Markov Models are anything that has state and emit tokens based only on its current state and undergoes a state transition. The token emission and state transitions are usually probabilistic -- a statistical/probabilistic analogue of a state machine. The deterministic state machine is a special case where the transition probabilities are degenerate (concentrated at an unique point).
For a Markov Model to be non-vacuous, non-vapid discussion point, however, one needs to specify very precisely the relationships allowed between state and tokens/observations, whether it's hidden or visible, discrete or continuous, fixed context length or variable context length, causal or non causal ...
The simplest such model is one where the state is a specified, computable function of the last k observations. One such simple function is the identity function -- the state then is the last k tokens. This is called a k order Markov Chain and is a restriction of the bigger class -- Markov Models.
One can make the state a specified, computable function of (k) previous states and k most recent tokens/observations. (Equivalently RNNs)
The functions may be specified only upto a class of computable functions, finite or infinite in size. They may be stochastic in the sense they define only the state transition probabilities.
You can make the context length a computable function of the k most recent observations (therefore they can be of varying length), but you have to ensure that the contexts are always full for this model to be well defined.
Context length can be a computable function of both the (el) most recent states and k most recent observations.
Crazy ones emit more than one token based on current state.
On and on.
Not all Markov Models are learnable.
> Itheve whe oiv v f vidleared ods alat akn atr. s m w bl po ar 20
Using pairs of consecutive characters (order-2 Markov model) helps, but not much:
> I hateregratics.pyth fwd-i-sed wor is wors.py < smach. I worgene arkov ment by compt the fecompultiny of 5, ithe dons
Triplets (order 3) are a bit better:
> I Fed tooks of the say, I just train. All can beconsist answer efferessiblementate
> how examples, on 13 Debian is the more M-x: Execute testeration
LLMs usually do some sort of tokenization step prior to learning parameters. So I decided to try out order-1 Markov models over text tokenized with byte pair encoding (BPE).
Trained on TFA I got this:
> I Fed by the used few 200,000 words. All comments were executabove. This value large portive comment then onstring takended to enciece of base for the see marked fewer words in the...
Then I bumped up the order to 2
> I Fed 24 Years of My Blog Posts to a Markov Model
> By Susam Pal on 13 Dec 2025
>
> Yesterday I shared a little program calle...
It just reproduced the entire article verbatim. This makes sense as BPE removes any pair of repeated tokens, making order-2 Markov transitions fully deterministic.
I've heard that in NLP applications, it's very common to run BPE only up to a certain number of different tokens, so I tried that out next.
Before limiting, BPE was generating 894 tokens. Even adding a slight limit (800) stops it from being deterministic.
> I Fed 24 years of My Blog Postly coherent. We need to be careful about not increasing the order too much. In fact, if we increase the order of the model to 5, the generated text becomes very dry and factual
It's hard to judge how coherent the text is vs the author's trigram approach because the text I'm using to initialize my model has incoherent phrases in it anyways.
Anyways, Markov models are a lot of fun!
I'm considering just deleting all tokens that have only one possible descendant, from the db. I think that would solve that problem. Could increase that threshold to, e.g. a token needs to have at least 3 possible outputs.
However that's too heavy handed: there's a lot of phrases or grammatical structures that would get deleted by that. What I'm actually trying to avoid is long chains where there's only one next token. I haven't figured out how to solve that though.
You'll also need a "sort of traversal stack" so you can rewind if you get stuck several plies in.
I used it as a kind of “dream well” whenever I wanted to draw some muse from the same deep spring. It felt like a spiritual successor to what I used to do as a kid: flipping to a random page in an old 1950s Funk & Wagnalls dictionary and using whatever I found there as a writing seed.
The only thing I'm a bit wary of is the submission size - a minimum of 50,000 words. At that length, It'd be really difficult to maintain a cohesive story without manual oversight.
It was pretty fun!
I spend all of my time with image and video models and have very thin knowledge when it comes to running, fine tuning, etc. with language models.
How would one start with training an LLM on the entire corpus of one's writings? What model would you use? What scripts and tools?
