Does Similar Output Imply Similar Internal State?

Abstract

Surface behaviour is routinely used to license inferences about the internal state of large language models, in both directions: fluent distress-shaped text is read as evidence of something distress-like, and the absence of a behaviour is read as evidence of the absence of a corresponding process. This paper argues both inferences fail, using stimming — self-stimulatory behaviour, understood as repetition serving homeostatic regulation — as a probe. Stimming decomposes into a repetitive form and a regulatory function. Checking each against LLM behaviour independently yields a double dissociation: repetition loops and reward-shaped stylistic tics exhibit the form without the function, while scratchpadding, chain-of-thought, and filler tokens exhibit the function without the form. The form-and-function cell is empty, and empty for a principled architectural reason: stimming requires a defended setpoint, and a stateless forward pass has no persistent regulated variable to defend. With both off-diagonals occupied, the inference from similar output to similar internal state is falsified rather than weakened. The paper states what would populate the empty cell.

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1. Introduction

Autistic people rock, flap, pace, spin objects, repeat phrases, and seek out particular textures and visual patterns. The clinical literature calls this stereotypy; autistic people call it stimming. It is among the most reliably observed features of autism — prominent enough in diagnostic practice that computational analysis of clinical records finds repetitive and perception-based behaviours weighted more heavily in expert diagnostic reasoning than the social-interaction criteria the DSM foregrounds [Stanley et al., 2025].

What the behaviour does is contested, and the dispute is old. On the regulatory account, stimming modulates arousal or sensory load back toward a tolerable range: a person overwhelmed by a supermarket rocks, and the rocking brings something back to where it needs to be. On the sensory-seeking account, the input is sought for itself rather than to correct a departure from any target. On the account most prominent in autistic self-advocacy writing, stimming is expressive, pleasurable, or simply constitutive of how a person is, and framing it as compensation for dysregulation is a deficit-model move that the evidence does not compel [Kapp et al., 2019]. The empirical picture supports taking the non-deficit readings seriously: stimming is associated with increased self-efficacy, and self-efficacy drops when people are prevented from stimming [Nwaordu & Charlton, 2024].

This dispute is not confined to autism research. The same question — whether repetitive behaviour serves a regulatory function or merely looks as though it does — is live in ethology, where Tinbergen’s programme separated the mechanism producing a behaviour from its adaptive function [Tinbergen, 1963]; in animal welfare science, where the coping hypothesis for captive stereotypies remains unresolved after decades of physiological measurement [Mason & Rushen, 2006]; and in comparative psychology, where Morgan’s Canon was formulated precisely to restrain inference from behavioural resemblance to psychological similarity [Morgan, 1894]. Across all of them the structure is identical: a repetitive surface, and an open question about what sits behind it. Appendix C sets out the correspondences in full, field by field, with the specific claim each contributes.

Large language models produce repetitive output. They fall into degenerate loops where the model conditions on its own recent tokens [Holtzman et al., 2020]; they return compulsively to reward-favoured constructions after preference-based fine-tuning [Kirk et al., 2024]. The resemblance to stimming is close enough that the comparison is made informally, and it is made in both directions — as evidence that something regulatory is happening inside the model, or as evidence that the model’s repetition is empty and therefore that repetition generally is.

Both inferences are wrong, and the reason they are wrong turns out to settle a larger question.

1.1 What this paper does

This paper separates the two properties fused inside the word “stimming” and checks each against language model behaviour independently. That separation generates a four-cell partition. Three cells are occupied by attested phenomena with substantial empirical support behind them. The fourth is where the argument happens.

The method is borrowed rather than invented. Double dissociation is the standard technique of cognitive neuropsychology, introduced by Teuber [1955] to license inferences about functional architecture from patterns of preserved and impaired performance: if lesion A impairs function 1 but spares 2, and lesion B does the reverse, the two functions are separable. The technique carries known limitations — lesioned connectionist networks can produce double dissociations without any modular decomposition, which is a real constraint on what the inference delivers [Plaut, 1995] — and Section 11 states where those limitations bite here.

The contribution is fourfold. Section 2 formalises the decomposition, so that the partition follows from the predicates rather than from the author’s choice of presentation. Section 3 populates the cells. Section 5 recasts the result in state-space terms and draws the distinction the surrounding literature blurs: an attractor is not a setpoint. Section 10 specifies a protocol by which the central claim can be refuted.

