their input is the context window. Markov chains also use their whole context window. Llms are a novel implementation that can work with much longer contexts, but as soon as something slides out of its window, it’s forgotten. just like any other markov chain. They don’t adapt. You add their token to the context, slide the oldest one out and then you have a different context, on which you run the same thing again. A normal markov chain will also give you a different outuut if you give it a different context. Their biggest weakness is that they don’t and can’t adapt. You are confusing the encoding of the context with the model itself. Just to see how static the model is, try setting temperature to 0, and giving it the same context. i.e. only try to predict one token with the exact same context each time. As soon as you try to predict a 2nd token, you’ve just changed the input and ran the thing again. It’s not adapting, you asked it something different, so it came up with a different answer
While both Markov models and LLMs forget information outside their window, that’s where the similarity ends. A Markov model relies on fixed transition probabilities and treats the past as a chain of discrete states. An LLM evaluates every token in relation to every other using learned, high-dimensional attention patterns that shift dynamically based on meaning, position, and structure.
Changing one word in the input can shift the model’s output dramatically by altering how attention layers interpret relationships across the entire sequence. It’s a fundamentally richer computation that captures syntax, semantics, and even task intent, which a Markov chain cannot model regardless of how much context it sees.
an llm also works on fixed transition probabilities. All the training is done during the generation of the weights, which are the compressed state transition table. After that, it’s just a regular old markov chain. I don’t know why you seem so fixated on getting different output if you provide different input (as I said, each token generated is a separate independent invocation of the llm with a different input). That is true of most computer programs.
It’s just an implementation detail. The markov chains we are used to has a very short context, due to combinatorial explosion when generating the state transition table. With llms, we can use a much much longer context. Put that context in, it runs through the completely immutable model, and out comes a probability distribution. Any calculations done during the calculation of this probability distribution is then discarded, the chosen token added to the context, and the program is run again with zero prior knowledge of any reasoning about the token it just generated. It’s a seperate execution with absolutely nothing shared between them, so there can’t be any “adapting” going on
Because transformer architecture is not equivalent to a probabilistic lookup. A Markov chain assigns probabilities based on a fixed-order state transition, without regard to deeper structure or token relationships. An LLM processes the full context through many layers of non-linear functions and attention heads, each layer dynamically weighting how each token influences every other token.
Although weights do not change during inference, the behavior of the model is not fixed in the way a Markov chain’s state table is. The same model can respond differently to very similar prompts, not just because the inputs differ, but because the model interprets structure, syntax, and intent in ways that are contextually dependent. That is not just longer context-it is fundamentally more expressive computation.
The process is stateless across calls, yes, but it is not blind. All relevant information lives inside the prompt, and the model uses the attention mechanism to extract meaning from relationships across the sequence. Each new input changes the internal representation, so the output reflects contextual reasoning, not a static response to a matching pattern. Markov chains cannot replicate this kind of behavior no matter how many states they include.
an llm works the same way! Once it’s trained,none of what you said applies anymore. The same model can respond differently with the same inputs specifically because after the llm does its job, sometimes we intentionally don’t pick the most likely token, but choose a different one instead. RANDOMLY. Set the temperature to 0 and it will always reply with the same answer. And llms also have a fixed order state transition. Just because you only typed one word doesn’t mean that that token is not preceded by n-1 null tokens. The llm always receives the same number of tokens. It cannot work with an arbitrary number of tokens.
all relevant information “remains in the prompt” only until it slides out of the context window, just like any markov chain.
Your conflating surface-level architectural limits with core functional behaviour. Yes, an LLM is deterministic at temperature 0 and produces the same output for the same input, but that does not make it equivalent to a Markov chain. A Markov chain defines transitions based on fixed-order memory and static probabilities. An LLM generates output by applying a series of matrix multiplications, activations, and attention-weighted context aggregations across multiple layers, where the representation of each token is conditioned on the entire input sequence, not just on recent tokens.
While the model has a maximum token limit, it does not receive a fixed-length input filled with nulls. It processes variable-length input sequences up to the context limit, and attention masks control which positions are used. These are not hardcoded state transitions; they are dynamically computed weightings over continuous embeddings, where meaning arises from the interaction of tokens, not from simple position or order alone.
Saying that output diversity is just randomness misunderstands why random sampling exists: to explore the rich distribution the model has learned from data, not to fake intelligence. The depth of its output space comes from how it models relationships, hierarchies, syntax, and semantics through training. Markov chains do not do any of this. They map sequences to likely next symbols without modeling internal structure. An LLM’s output reflects high-dimensional reasoning over the prompt. That behavior cannot be reduced to fixed transition logic.
the probabilities are also fixed after training. You seem to be conflating running the llm with different input to the model somehow adapting. The new context goes into the same fixed model. And yes, it can be reduced to fixed transition logic, you just need to have all possible token combinations in the table. This is obviously intractable due to space issues, so we came up with a lossy compression scheme for it. The table itself is learned once, then it’s fixed. The training goes into generating a huge markov chain. Just because the table is learned from data, doesn’t change what it actually is.
