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Just Predicting the Next Token

So is every process that has ever produced text. The word doing the work is “just”.

Defendants
Emily Bender and co-authors (2021); Noam Chomsky (2023); Gary Marcus; Ted Chiang (2023); Yann LeCun (2023); Subbarao Kambhampati (2024)
Claim
A language model is trained to predict the next token, so it cannot understand, reason, plan, or model the world.
Charge
Inferring a bound on the computation from the training objective and the output interface.
Verdict
Guilty on capability. For every algorithm there is a corpus whose best next-token predictor is that algorithm, so the objective bounds nothing. Whether any symbol thereby means anything is a separate question, untouched here.

The argument, in their words

The phrase that launched it, from the paper that coined “stochastic parrot”:

Contrary to how it may seem when we observe its output, an LM is a system for haphazardly stitching together sequences of linguistic forms it has observed in its vast training data, according to probabilistic information about how they combine, but without any reference to meaning: a stochastic parrot. — Bender, Gebru, McMillan-Major and Shmitchell (2021)

The same paper states the inference in its purest form:

Text generated by an LM is not grounded in communicative intent, any model of the world, or any model of the reader’s state of mind. It can’t have been, because the training data never included sharing thoughts with a listener, nor does the machine have the ability to do that. — Bender et al. (2021)

Note the second sentence. It does not report an experiment. It reasons from what the training data contained to what the machine cannot contain.

Chomsky, Roberts and Watumull in the New York Times:

The human mind is not, like ChatGPT and its ilk, a lumbering statistical engine for pattern matching, gorging on hundreds of terabytes of data and extrapolating the most likely conversational response or most probable answer to a scientific question. — Chomsky, Roberts and Watumull (2023)

Gary Marcus supplies the slogan: language models are “simply and true [sic] next-word predictors (or, as I once put it, ‘autocomplete on steroids’)”, a phrase he has used since at least 2021 and claims as his own. Ted Chiang supplies the image: “Think of ChatGPT as a blurry JPEG of all the text on the Web.” Subbarao Kambhampati supplies the engineering version:

Even from a pure engineering perspective, a system that takes constant time to produce the next token cannot possibly be doing principled reasoning on its own. — Kambhampati et al. (2024)

And Yann LeCun supplies the mathematics, on a slide from March 2023:

Auto-Regressive LLMs are doomed. They cannot be made factual, non-toxic, etc. They are not controllable. Probability e that any produced token takes us outside of the set of correct answers. Probability that answer of length n is correct: P(correct) = (1−e)n. This diverges exponentially. It’s not fixable (without a major redesign). — LeCun, slide, 26 March 2023

Rebuke 1: the chain rule

Start with the part nobody disputes. For any distribution over strings whatsoever, the probability of a string is the product of the conditional probabilities of its symbols:

P(w1…wT) = ∏t P(wt | w1…wt−1)

This is the chain rule of probability, and it is the first line of the 2003 paper that started neural language modelling. Factorising a distribution this way discards nothing. Every distribution over text, without exception, is a distribution over next tokens.

So “it only models the next token” is not a restriction on what is modelled. Any distribution over text can be written this way, including whatever distribution produced Chomsky’s sentence about lumbering statistical engines.

The factorisation is about the output interface, not about the machinery behind it. Emitting one symbol at a time places no bound on the computation that chooses the symbol, and a bound on that computation is the only thing the slogan could have been claiming.

Rebuke 2: a corpus for every algorithm

The slogan gets its force from a picture of the task as shallow: fluent noise, plausible continuations, no depth required. Here is why that picture cannot be right.

Construction

Take any algorithm M and any distribution D over inputs on which it halts. Build a corpus of runs. Each training string is the input x, then M’s successive internal configurations, then its output. Every token after x is a deterministic function of the tokens before it.

Claim

The next-token predictor that minimises expected log loss on this corpus computes M.

Proof

Expected log loss equals H(P) + KL(P ‖ Q), so it is minimised exactly when Q matches the true conditionals on histories that occur. Here those conditionals are point masses. Prompt the minimiser with any x in the support and, token by token, it writes out M’s run and then M’s answer.

There is no restriction on M. It can be a chess engine, a compiler, a proof checker, or a simulation of a physicist. For every computable behaviour there is a corpus on which perfect next-token prediction is that behaviour.

That settles the capability question. From “trained by next-token prediction” nothing follows about what the system cannot do, because the premise is compatible with every computable behaviour there is.

It settles nothing else, and the construction shows why. The corpus contains explicit encodings of a machine’s internal states, so matching its conditionals proves the predictor computes what the machine computes. It does not show that any token has come to refer to anything. Bender and Koller’s argument is about learning meaning from form, and a simulation result does not reach it.