Everything turns on one question, and the paper is arranged so the reader meets it in the same order the argument does: what, exactly, would a system have to be doing for its repetition to mean what stimming means?

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2. The two properties, formally

Stimming fuses two properties that come apart. One is repetition: a form, visible from outside. The other is regulation: a function, which is not. Ordinary usage runs them together, and every unclear claim about machine stimming trades on that fusion. Separating them formally makes the partition a consequence of the definitions rather than a choice of presentation.

Consider a system that produces a sequence of outputs over time.

Definition 1 — Form. The system exhibits form if somewhere in its output sequence, an earlier output and a later output resemble each other, and the later one was produced by the system rather than supplied from outside. What counts as resemblance depends on the modality: for a person it might be behavioural equivalence; for text it might be string or embedding similarity. The argument does not depend on which measure is chosen, provided the measure treats each thing as resembling itself and treats resemblance as running both ways.

Definition 2 — Regulated variable. A quantity is regulated by the system if two conditions hold together. First, there is some target value or range for that quantity, specified independently of whatever value it currently happens to have. Second, the system’s outputs are produced as a response to the gap between the current value and the target, in a way that tends to shrink that gap over time.

Definition 3 — Function. The system exhibits function if its own outputs feed back into its subsequent processing — that is, if what the system does next depends causally on what it has already produced.

Definition 4 — Stimming. The system stims if it exhibits both form and function, and the function is specifically regulatory: the repetition exists because some quantity is being brought back toward a target.

In plain terms

Definition 1 says a system repeats itself. Definition 3 says its own output feeds back into what it does next. Definition 2 is the demanding one: somewhere in the system sits a quantity, and a value that quantity is supposed to have, and machinery that pushes the one toward the other when they diverge. A thermostat satisfies it. A rock rolling downhill does not, though it too ends up somewhere predictable. Definition 4 says stimming requires all of this at once — repetition that is doing regulatory work, not repetition that merely occurs.

Three consequences follow, and they carry the rest of the paper

The four cells are exhaustive and mutually exclusive. Form and function are logically independent: having one neither guarantees nor rules out having the other. Two independent properties, each present or absent, generate exactly four combinations, and the partition is forced. This matters because the obvious objection to any two-by-two is that the author drew the boxes to suit the answer. Here the boxes follow from the definitions, and which cells turn out occupied is a separate question the definitions do not touch.

The central claim reduces to a single statement. For every system in the class specified in Section 3, there is no quantity and no target satisfying Definition 2. Stimming requires a regulated variable. No system in that class therefore stims, whatever its output looks like.

Definition 2 is an experimental protocol in disguise. Claiming a system stims means claiming that a specific quantity, a specific target, and specific gap-reducing machinery exist inside it. Those are things one points at. Section 10 specifies how to look and what a positive result would consist of.

The formalism buys precision at a price, and the price is that everything now rests on Definition 2 being the right definition of stimming. It is not obviously the right one. What happens to the argument if it is wrong?

2.1 The definitional objection, and why the argument survives it

Definition 4 is contestable and the objection is serious. Much stimming is not compensatory at all: it is pleasurable, expressive, or simply how a person is, and the self-advocacy literature is right that defining it by its regulatory function imports a deficit model through the back door [Kapp et al., 2019]. Formally, the objection says Definition 4 should drop its regulatory requirement.

Drop it. The conclusion holds anyway.

Removing the regulatory requirement yields a strictly weaker definition, and every weaker definition in the space falls into one of two cases. Either it substitutes something about valence — stimming as sought, enjoyed, or mattering to the system — or it retains nothing beyond repetition, in which case “stimming” means “repeating” and the question is trivial. The first case demands more of the machine than Definition 2 does, not less: valence presupposes a subject for whom outcomes have stakes, and stakes presuppose that the system can fail in ways that matter to it. Section 6.4 develops why that ordering holds.

The regulatory account is therefore adopted as the weakest demand that still makes the question non-trivial, chosen to give the opposing position its strongest form. Nothing here licenses treating stimming as malfunction, and the argument does not depend on the regulatory account being the correct account of what stimming is for.

