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.
vrighter@discuss.tchncs.de 2 days ago
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.
auraithx@lemmy.dbzer0.com 2 days ago
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.
vrighter@discuss.tchncs.de 2 days ago
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.
auraithx@lemmy.dbzer0.com 1 day ago
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.