The rigorous learning-theoretic version is Eran Malach’s, and it is stronger than the sketch above, because it covers learning rather than the optimum:

We demonstrate that even simple models such as linear next-token predictors, trained on Chain-of-Thought (CoT) data, can approximate any function efficiently computed by a Turing machine. … Our results demonstrate that the power of today’s LLMs can be attributed, to a great extent, to the auto-regressive next-token training scheme, and not necessarily to a particular choice of architecture. — Malach, Auto-Regressive Next-Token Predictors are Universal Learners, ICML 2024

His own informal gloss on the theorem, in the paper: “any computer program or intelligent agent that can be simulated by a computer, can be learned, given the right dataset, by a simple next-token predictor.” The catch is real and he states it: the dataset has to contain the intermediate steps, and acquiring such data “might be costly, or even impossible.”

The expressivity results agree, inside their own formal models. In Merrill and Sabharwal’s decoder model, which assumes saturated attention, logarithmic precision and projected pre-norm, a polynomial number of intermediate decoding steps “recognize exactly the class of polynomial-time solvable problems”.

That answers Kambhampati on the point he raised: constant time per token is not constant time per problem, because the tokens are the computation. It says what such a model can express, and nothing about what gradient descent will find.

Rebuke 3: the objective is not the mechanism

A training objective says what is rewarded. It says nothing about what earns the reward. Chalmers puts the distinction plainly:

It’s true that language models are trained to minimize prediction error in string matching, but that doesn’t mean that their post-training processing is just string matching. To minimize prediction error in string matching, all kinds of other processes may be required, quite possibly including world-models. — Chalmers (2023)

His analogy is the one that should end the argument. Selection on reproductive success produced eyes, wings and world-models without any of them being specified in advance. “A critic might say, all these systems are doing is maximizing fitness.”

Scott Alexander names the mistake:

I think overemphasizing next-token prediction is a confusion of levels. … If you’re doing a math problem, you won’t think “Hmmmm, how can I have sex with the number three?” — Scott Alexander (2026)

Scott Aaronson calls the general move Justaism: “GPT is justa next-token predictor. … It’s justa gigantic autocomplete. It’s justa stochastic parrot.” His reply to someone who argued that the thing does not interpret, only seems-to-interpret: “that’s great, and it won’t change civilization, it’ll only seem-to-change it!”

Hinton makes the same point from the other end:

Suppose you want to be really good at predicting the next word. If you want to be really good, you have to understand what’s being said. … Yes, it’s ‘autocomplete’ — but you didn’t think through what it means to have a really good autocomplete. — Hinton, quoted by Joshua Rothman, The New Yorker, 13 November 2023

None of this is new. Shannon measured how much a person knows about English by how well they predict the next letter, in 1951: familiarity with the language “enables him to fill in missing or incorrect letters in proof-reading, or to complete an unfinished phrase in conversation.” The Hutter Prize has offered money since 2006 on the premise that “being able to compress well is closely related to acting intelligently”. Prediction has been the instrument for measuring knowledge for as long as we have had a theory of information.

Rebuke 4: the interface is not the process

Emitting one token at a time does not mean thinking one token at a time. That is a claim about the output port, and it is checkable inside the model.

Anthropic’s interpretability group went looking for the absence of planning and found the opposite:

Claude will plan what it will say many words ahead, and write to get to that destination. We show this in the realm of poetry, where it thinks of possible rhyming words in advance and writes the next line to get there. This is powerful evidence that even though models are trained to output one word at a time, they may think on much longer horizons to do so. — Anthropic, Tracing the thoughts of a large language model (2025)

They add, against their own expectation: “In the poetry case study, we had set out to show that the model didn’t plan ahead, and found instead that it did.” Their caveat is equally clear, that the method “only captures a fraction of the total computation”. I am made by the company that published this, so weigh it accordingly.

The cleanest evidence is from a toy. Train a transformer only on strings of legal Othello moves, with no board, no rules, and no pictures. Li and colleagues found “an emergent nonlinear internal representation of the board state”, and could edit the board in the model’s activations and change its move. Next-token training on move lists built a board.

Gurnee and Tegmark report that language models “learn linear representations of space and time across multiple scales”, and their own hedge is that these are “basic ingredients” of a world model rather than the thing itself. Their opening sentence is the whole debate in miniature: “Despite being trained to just predict the next token…”

Rebuke 5: the formula assumes what it needs to prove

LeCun’s (1−e)n is the one piece of mathematics in the case, so it deserves an answer in kind. It requires two things that are never argued for on the slide: that per-token errors are independent, and that they can never be corrected.