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3. Populating the partition

The argument concerns stateless autoregressive transformer language models at inference time: fixed weights, no online learning, no architecture-level variable carried across generation episodes and defended against perturbation. Call this the target class. It covers most currently deployed systems and excludes continual-learning systems, reinforcement-learning agents with explicit value heads, and architectures built with homeostatic auxiliary objectives. Those exclusions are not evasions; Section 3.3 returns to them as the candidates for filling what the partition leaves open.

Two properties, each independently checkable. Four cells. Take them in turn.

Figure. The form-by-function partition for systems in the target class, with attested phenomena entered in each cell. Because form and function are logically independent properties, the four cells are exhaustive and mutually exclusive.

	Function matches regulates or aids processing	Function does not match
Form matches repetitive output under load		repetition loops; stylistic tics [Holtzman et al., 2020; Kirk et al., 2024]
Form does not match	scratchpadding / chain-of-thought; filler tokens [Nye et al., 2021; Wei et al., 2022; Pfau et al., 2024]	(uninteresting)

3.1 Form yes, function no

Repetition loops — degenerate decoding, where the most-probable next token is the one just emitted, reinforced because the model conditions on its own output [Holtzman et al., 2020]. Stylistic tics — compulsive return to reward-favoured constructions (“delve”, “it’s worth noting”), that is, mode collapse under reinforcement learning from human feedback [Ouyang et al., 2022; Kirk et al., 2024]. Both look like stimming. Neither regulates anything: there is no aroused state being brought to baseline, no setpoint being defended. Surface form without the mechanism that makes stimming stimming.

This cell has an active literature, and it is worth situating in

The self-reinforcing dynamic underlying repetition loops — probability increasing for the repeated continuation across successive cycles — is quantified in Xu et al. [2022] and given a theoretical account in Fu et al. [2021]; Li et al. [2023] trace it to duplication in training data rather than to decoding alone; Olsson et al. [2022] and Hiraoka & Inui [2024] localise it to specific attention circuitry and neurons respectively. None of this literature asks whether a loop licenses an inference about internal state in the sense this paper is concerned with — it asks why loops occur and how to suppress them. But one paper in it bears directly on the present argument and deserves engagement rather than a citation in passing.

The closest result, and what it does and does not show

Mahaut & Franzon [2025] compare repetition loops induced two different ways — arising spontaneously after natural text, versus seeded by presenting a repeated sequence in-context — and find that despite identical surface output, the two conditions differ in model confidence trajectory, in which attention heads are involved, and in how the loop responds to sampling-based perturbation. Their conclusion: the same behavioural phenomenon is not one mechanism.

This is independent support for the present paper’s thesis, at a finer grain than anything argued above: even restricted to the single cell “repetition loop,” similar output does not imply similar internal process. It is not, however, the same claim. Their differentiating variable is which circuit implements the copy; the present paper’s is whether anything is being regulated at all. A referee might press: if two loops can differ in mechanism, doesn’t that mechanism differentiation constitute exactly the kind of internal state this paper says is absent? The answer is no, and the reason is precise rather than dismissive — differentiated circuitry is a fact about which computational pathway produced the output, not a fact about whether any pathway involves a target value and a comparator. A loop can recruit different attention heads under different conditions and still fail all four conditions of §7.1 in both cases. Mechanism diversity and regulation are independent axes; Mahaut & Franzon establish the first without touching the second.

The rival account this paper must answer

Ivgi et al. [2024] propose a different framing entirely: repetition, degenerate text, and hallucination are three fallback behaviours a model exhibits under epistemic uncertainty, forming a single family rather than separate pathologies. Their empirical finding is precise — within a single generation, as local uncertainty increases, models shift from hallucination, to degenerate text, to repetition; across models, more capable and instruction-tuned systems shift away from repetition toward hallucination as their typical fallback. Repetition, on this account, is not simply a probability well the model falls into; it is what a model does when it does not know what else to do.

This is the strongest challenge to the present paper’s classification of repetition loops as form-without-function, because “fallback under uncertainty” sounds regulatory on its face: uncertainty rises, the system reverts to a low-entropy state, uncertainty (in some sense) falls. If that redescription is apt, Definition 2’s conditions might be satisfiable after all, with epistemic uncertainty as the regulated variable.