This argument collapses the entire distinction between parametric modeling and symbolic lookup. Yes, the weights are fixed after training, but the key point is that an LLM does not store or retrieve a state transition table. It learns to approximate the probability of the next token given a sequence through function approximation, not by memorizing discrete transitions. What appears to be a “table” is actually a deep, distributed representation compressed into continuous weight matrices. It is not indexing state transitions, it is computing probabilities from patterns in the input space.
A true Markov chain defines transition probabilities over explicit states. An LLM embeds tokens into high-dimensional vectors, then transforms them repeatedly using self-attention and feedforward layers that can capture subtle syntactic, semantic, and structural features. These features interact in nonlinear ways that go far beyond what any finite transition table could express. You cannot meaningfully represent an LLM’s behavior as a finite Markov model, even in principle, because its representations are not enumerable states but regions of a continuous latent space.
Saying “you just need all token combinations in a table” ignores the fact that the model generalizes to combinations never seen during training. That is the core of its power. It doesn’t look up learned transitions-it constructs responses by interpolating through an embedding space guided by attention and weight structure. No Markov chain does this. A lossy compressor of a transition table still implies a symbolic map; a neural network is a differentiable function trained to fit a distribution, not to encode it explicitly.
yes, the matrix and several levels are the “decompression”. At the end you get one probability distribution, deterministically. And the state is the whole context, not just the previous token. Yes, if we were to build the table manually with only available data, lots of cells would just be 0. That’s why the compression is lossy. There would actually be nothing stopping anyone from filling those 0 cells out, it’s just infeasible. you could still put states you never actually saw, but are theoretically possible in the table. And there’s nothing stopping someone from putting thought into it and filling them out.
Also you seem obsessed by the word table. A table is just one type of function mapping a fixed input to a fixed output. If you replaced it with a function that gives the same outputs for all inputs, then it’s functionally equivalent. It being a table or some code in a function is just an implementation detail.
As a thought exercise imagine setting temperature to 0, passing all the combinations of tokens of input, and record the output for every single one of them. put them all in a “table” (assuming you have practically infinite space) and you have a markov chain that is 100% functionally equivalent to the neural network with all its layers and complexity. But it does it without the neural network, and gives 100% identical results every single time in O(1). Because we don’t have infinite time and space, we had to come up with a mapping function to replace the table. And because we have no idea how to make a good approximation of such a huge function, we use machine learning to come up with a suitable function for us, given tons of data. You can introduce some randomness in the sampling of that, and you now have nonzero temperature again.
Ex. A table containing the digits of pi, in order, could be transparently replaced with a spigot algorithm that calculates the nth digit on-demand. Output would be exactly the same
their input is the context window. Markov chains also use their whole context window. Llms are a novel implementation that can work with much longer contexts, but as soon as something slides out of its window, it’s forgotten. just like any other markov chain. They don’t adapt. You add their token to the context, slide the oldest one out and then you have a different context, on which you run the same thing again. A normal markov chain will also give you a different outuut if you give it a different context. Their biggest weakness is that they don’t and can’t adapt. You are confusing the encoding of the context with the model itself. Just to see how static the model is, try setting temperature to 0, and giving it the same context. i.e. only try to predict one token with the exact same context each time. As soon as you try to predict a 2nd token, you’ve just changed the input and ran the thing again. It’s not adapting, you asked it something different, so it came up with a different answer
While both Markov models and LLMs forget information outside their window, that’s where the similarity ends. A Markov model relies on fixed transition probabilities and treats the past as a chain of discrete states. An LLM evaluates every token in relation to every other using learned, high-dimensional attention patterns that shift dynamically based on meaning, position, and structure.
Changing one word in the input can shift the model’s output dramatically by altering how attention layers interpret relationships across the entire sequence. It’s a fundamentally richer computation that captures syntax, semantics, and even task intent, which a Markov chain cannot model regardless of how much context it sees.
an llm also works on fixed transition probabilities. All the training is done during the generation of the weights, which are the compressed state transition table. After that, it’s just a regular old markov chain. I don’t know why you seem so fixated on getting different output if you provide different input (as I said, each token generated is a separate independent invocation of the llm with a different input). That is true of most computer programs.
It’s just an implementation detail. The markov chains we are used to has a very short context, due to combinatorial explosion when generating the state transition table. With llms, we can use a much much longer context. Put that context in, it runs through the completely immutable model, and out comes a probability distribution. Any calculations done during the calculation of this probability distribution is then discarded, the chosen token added to the context, and the program is run again with zero prior knowledge of any reasoning about the token it just generated. It’s a seperate execution with absolutely nothing shared between them, so there can’t be any “adapting” going on
Because transformer architecture is not equivalent to a probabilistic lookup. A Markov chain assigns probabilities based on a fixed-order state transition, without regard to deeper structure or token relationships. An LLM processes the full context through many layers of non-linear functions and attention heads, each layer dynamically weighting how each token influences every other token.
Although weights do not change during inference, the behavior of the model is not fixed in the way a Markov chain’s state table is. The same model can respond differently to very similar prompts, not just because the inputs differ, but because the model interprets structure, syntax, and intent in ways that are contextually dependent. That is not just longer context-it is fundamentally more expressive computation.