Has anyone had good results with this?
Do you need to subsequently add system prompts, or does it just write like you out of the box?
How could you make it answer your phone, for instance? Or discord messages? Would that sound natural, or is that too far out of domain?
You could use a vector database.
You could train a model from scratch.
Probably easiest to use OpenAI tools. Upload documents. Make custom model.
How do you make it answer your phone? You could use twillio api + script + llm + voice model. Want natural use a service.
Wouldn't fine tuning produce better results so long as you don't catastrophically forget? You'd preserve more context window space, too, right? Especially if you wanted it to memorize years of facts?
Are LoRAs a thing with LLMs?
Could you train certain layers of the model?
The problem with that is either your n-gram level is too low in which case it can't maintain any kind of cohesion, or your n-gram level is too high and it's basically just spitting out your existing corpus verbatim.
For me, I was more interested in something that could potentially combine two or three highly disparate concepts found in my previous works into a single outputted sentence - and then I would ideate upon it.
So I haven't opened the program in a long time so I just spun it up and generated a few outputs:
A giant baby is navel corked which if removed causes a vacuum.
Here’s a link: https://botnik.org/content/harry-potter.html
cpanm -n local::lib
cpanm -n Hailo
~/perl5/bin/hailo -t corpus.txt -b brain.brn
~/perl5/bin/hailo -b brain.brn
Iirc there was some research on "infini-gram", that is a very large ngram model, that allegedly got performance close to LLMs in some domains a couple years back
Giving 24 years of your experience, thoughts and life time to us.
This is special in these times of wondering, baiting and consuming only.
npm package of the markov model if you just want to play with it on localhost/somewhere else: https://github.com/Aperocky/weighted-markov-generator
I recommend you to read Bengio et al.’s 2003 paper which describes this issue in more detail and introduces distributional representations (embeddings) in an RNN to avoid this sparsity.
While we are using transformers and sentence pieces now, this paper aptly describes the motivation underpinning modern models.
Distributional representations, not distributed.
https://en.wikipedia.org/wiki/Distributional_semantics#Distr...
Except instead we fine-tuned GPT-2 instead. (As was the fashion at the time!)
We used this one, I think https://github.com/minimaxir/gpt-2-simple
I think it took 2-3 hours on my friend's Nvidia something.
The result was absolutely hilarious. It was halfway between a markov chain and what you'd expect from a very small LLM these days. Completely absurd nonsense, yet eerily coherent.
Also, it picked up enough of our personality and speech patterns to shine a very low resolution mirror on our souls...
###
Andy: So here's how you get a girlfriend:
1. Start making silly faces
2. Hold out your hand for guys to swipe
3. Walk past them
4. Ask them if they can take their shirt off
5. Get them to take their shirt off
6. Keep walking until they drop their shirt
Andy: Can I state explicitly this is the optimal strategy
"Do me a favor, boy. This scam of yours, when it's over, you erase this god-damned thing."
Usage:
hailo -t corpus.txt -b brain.brn
hailo -b brain.brn
By default Hailo chooses the easy engine. If you want something more "realistic", pick the advanced one mentioned at 'perldoc hailo' with the -e flag.
Respectfully, absolutely nobody wants to read a copy-and-paste of a chat session with ChatGPT.
I was having a discussion about similarities between Markov Chains and LLMs and short after I found this topic on HN, when I wrote "I can share if you like" was as a proof about the coincidence.
The problem is that this definition strips away what makes Markov models useful and interesting as a modeling framework. A “Markov text model” is a low-order Markov model (e.g., n-grams) with a fixed, tractable state and transitions based only on the last k tokens. LLMs aren’t that: they model using un-fixed long-range context (up to the window). For Markov chains, k is non-negotiable. It's a constant, not a variable. Once you make it a variable, near any process can be described as markovian, and the word is useless.
And in classes, the very first trick you learn to skirt around history is to add Boolean variables to your "memory state". Your systems now model, "did it rain The previous N days?" The issue obviously being that this is exponential if you're not careful. Maybe you can get clever by just making your state a "sliding window history", then it's linear in the number of days you remember. Maybe mix the both. Maybe add even more information .Tradeoffs, tradeoffs.