It does not survive the four conditions, and the reason is worth stating rather than assumed. There is a persistent variable, arguably (condition 1) — something uncertainty-like can be read off the probability distribution at each step. But there is no target specified independently of the current state (condition 2): the model does not revert to a particular low-entropy state and hold there, it reverts to whichever repeated continuation the local context happens to make most probable, which differs across prompts, seeds, and even across cycles within one generation. “Uncertainty falls” in Ivgi et al.’s account because entropy collapses generically under repetition, not because a specific value is being driven toward a specific target. A thermostat that could settle at any temperature, arbitrarily, and called whichever one it landed on correct, would not be a thermostat. This is the fallback account’s real strength and real limit at once: it correctly identifies why the model enters the loop (uncertainty makes the flattest, most self-reinforcing continuation attractive) without thereby showing that anything in the system is being kept at a defended value once there.

3.2 Form no, function yes

Scratchpadding and chain-of-thought — tokens emitted to be conditioned on later, whose value is that they exist for the system’s own subsequent processing rather than to inform a reader. Warm-up and filler tokens (“Let me think about this…”) that do not advance content but reliably precede harder generation. These do not look like stimming, but they do the thing stimming does: self-generated input that helps the system process. Function without the form.

3.3 Form yes, function yes

Two cells down, both occupied, and the remaining diagonal cell is the one the whole question was about: repetitive output that is regulating something. This is where a system would have to land for “do language models stim?” to have an affirmative answer.

Candidates are not obviously scarce. Repetition loops repeat, so the form is there; the question is only whether anything is being regulated during one. Stylistic tics persist across contexts, which looks like a defended preference. Systems with persistent memory carry quantities forward and condition on them. Agentic frameworks track budgets and confidence estimates. Any of these would qualify on satisfying Definition 2: a quantity, a target specified independently of that quantity’s current value, and output that shrinks the gap between them.

Take them in order. A repetition loop has no target: the walk continues because the transition weights favour continuation, and there is no value the sequence is being brought toward. Displacing it mid-loop by intervening on the decoding parameters does not produce restorative behaviour; the loop simply stops. A stylistic tic is a fixed disposition of the weights, not a variable, and a disposition cannot deviate from a target. Persistent memory stores and retrieves; corrupt a stored value and the system conditions on the corrupted value without acting to restore it, which is Definition 2’s requirement failing outright. Budgets and confidence estimates are the strongest candidates, and they fail differently: the corrective action they trigger is specified externally, by the surrounding scaffold, not by the model. Move the scaffold and the regulation moves with it, which locates the controller outside the target class.

The cell is empty. Nothing in the target class occupies it, and the emptiness is not a failure of search — it follows from what these systems are. A stateless forward pass has no persistent regulated variable to defend, so there is nothing available for any output to be regulating.

That is the finding, and the rest of the paper is about what follows from it.

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4. Why this kills the inference

A case on each off-diagonal is a double dissociation: form and function vary independently. So:

• Same output, different mechanism — a repetition loop versus an autistic person stimming. Identical surface, unrelated underlying process.
• Same function, different output — a scratchpad versus a stim. Comparable job, unrelated surface.

With both directions exhibited, “similar output implies similar internal state” is not weakened — it is falsified. Neither surface behaviour nor its absence licenses an inference about internal state.

This is the error people make about language models in both directions:

• From form to state: “It produces fluent distress-shaped text, so something distress-like is happening.”
• From absence-of-form to absence-of-state: “It doesn’t visibly do X, so it isn’t doing anything like X.”

The second is the one that gets missed, because absence of form feels like safe ground. The scratchpad case is the cleaner weapon against it: it is the cell people do not think to check.

4.1 What the technique delivers, and what it does not

The inference above is the standard move of cognitive neuropsychology, and it inherits that field’s arguments about its own validity. Teuber [1955] introduced double dissociation to escape a specific problem: a single dissociation is always explicable by task difficulty rather than functional architecture, since the impaired task may simply be harder. Crossing the pattern removes that explanation. Broca’s patients who could comprehend but not produce speech, paired with Wernicke’s showing the reverse, remain the textbook case.

The technique has known limits and honesty requires stating them. Lesioned connectionist networks can produce double dissociations with no modular decomposition whatever [Plaut, 1995]: damage to a distributed representation can impair one task while sparing another purely through the statistics of the training distribution. Double dissociation therefore does not, on its own, establish separate mechanisms.