The process is stateless across calls, yes, but it is not blind. All relevant information lives inside the prompt, and the model uses the attention mechanism to extract meaning from relationships across the sequence. Each new input changes the internal representation, so the output reflects contextual reasoning, not a static response to a matching pattern. Markov chains cannot replicate this kind of behavior no matter how many states they include.
an llm works the same way! Once it’s trained,none of what you said applies anymore. The same model can respond differently with the same inputs specifically because after the llm does its job, sometimes we intentionally don’t pick the most likely token, but choose a different one instead. RANDOMLY. Set the temperature to 0 and it will always reply with the same answer. And llms also have a fixed order state transition. Just because you only typed one word doesn’t mean that that token is not preceded by n-1 null tokens. The llm always receives the same number of tokens. It cannot work with an arbitrary number of tokens.
all relevant information “remains in the prompt” only until it slides out of the context window, just like any markov chain.
Your conflating surface-level architectural limits with core functional behaviour. Yes, an LLM is deterministic at temperature 0 and produces the same output for the same input, but that does not make it equivalent to a Markov chain. A Markov chain defines transitions based on fixed-order memory and static probabilities. An LLM generates output by applying a series of matrix multiplications, activations, and attention-weighted context aggregations across multiple layers, where the representation of each token is conditioned on the entire input sequence, not just on recent tokens.
While the model has a maximum token limit, it does not receive a fixed-length input filled with nulls. It processes variable-length input sequences up to the context limit, and attention masks control which positions are used. These are not hardcoded state transitions; they are dynamically computed weightings over continuous embeddings, where meaning arises from the interaction of tokens, not from simple position or order alone.
Saying that output diversity is just randomness misunderstands why random sampling exists: to explore the rich distribution the model has learned from data, not to fake intelligence. The depth of its output space comes from how it models relationships, hierarchies, syntax, and semantics through training. Markov chains do not do any of this. They map sequences to likely next symbols without modeling internal structure. An LLM’s output reflects high-dimensional reasoning over the prompt. That behavior cannot be reduced to fixed transition logic.
the probabilities are also fixed after training. You seem to be conflating running the llm with different input to the model somehow adapting. The new context goes into the same fixed model. And yes, it can be reduced to fixed transition logic, you just need to have all possible token combinations in the table. This is obviously intractable due to space issues, so we came up with a lossy compression scheme for it. The table itself is learned once, then it’s fixed. The training goes into generating a huge markov chain. Just because the table is learned from data, doesn’t change what it actually is.
This argument collapses the entire distinction between parametric modeling and symbolic lookup. Yes, the weights are fixed after training, but the key point is that an LLM does not store or retrieve a state transition table. It learns to approximate the probability of the next token given a sequence through function approximation, not by memorizing discrete transitions. What appears to be a “table” is actually a deep, distributed representation compressed into continuous weight matrices. It is not indexing state transitions, it is computing probabilities from patterns in the input space.
A true Markov chain defines transition probabilities over explicit states. An LLM embeds tokens into high-dimensional vectors, then transforms them repeatedly using self-attention and feedforward layers that can capture subtle syntactic, semantic, and structural features. These features interact in nonlinear ways that go far beyond what any finite transition table could express. You cannot meaningfully represent an LLM’s behavior as a finite Markov model, even in principle, because its representations are not enumerable states but regions of a continuous latent space.
Saying “you just need all token combinations in a table” ignores the fact that the model generalizes to combinations never seen during training. That is the core of its power. It doesn’t look up learned transitions-it constructs responses by interpolating through an embedding space guided by attention and weight structure. No Markov chain does this. A lossy compressor of a transition table still implies a symbolic map; a neural network is a differentiable function trained to fit a distribution, not to encode it explicitly.
yes, the matrix and several levels are the “decompression”. At the end you get one probability distribution, deterministically. And the state is the whole context, not just the previous token. Yes, if we were to build the table manually with only available data, lots of cells would just be 0. That’s why the compression is lossy. There would actually be nothing stopping anyone from filling those 0 cells out, it’s just infeasible. you could still put states you never actually saw, but are theoretically possible in the table. And there’s nothing stopping someone from putting thought into it and filling them out.
Also you seem obsessed by the word table. A table is just one type of function mapping a fixed input to a fixed output. If you replaced it with a function that gives the same outputs for all inputs, then it’s functionally equivalent. It being a table or some code in a function is just an implementation detail.
As a thought exercise imagine setting temperature to 0, passing all the combinations of tokens of input, and record the output for every single one of them. put them all in a “table” (assuming you have practically infinite space) and you have a markov chain that is 100% functionally equivalent to the neural network with all its layers and complexity. But it does it without the neural network, and gives 100% identical results every single time in O(1). Because we don’t have infinite time and space, we had to come up with a mapping function to replace the table. And because we have no idea how to make a good approximation of such a huge function, we use machine learning to come up with a suitable function for us, given tons of data. You can introduce some randomness in the sampling of that, and you now have nonzero temperature again.
Ex. A table containing the digits of pi, in order, could be transparently replaced with a spigot algorithm that calculates the nth digit on-demand. Output would be exactly the same