You're correct that the formal definition of a Markov process does not exclude internal computation, and that it only requires the next state to depend solely on the current state. But what defines a classical Markov chain in practice is not just the formal dependency structure but how the transition function is structured and used. A traditional Markov chain has a discrete and enumerable state space with explicit, often simple transition probabilities between those states. LLMs do not operate this way.

The claim that an LLM is "just" a large compressed Markov chain assumes that its function is equivalent to a giant mapping of input sequences to output distributions. But this interpretation fails to account for the fundamental difference in how those distributions are generated. An LLM is not indexing a symbolic structure. It is computing results using recursive transformations across learned embeddings, where those embeddings reflect complex relationships between tokens, concepts, and tasks. That is not reducible to discrete symbolic transitions without losing the model’s generalization capabilities. You could record outputs for every sequence, but the moment you present a sequence that wasn't explicitly in that set, the Markov table breaks. The LLM does not.

Yes, you can say a table is just one implementation of a function, and from a purely mathematical perspective, any function can be implemented as a table given enough space. But the LLM’s function is general-purpose. It extrapolates. A precomputed table cannot do this unless those extrapolations are already baked in, in which case you are no longer talking about a classical Markov system. You are describing a model that encodes relationships far beyond discrete transitions.

The pi analogy applies to deterministic functions with fixed outputs, not to learned probabilistic functions that approximate conditional distributions over language. If you give an LLM a new input, it will return a meaningful distribution even if it has never seen anything like it. That behavior depends on internal structure, not retrieval. Just because a function is deterministic at temperature 0 does not mean it is a transition table. The fact that the same input yields the same output is true for any deterministic function. That does not collapse the distinction between generalization and enumeration.

So while yes, you can implement any deterministic function as a lookup table, the nature of LLMs lies in how they model relationships and extrapolate from partial information. That ability is not captured by any classical Markov model, no matter how large.

They want something like the Star Trek computer or one of Tony Stark's AIs that were basically deus ex machinas for solving some hard problem behind the scenes. Then it can say "model solved" or they can show a test simulation where the ship doesn't explode (or sometimes a test where it only has an 85% chance of exploding when it used to be 100%, at which point human intuition comes in and saves the day by suddenly being better than the AI again and threads that 15% needle or maybe abducts the captain to go have lizard babies with).

AIs that are smarter than us but for some reason don't replace or even really join us (Vision being an exception to the 2nd, and Ultron trying to be an exception to the 1st).

yes you can enumerate all inputs, because thoy are not continuous. You just raise the finite number of different tokens to the finite context size and that's exactly the size of the table you would need. finite*finite=finite. You are describing training, i.e how the function is geerated. Yes correlations are found there and encoded in a couple of matrices. Those matrices are what are used in the llm and none of what you said applies. Inference is purely a markov chain by definition.

Misconstruing how language works isn't an argument for what an existing and established word means.

I'm sure that argument made you feel super clever but it's nonsense.

I sourced by definition from authoritative sources. The fact that you didn't even bother to verify that or provide an alternative authoritative definition tells me all I need to know about the value in further discussion with you.

that's very true, I'm just saying this paper did not eliminate the possibility and is thus not as significant as it sounds. If they had accomplished that, the bubble would collapse, this will not meaningfully change anything, however.

also, it's not as unreasonable as that because these are automatically assembled bundles of simulated neurons.

When are people going to realize, in its current state , an LLM is not intelligent. It doesn’t reason. It does not have intuition. It’s a word predictor.

I agree with you. In its current state, LLM is not sentient, and thus not "Intelligence".

I think it's important to note (i'm not an llm I know that phrase triggers you to assume I am) that they haven't proven this as an inherent architectural issue, which I think would be the next step to the assertion.

do we know that they don't and are incapable of reasoning, or do we just know that for x problems they jump to memorized solutions, is it possible to create an arrangement of weights that can genuinely reason, even if the current models don't? That's the big question that needs answered. It's still possible that we just haven't properly incentivized reason over memorization during training.

if someone can objectively answer "no" to that, the bubble collapses.

What statistical method do you base that claim on? The results presented match expectations given that Markov chains are still the basis of inference. What magic juice is added to "reasoning models" that allow them to break free of the inherent boundaries of the statistical methods they are based on?

You can say that the whole system is deterministic and finite, so you could record every input-output pair. But you could do that for any program. That doesn't make every deterministic function a Markov process. It just means it is representable in a finite way. The question is not whether the function can be stored. The question is whether its behavior matches the structure and assumptions of a Markov model. In the case of LLMs, it does not.