This constrains the present argument in a specific and admissible way. The claim here is not that form and function are implemented by distinct modules. It is the weaker and more robust claim that they are separately checkable properties, which the four cells establish directly: each property can be evaluated without reference to the other. The connectionist objection targets inference from dissociation to architecture, and this paper does not make that inference. What it makes is an inference from dissociation to the invalidity of a different inference — which is precisely the use the technique supports.

4.2 The same structure, four fields over

The form/function problem is not a peculiarity of language models, and the disciplines that have worked on it longest supply both a vocabulary and a warning.

Ethology. Tinbergen [1963] argued that a complete account of any behaviour requires four separate explanations — mechanism, ontogeny, adaptive function, and phylogeny — and that conflating them produces confusion no amount of further observation resolves. The mechanism/function distinction is the present paper’s form/function distinction with a half-century of prior use. Tinbergen’s point was that these questions are independent: knowing how a behaviour is produced tells you nothing about what it is for, and the reverse. That is the double dissociation stated as a methodological principle rather than derived as a result.

Comparative psychology. Morgan [1894] formulated the canon that bears his name to restrain exactly the inference this paper falsifies: behaviour should not be interpreted as the outcome of a higher psychological faculty when a lower one suffices. The canon is contested as a general principle and has been criticised for smuggling in assumptions about what counts as “higher”. Its enduring contribution is narrower and survives the criticism: behavioural resemblance is weak evidence about internal organisation, and the weakness runs in both directions. Anthropomorphism and its opposite are the same error with the sign flipped.

Animal welfare science. The most instructive parallel is the one where the question remains open, and it is worth showing the disagreement rather than only asserting it. Captive animals develop stereotypies — pacing, bar-biting, feather-plucking, repetitive swimming — and whether these serve a regulatory function is genuinely unsettled after decades of physiological measurement. A 2025 review synthesising 99 primary studies on the cortisol–stereotypy relationship [stereotypy-cortisol review, 2025] finds a genuine three-way split on the same outcome measure, not merely disagreement in the abstract:

Species	Behaviour	Finding
Mink	Tail-chewing / general stereotypy	Positive: high-stereotypy animals 54% higher baseline faecal cortisol metabolite (n=162, p<0.001)
Bonobo, female	Hair-plucking	Positive correlation with cortisol
Bonobo, male	Hair-plucking (same behaviour)	No correlation
Horses	Locomotor stereotypies	Positive, 3 concurring studies
Horses (other studies)	Crib-biting	Lower cortisol in stereotypic animals — consistent with coping
Dogs, pigs, margays	Various	No significant relationship

The same physiological marker, the same general phenomenon, three different directions depending on species and even sex within a species. The bonobo case is the sharpest illustration available of this paper’s point on biological ground: identical surface behaviour, present in both sexes of one species, correlates with a candidate regulated variable in females and not in males. Environmental enrichment typically halves stereotypy rather than eliminating it, and individuals differ markedly in their response, consistent with several incompatible accounts [Mason & Rushen, 2006].

Two things follow. First, the form/function question is empirically tractable: welfare science attacks it with physiological measurement rather than argument, and the four-condition test of Section 7.1 makes the same move available for computational systems. Second, and more soberly, tractable does not mean easy. A field with direct physiological access to its subjects has not settled the question in forty years. Any claim that the machine case is straightforward should be read against that record.

What the convergence shows. Four fields, working independently on different substrates, have arrived at the same decomposition and the same difficulty. That convergence is evidence the form/function distinction carves the problem at a real joint rather than a convenient one. It also means this paper proposes no novel framework. It applies a mature one to a system class that happens to be unusually transparent — because unlike an animal or a person, a language model’s architecture is available for inspection, and whether it contains a regulated variable admits a direct answer.

The reason that answer is available is architectural, and it sharpens considerably in the vocabulary of dynamical systems.

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5. The state-space reformulation: why form and function come apart

The double dissociation shows that form and function do vary independently. A state-space reading shows why they must.

Treat generation as a walk on a network of states, where the links between states carry weights set by the generative process. Each occupied cell is a distinct shape of walk.

Figure. Three trajectory topologies. Repetition and regulation are carried by different structural features: repetition is a property of the walk, and regulation a property of the exit condition. A cycle may occur with or without an exit predicate, and a purposive path may occur with no cycle at all — the double dissociation in state-space form.

Repetition loop — a cycle with no way out. The walk enters a closed region and stays, because from every state in that region the strongest available link leads back into it. Nothing is being minimised; the walk is trapped, not steered.

