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.

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

I think it's an easy mistake to confuse sentience and intelligence. It happens in Hollywood all the time - "Skynet began learning at a geometric rate, on July 23 2004 it became self-aware" yadda yadda

But that's not how sentience works. We don't have to be as intelligent as Skynet supposedly was in order to be sentient. We don't start our lives as unthinking robots, and then one day - once we've finally got a handle on calculus or a deep enough understanding of the causes of the fall of the Roman empire - we suddenly blink into consciousness. On the contrary, even the stupidest humans are accepted as being sentient. Even a young child, not yet able to walk or do anything more than vomit on their parents' new sofa, is considered as a conscious individual.

So there is no reason to think that AI - whenever it should be achieved, if ever - will be conscious any more than the dumb computers that precede it.

Meaningful change is not happening because of this paper, either, I don't know why you're playing semantic games with me though.

I don't know why you're playing semantic games

I'm trying to highlight the goal of this paper.

This is a knock them down paper by Apple justifying (to their shareholders) their non investment in LLMs. It is not a build them up paper trying for meaningful change and to create a better AI.

I hate this analogy. As a throwaway whimsical quip it'd be fine, but it's specious enough that I keep seeing it used earnestly by people who think that LLMs are in any way sentient or conscious, so it's lowered my tolerance for it as a topic even if you did intend it flippantly.

the fact that it is a fixed function, that only depends on the context AND there are a finite number of discrete inputs possible does make it equivalent to a huge, finite table. You really don't want this to be true. And again, you are describing training. Once training finishes anything you said does not apply anymore and you are left with fixed, unchanging matrices, which in turn means that it is a mathematical function of the context (by the mathematical definition of "function". stateless, and deterministic) which also has the property that the set of all possible inputs is finite. So the set of possible outputs is also finite and strictly smaller or equal to the size of the set of possible inputs. This makes the actual function that the tokens are passed through CAN be precomputed in full (in theory) making it equivalent to a conventional state transition table.

This is true whether you'd like it to or not. The training process builds a markov chain.

I'd encourage you to research more about this space and learn more.

As it is, the statement "Markov chains are still the basis of inference" doesn't make sense, because markov chains are a separate thing. You might be thinking of Markov decision processes, which is used in training RL agents, but that's also unrelated because these models are not RL agents, they're supervised learning agents. And even if they were RL agents, the MDP describes the training environment, not the model itself, so it's not really used for inference.

I mean this just as an invitation to learn more, and not pushback for raising concerns. Many in the research community would be more than happy to welcome you into it. The world needs more people who are skeptical of AI doing research in this field.

You’re absolutely right that inference in an LLM is a fixed, deterministic function after training, and that the input space is finite due to the discrete token vocabulary and finite context length. So yes, in theory, you could precompute every possible input-output mapping and store them in a giant table. That much is mathematically valid. But where your argument breaks down is in claiming that this makes an LLM equivalent to a conventional Markov chain in function or behavior.

A Markov chain is not simply defined as “a function from finite context to next-token distribution.” It is defined by a specific type of process where the next state depends on the current state via fixed transition probabilities between discrete states. The model operates over symbolic states with no internal computation. LLMs, even during inference, compute outputs via multi-layered continuous transformations, with attention mixing, learned positional embeddings, and non-linear activations. These mechanisms mean that while the function is fixed, its structure does not resemble a state machine—it resembles a hierarchical pattern recognizer and function approximator.

Your claim is essentially that “any deterministic function over a finite input space is equivalent to a table.” This is true in a computational sense but misleading in a representational and behavioral sense. If I gave you a function that maps 4096-bit inputs to 50257-dimensional probability vectors and said, “This is equivalent to a transition table,” you could technically agree, but the structure and generative capacity of that function is not Markovian. That function may simulate reasoning, abstraction, and composition. A Markov chain never does.

You are collapsing implementation equivalence (yes, the function could be stored in a table) with model equivalence (no, it does not behave like a Markov chain). The fact that you could freeze the output behavior into a lookup structure doesn’t change that the lookup structure is derived from a fundamentally different class of computation.

The training process doesn’t “build a Markov chain.” It builds a function that estimates conditional token probabilities via optimization over a non-Markov architecture. The inference process then applies that function. That makes it a stateless function, yes—but not a Markov chain. Determinism plus finiteness does not imply Markovian behavior.

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