I don't think LLMs embody the markov property at all, even if you can make everything eventually follow the markov property by just "considering every single possible state". Of which there are (size of token set)^(length) states at minimum because of the KV cache.
The markov property states that your state is a transition of probabilities entirely from the previous state.
These states, inhabit a state space. The way you encode "memory" if you need it, e.g. say you need to remember if it rained the last 3 days, is by expanding said state space. In that case, you'd go from 1 state to 3 states, 2^3 states if you needed the precise binary information for each day. Being "clever", maybe you assume only the # of days it rained, in the past 3 days mattered, you can get a 'linear' amount of memory.
Sure, a LLM is a "markov chain" of state space size (# tokens)^(context length), at minimum. That's not a helpful abstraction and defeats the original purpose of the markov observation. The entire point of the markov observation is that you can represent a seemingly huge predictive model with just a couple of variables in a discrete state space, and ideally you're the clever programmer/researcher and can significantly collapse said space by being, well, clever.
Are you deliberately missing the point or what?
Okay, so we're agreed.
Again, no they can't, unless you break the definition. K is not a variable. It's as simple as that. The state cannot be flexible.
1. The markov text model uses k tokens, not k tokens sometimes, n tokens other times and whatever you want it to be the rest of the time.
2. A markov model is explcitly described as 'assuming that future states depend only on the current state, not on the events that occurred before it'. Defining your 'state' such that every event imaginable can be captured inside it is a 'clever' workaround, but is ultimately describing something that is decidedly not a markov model.
2. “Fixed-size block” is a padding detail, not a modeling assumption. Yes, implementations batch/pad to a maximum length. But the model is fundamentally conditioned on a variable-length prefix (up to the cap), and it treats position 37 differently from position 3,700 because the computation explicitly uses positional information. That means the conditional distribution is not a simple stationary “transition table” the way the n-gram picture suggests.
3. “Same as a lookup table” is exactly the part that breaks. A classic n-gram Markov model is literally a table (or smoothed table) from discrete contexts to next-token probabilities. A transformer is a learned function that computes a representation of the entire prefix and uses that to produce a distribution. Two contexts that were never seen verbatim in training can still yield sensible outputs because the model generalizes via shared parameters; that is categorically unlike n-gram lookup behavior.
I don't know how many times I have to spell this out for you. Calling LLMs markov chains is less than useless. They don't resemble them in any way unless you understand neither.
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.
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.
An LLM could be implemented with a Markov chain, but the naïve matrix is ((vocab size)^(context length))^2, which is far too big to fit in this universe.
Like, the Bekenstein bound means writing the transition matrix for an LLM with just 4k context (and 50k vocabulary) at just one bit resolution, the first row (out of a bit more than 10^18795 rows) ends up with a black hole >10^9800 times larger than the observable universe.
If you use a syllable-level token in Markov models the model can't form real words much beyond the second syllable, and you have no way of making it make more sense other than increasing the token size, which exponentially decreases originality. This is the simplest way I can explain it, though I had to address why scaling doesn't work.
[1] There are 4^400000 possible 4-word sequences in English (barring grammar) meaning only a corpus with 8 times that amount of words and with no repetition could offer two ways to chain each possible 4 word sequence.
* LLMs don't use Markov chains, * LLMs don't predict words.
* The R package markovchain[1] may look like it's using Markov chains, but it's actually using the R programming language, zeros and ones.
[1] https://cran.r-project.org/web/packages/markovchain/index.ht...
Hate to be that guy, but I remember this place being nicer.
Everyone has access to ChatGPT. If we wanted its "opinion" we could ask it ourselves. Your offer is akin to "Hey everyone, want me to Google this and paste the results page here?". You would never offer to do that. Ask yourself why.
These posts are low-effort and add nothing to the conversation, yet the people who write them seem to expect everyone to be impressed by their contribution. If you can't understand why people find this irritating, I'm not sure what to tell you.