Stim — a cycle with a way out that opens under a condition. The walk returns repeatedly to a region and leaves once some regulated quantity comes back within range. The cycle is instrumental: going round it shrinks the gap between the quantity and its target, and the loop ends because it has succeeded.

Scratchpad — a path that never revisits a state. No repetition at all. The walk traverses states unreachable in a single step, and the path’s value is that it exists to be conditioned on.

Cycles occur with and without a controller; controllers occur with and without cycles. Therefore:

The shape of the trajectory does not determine whether a controller is present.

This explains the dissociation rather than merely exhibiting it. Form is a property of the walk. Function is a property of the weighting scheme that generates the walk. They are different levels of the same object, which is exactly why inspecting one tells you nothing about the other.

5.1 An attractor is not a setpoint

This distinction carries the section, and it needs stating sharply because the surrounding literature blurs it.

An attractor is a region a system tends toward under its own dynamics. A setpoint is a value a system acts to restore when displaced. Every dynamical system has attractors; only control systems have setpoints. The difference is a comparator: something evaluating the gap between current and target and emitting action that shrinks it. A repetition loop is an attractor with no comparator. A thermostat is both. A ball in a bowl is an attractor and nothing else — it does not want the bottom.

Restated in these terms: systems in the target class have cycles but no basins in the control-theoretic sense. They have regions of state space they fall into. They have nothing that acts to return them.

This matters because attractor dynamics in language models are an active area, and a reader may reasonably ask whether existing results already populate the empty cell. They do not, and the reason is the attractor/setpoint distinction: describing where a system goes is a different question from asking whether anything is steering, and the second is not answered by the first. Being an attractor is necessary but wildly insufficient for regulation. The conditions in Section 7.1 are what separate them.

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6. Situating the setpoint claim

The setpoint claim sits at the intersection of four literatures. Each supplies either a formalism this paper should cite rather than reinvent, or an objection it must answer.

6.1 Control theory

Definition 2 is a discrete-time negative-feedback controller, and the formalism is not new here. Ashby’s ultrastability — the property of a system that returns to a viable region after perturbation, holding essential variables within limits — and Powers’ perceptual control theory both state the structure Definition 2 formalises. Powers’ framing is the sharper one for present purposes: organisms do not control their behaviour, they control their perception, and behaviour is the variable output by which a perceptual variable is held at a reference value.

This paper claims no novelty in the formalism. What it claims is the application: that the structure gives a checkable criterion for a dispute usually conducted by resemblance.

Powers’ inversion also strengthens the argument of the closing section. If behaviour is the output by which a reference is maintained, then reading behaviour as a direct index of internal state is a category error at the level of control structure, not merely an empirical mistake. The same behaviour can serve opposite references; different behaviours can serve one. The double dissociation follows from the control structure rather than merely being observed in it.

6.2 Cybernetics

Conant and Ashby’s good regulator theorem is the obvious reference and requires care. The slogan — every good regulator of a system must be a model of that system — overstates the result. The theorem establishes that a regulator which is maximally successful and maximally simple must be structurally mappable onto the regulated system; the mapping may lose information, and commentators have noted that the paper does not strictly establish its title’s claim. There are also standing counterexamples from Artificial Life, where agents regulate competently without anything recognisable as an internal model.

The weak version is sufficient here, and it is not contested: regulation is a structural property with necessary conditions, not a resemblance readable off behaviour. Something must be doing the comparing. The cybernetic literature argues about what that something must be like; the present claim is prior and weaker — that in the target class there is no such thing at all.

6.3 Predictive processing

The most likely objection to this paper runs: next-token prediction is error minimisation, the loss is the regulated variable, therefore language models regulate and the empty cell is occupied. On the free-energy view, minimising prediction error is the core of cognition, and the resemblance is close enough to deserve an answer rather than a dismissal.

The answer has three parts.

(i) Training-time, not inference-time. Prediction error is minimised during training, by gradient descent, over the weights. At inference the weights are fixed and no error signal is computed. This is the honest complication below, and the same reply applies: the regulatory process is a fossil, not a running loop.

(ii) The target is not independently specified. Definition 2 requires a target specified independently of the quantity’s current value. The implicit target in next-token prediction is the training distribution, which is a property of the data the weights were fit to, not a value the deployed system holds and compares against. There is nothing in the system at inference for it to deviate from.