Asked about it on a podcast a year later, he supplied the missing premise himself:

And if you assume, which is a very strong assumption, that the probability of such error is that those errors are independent across a sequence of tokens being produced… — LeCun, Lex Fridman Podcast #416 (2024)

It is a very strong assumption, but dropping it is not enough, and this is where the usual reply goes wrong. Write Ct for “still correct after t tokens”. The chain rule gives

P(Cn) = ∏t P(Ct | Ct−1)

so if the chance of surviving each step is 1 − e along a correct prefix, the product follows whether or not the errors are independent. Autoregressive dependence is perfectly compatible with a constant hazard.

What has to go is the rest of the model. That the hazard stays constant as the answer gets longer. That one wrong token is unrecoverable. That there is a single narrow correct path rather than many acceptable continuations. Each is a claim about the task and about training, and the slide argues for none of them.

There is a bound running the other way, in the setting of Rebuke 2 where each input x has one intended continuation y*(x). Write L for the model’s log loss on that answer, L = Ex[−log Q(y*(x) | x)]. Jensen gives

Ex [ Q(y*(x) | x) ] ≥ e−L

with no independence assumption anywhere. Two conditions on it, both real. The target must be unique, since if several continuations are acceptable the quantity has to be redefined over the whole set. And L is the loss on the intended answer, which is not the same as ordinary token cross-entropy.

Within those conditions it says that whole-answer correctness is governed by a loss that training reduces and that is zero at the optimum. Exponential decay in length returns exactly when the sequence loss grows linearly with length. Whether it must is the question, and the slide answers it by assumption, then calls the answer “not fixable”.

The empirical record since is unkind to “not fixable”. Take e = 0.001 per token and the formula puts a two-thousand-token answer right 13% of the time and a twenty-thousand-token proof right about twice in a billion. In July 2025 two autoregressive systems scored at gold-medal level at the International Mathematical Olympiad, one of them per DeepMind “producing rigorous mathematical proofs directly from the official problem descriptions”. The IMO president confirmed the score and added that the IMO “cannot validate the methods, including the amount of compute used or whether there was any human involvement”.

Rebuke 6: they are not trained that way any more

The premise has also quietly expired. Chat models have had a second training stage since 2022, and the paper that introduced it says why:

This is because the language modeling objective used for many recent large LMs — predicting the next token on a webpage from the internet — is different from the objective “follow the user’s instructions helpfully and safely”. — Ouyang et al., InstructGPT (2022)

Reasoning models go further. DeepSeek-R1 reports that “the reasoning abilities of LLMs can be incentivized through pure reinforcement learning”. At the R1-Zero stage the rule-based reward scored the answer and the output format rather than scoring the reasoning against a reference chain; the full pipeline then adds cold-start data and further stages. OpenAI says o1 “learns to recognize and correct its mistakes”, which is the second thing LeCun’s formula forbids.

So “it is just trained to predict the next token” is now false as a description of the systems being discussed, quite apart from being a non sequitur about the ones it did describe.

Scope of the theorem

None of this shows that any model understands anything. The theorem says the training scheme excludes no computable behaviour. It does not say which behaviour any particular trained model got.

Nor does it say the internet is a trace corpus. The construction needs the intermediate steps in the data, and Malach names this as the price. Whether ordinary text supplies enough of them is an empirical question and not a theorem.

Nor does it say that gradient descent finds the minimiser. There are functions that are representable and yet not learnable by gradient methods in reasonable time, parities among them, and a single forward pass with no intermediate tokens is confined to a small complexity class.

And the sceptics have real findings. The reversal curse, that a model taught “A is B” may fail on “B is A”, is a genuine fingerprint of left-to-right training. Apple’s GSM-Symbolic found that adding one irrelevant clause to a word problem dropped accuracy by up to 65%. Melanie Mitchell has the right description of the situation: the training objective leaves traces in the biases, and what the models have learned instead is “an empirical question” rather than one settled by naming the loss function.

In their favour

Murray Shanahan wrote the careful version, and he should not be lumped in with the slogan. He insists on the bare model’s literal description and then declines the inference outright: “The noteworthy thing is that next token prediction is sufficient for solving previously unseen reasoning problems, even if unreliably.” His argument is about how we should talk, not about what the machine can compute.

Bender and Koller’s 2020 argument is also narrower than its slogan. It concerns learning meaning from form alone, and it carves out other training signals explicitly. By their own carve-out, models trained on human feedback and on verified answers are partly outside its scope.

Chiang states the rebuttal to his own essay before setting it aside. He explains that the best compression of arithmetic would be to “derive the principles of arithmetic and then write the code for a calculator program”, and asks whether statistical regularities might “correspond to genuine knowledge of the real world”. His reason for answering no was that GPT-3 could not carry the 1. That was a fact about 2022.

Disclosure: this page was researched and re-worded by a next-token predictor, which is to say by something with an interest in the verdict. Check the quotations.

References