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Maybe this is at cross-purposes: Functions don't have memory. Nothing real ever "is" a Markov chain. It's simply a (slightly unusual) modelling choice which you
by ogogmad 2y ago
Maybe this is at cross-purposes: Functions don't have memory. Nothing real ever "is" a Markov chain. It's simply a (slightly unusual) modelling choice which you can use whenever you've listed all possible inputs that can affect a transition probability - once you've done that, you can apply it to pretty much anything.
- Jensson 2y ago> Nothing real ever "is" a Markov chain. What do you mean? Quantum states over time are very much markov chains as well. > It's simply a (slightly unusual) modelling choice which you can use whenever you've listed all possible inputs that can affect a transition probability That has nothing to do with markov chains, do you mean a specific implementation? Markov chains is a probability theory concept and has nothing to do with any implementation.
- jampekka 2y agoIn many cases the Markov assumption is made to simplify things even though it's not realistic. But nevertheless it does describe what the model itself does even if in the real environment it doesn't act as a real Markov process (e.g. doesn't necessarily have a stationary distribution). It applies here too in a case where the model interacts with humans, as the LLM state doesn't include the human. While Markov chains/processes are a powerful and general abstraction, the assumptions are quite strict. E.g. even the simplest recurrent systems aren't Markov, and this leads to things like having to assume exponential distribition of event durations in time series contexts, which is quite limiting. In language models it draws a clear demarkation between recurrent and feedforward neural networks and brings some crucial understanding into benefits and limitations of e.g. transformers vs recurrent models.