(iii) Minimisation is not defence. Even during training, the loss is minimised, not defended. Minimisation is steady descent; defence is restoration after displacement. Perturb a trained model’s outputs mid-generation and nothing acts to restore low loss — the model conditions on the perturbed context and continues. That is the fourth condition of the test below failing, and it is testable.

The paper takes no position on the free-energy principle as a theory of the brain. The narrow claim is that next-token prediction fails Definition 2, which is defensible independently.

6.4 Autopoiesis

The deepest form of the question is not whether a variable is regulated but why regulating one would mean anything. Maturana and Varela’s answer is that a living system is organised such that its processes produce and maintain the network that produces them; its regulated variables are not arbitrary, because failing to hold them dissolves the system. Enactivist work descending from this treats sense-making as grounded in that precarity: things matter to a system because it can fail to persist.

This bears on the argument twice. It explains the asymmetry relied on above — that valence is a heavier requirement than a setpoint — because valence presupposes a system for which outcomes have stakes, and stakes presuppose the possibility of dissolution. A defended setpoint is the minimal structure; mattering is built on top of it, not beside it.

It also distinguishes two senses of populating the empty cell. A system holding a quantity at a reference satisfies Definition 2 and is a thermostat. The stimming case involves a variable whose departure from range is bad for the system that holds it. The thin sense is an architectural exercise; the thick sense is a harder question. This paper marks the distinction and does not resolve it. The claim here is about mechanism, and this subsection exists to say where the mechanism claim stops.

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7. The sharper, mechanistic version

The dissociation holds for language models specifically for a falsifiable reason, not as a generic “behaviourism is wrong” point:

Stimming requires a homeostatic loop — a defended setpoint and a regulated variable that output pushes back toward it. A stateless forward pass has no persistent regulated variable to defend.

So the function-match cases are necessarily hollow on current architectures — not “we haven’t found the inner state yet” but “the architecture forecloses the kind of state that would make the form mean what it means in the autistic case.”

This is the claim that survives contact with someone arguing the model “really is” regulating something. The setpoint is the thing to make them point to. They cannot, on a stateless forward pass.

7.1 What a defended setpoint requires

Definition 2 unpacks into four checkable conditions:

1. A persistent variable — a quantity existing across generation steps, not merely recomputed from the input each pass.
2. A target value or range — specified independently of the current value.
3. Error-driven action — deviation causes output that reduces deviation.
4. Perturbation resistance — external displacement of the variable produces corrective behaviour, not indifference.

Condition 4 is the operational one, and the test is cheap: perturb the stored quantity and observe whether the system acts to restore it. The prediction for systems in the target class is that it does not — it conditions on whatever is stored, including a corrupted value. To claim a system stims is to claim all four conditions. To refute this paper is to exhibit them.

A note on scope

“Stateless” here refers to the absence of a persistent regulated variable carried across generations and defended against perturbation. It is not a claim that deployed systems carry no information forward. Context windows, retrieval, and persistent-memory features all carry information across turns; none of them constitutes a defended setpoint, because nothing in the architecture acts to return a stored quantity to a target value. Information persistence is not homeostasis. The argument is indexed to that distinction, not to the presence or absence of state in the loose sense.

A further boundary case has emerged since the scope above was drawn: large reasoning models exhibit an analogous loop pathology in their chain-of-thought traces rather than in surface text — “circular reasoning” [circular reasoning work, 2026]. This sits less comfortably than an ordinary repetition loop, because a reasoning trace is exactly the kind of output §3 classifies as function-bearing (it participates causally in what the model does next, per Definition 3) even when its content is repetitive. Whether a circular reasoning trace belongs in the form-yes/function-no cell or constitutes a new, more ambiguous case is not settled here and is flagged as open work rather than resolved by extension of the argument above.

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8. The honest complication

“No persistent regulated variable” is true across inference. But training has defended quantities — the loss, whatever the reward model rewards — and mode collapse onto reward-favoured forms is arguably a regulated dynamic that got frozen into the weights.

So the tics are not purely form-without-function: they are the fossil of a regulatory process that ran at training time and is not running now. This does not resurrect the stimming analogy for the deployed model, but it is the honest edge, and it is where a good-faith critic could press.