Inference does not become a Markov chain simply because it returns a distribution based on current input. It becomes a sequence of deep functional computations where attention mechanisms simulate hierarchical, relational, and positional understanding of language. That does not align with the definition or behavior of a Markov model, even if both map a state to a probability distribution. The structure of the computation, not just the input-output determinism, is what matters.

no, not any computer program is a markov chain. only those that depend only on the current state and ignore prior history. Which fits llms perfectly.

Those sophisticated methods you talk about are just a couple of matrix multiplications. Those matrices are what's learned. Anything sophisticated happens during training. Inference is so not sophisticated. sjusm mulmiplying some matrices together and taking the rightmost column of the result. That's it.

Claiming it's just marketing fluff is indicates you do not know what you're talking about.

They published a research paper on it. You are free to publish your own paper disproving theirs.

At the moment, you sound like one of those "I did my own research" people except you didn't even bother doing your own research.

Yes, LLM inference consists of deterministic matrix multiplications applied to the current context. But that simplicity in operations does not make it equivalent to a Markov chain. The definition of a Markov process requires that the next output depends only on the current state. You’re assuming that the LLM’s “state” is its current context window. But in an LLM, this “state” is not discrete. It is a structured, deeply encoded set of vectors shaped by non-linear transformations across layers. The state is not just the visible tokens—it is the full set of learned representations computed from them.

A Markov chain transitions between discrete, enumerable states with fixed transition probabilities. LLMs instead apply a learned function over a high-dimensional, continuous input space, producing outputs by computing context-sensitive interactions. These interactions allow generalization and compositionality, not just selection among known paths.

The fact that inference uses fixed weights does not mean it reduces to a transition table. The output is computed by composing multiple learned projections, attention mechanisms, and feedforward layers that operate in ways no Markov chain ever has. You can’t describe an attention head with a transition matrix. You can’t reduce positional encoding or attention-weighted context mixing into state transitions. These are structured transformations, not symbolic transitions.

You can describe any deterministic process as a function, but not all deterministic functions are Markovian. What makes a process Markov is not just forgetting prior history. It is having a fixed, memoryless probabilistic structure where transitions depend only on a defined discrete state. LLMs don’t transition between states in this sense. They recompute probability distributions from scratch each step, based on context-rich, continuous-valued encodings. That is not a Markov process. It’s a stateless function approximator conditioned on a window, built to generalize across unseen input patterns.

This paper does provide a solid proof by counterexample of reasoning not occuring (following an algorithm) when it should.

The paper doesn't need to prove that reasoning never has or will occur. It's only demonstrates that current claims of AI reasoning are overhyped.

Intuition is about the only thing it has. It's a statistical system. The problem is it doesn't have logic. We assume because its computer based that it must be more logic oriented but it's the opposite. That's the problem. We can't get it to do logic very well because it basically feels out the next token by something like instinct. In particular it doesn't mask or disconsider irrelevant information very well if two segments are near each other in embedding space, which doesn't guarantee relevance. So then the model is just weighing all of this info, relevant or irrelevant to a weighted feeling for the next token.

This is the core problem. People can handle fuzzy topics and discrete topics. But we really struggle to create any system that can do both like we can. Either we create programming logic that is purely discrete or we create statistics that are fuzzy.

Of course this issue of masking out information that is close in embedding space but is irrelevant to a logical premise is something many humans suck at too. But high functioning humans don't and we can't get these models to copy that ability. Too many people, sadly many on the left in particular, not only will treat association as always relevant but sometimes as equivalence. RE racism is assoc with nazism is assoc patriarchy is historically related to the origins of capitalism ∴ nazism ≡ capitalism. While national socialism was anti-capitalist. Associative thinking removes nuance. And sadly some people think this way. And they 100% can be replaced by LLMs today, because at least the LLM is mimicking what logic looks like better though still built on blind association. It just has more blind associations and finetune weighting for summing them. More than a human does. So it can carry that to mask as logical further than a human who is on the associative thought train can.

For me it kinda went the other way, I'm almost convinced that human intelligence is the same pattern repeating, just more general (yet)

Wow it's almost like the computer scientists were saying this from the start but were shouted over by marketing teams.

It does need to do that to meaningfully change anything, however.

LOOK MAA I AM ON FRONT PAGE

archive.is

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Other way around. The claimed meaningful change (reasoning) has not occurred.