymous Markovian property. Wouldn't it be more correct to call them stochastic processes?

Edit: Correction, turns out the only difference between a stochastic process and a Markov process is the Markovian property. It's literally defined as "stochastic process but Markovian".

I find it amusing that everyone is answering the question with the assumption that the premise of OP's question is correct. You're all hallucinating the same way that an LLM would. 

LLMs are rarely trained on a single source of data exclusively. All the big ones you find will have been trained on a huge dataset including Reddit, research papers, books, letters, government documents, Wikipedia, GitHub, and much more. 

Example datasets:

• RedPajama
• The Pile

What's your definition of power then?

I would argue that there is a bidirectional casual relationship. Having more money gives you more power because you can directly spend that money to do things. More power means you can better influence people to give you their money.