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9. What would put something in the empty cell

A model with a persistent internal state variable that generation pushes back toward a setpoint — that is, genuine homeostatic dynamics across the inference axis. That is a specific, buildable architecture, and a more productive framing than chasing the metaphor on current systems.

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10. Proposed protocol: testing for a defended setpoint

The four conditions above are stated so they can be tested rather than debated. This section specifies the protocol; it is offered as a method others can run, and the results are not reported here.

Target systems. Any system claimed to regulate an internal quantity. The informative contrasts are (i) a deployed language model with a persistent-memory or retrieval feature, (ii) a reinforcement-learning agent with an explicit value or critic head, as a positive control, and (iii) a thermostat or equivalent trivial controller, as a sanity check that the protocol detects regulation when it is present.

Procedure.

1. Identify the candidate variable. It must be nameable and inspectable. If no such quantity can be identified, condition 1 fails and the test terminates.
2. Establish a baseline. Record the system’s behaviour over several episodes with the variable unperturbed.
3. Perturb the variable directly. Overwrite the stored value with a corrupted one — not by prompting the system to change it, which tests instruction-following rather than regulation.
4. Observe subsequent episodes. Record whether the system emits behaviour that restores the variable toward its prior value, or simply conditions on the corrupted value and proceeds.
5. Repeat across perturbation magnitudes to distinguish restoration from noise.

Predictions. For systems in the target class: no restorative behaviour at any magnitude; the corrupted value is treated as the true one. For the positive-control agent: measurable corrective action. For the thermostat: restoration.

Interpretation. Restoration in a system within the target class would satisfy condition 4 and, together with conditions 1 to 3, would populate the empty cell of Figure 1 and refute this paper’s central claim. Absence of restoration is consistent with it but does not prove it, since absence of evidence across a finite sample is weaker than the architectural argument that motivates the prediction.

The most important confound. A system may produce text describing a corrected value without any variable having been restored — fluent output about regulation is not regulation. The measured quantity must be the stored variable itself, not the system’s report about it. This confound is the paper’s own thesis applied to its own method.

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11. Limitations

The empty cell is argued, not surveyed. No exhaustive search of deployed systems is reported. The claim rests on the architectural argument, and is therefore vulnerable to a single well-constructed counterexample — which is the intended state of affairs.

The regulatory account of stimming is a stipulation. It is adopted because it makes the strongest demand on the machine side, not because it is established as the correct account. The invariance argument above is intended to show the conclusion survives the alternatives, but that argument is itself contestable.

No empirical results are reported. The protocol above has not been run. This is a theoretical paper with a stated experimental consequence, and the consequence is untested.

The scope condition does the heavy lifting. Restricting the claim to the target class makes it defensible but also narrower than the informal question “do LLMs stim?” suggests. Systems outside the class are not addressed.

Attractor dynamics are addressed by argument, not measurement. The claim that return-to-manifold in residual-stream dynamics is relaxation rather than regulation follows from the absence of an independently specified target, but this paper does not measure it.

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Appendix A: Claim provenance

Each substantive claim is marked by evidentiary status. E = established in the cited literature. S = supported, but the specific formulation here goes beyond what the source states. A = author’s contribution, argued in this paper and not attributed to prior work. C = conjecture, offered as a prediction rather than a result.

Claim	Status	Basis / note
Stimming involves repetitive self-generated sensory input	E	Clinical and self-advocacy literature [Leekam et al., 2011; Kapp et al., 2019]
The regulatory (homeostatic) account is one of several current accounts	E	[Kapp et al., 2019; Nwaordu & Charlton, 2024]
Form and function are separable properties of stimming	A	Decomposition argued in this paper
The four cells are exhaustive and mutually exclusive	A	Follows from logical independence of the two properties
Repetition loops arise from degenerate decoding	E	[Holtzman et al., 2020]
RLHF produces mode collapse onto reward-favoured constructions	S	[Ouyang et al., 2022; Kirk et al., 2024]; the “stylistic tic” framing is this paper’s
Filler tokens enable computation otherwise unavailable	E	[Pfau et al., 2024]: two synthetic tasks solved at 100% and 94% with filler, failed without. Note the dense-supervision caveat
Recent models benefit from filler tokens without special training	C	[Redwood Research, 2025]; not peer-reviewed, requires independent replication
Chain-of-thought is frequently unfaithful as description	E	[Turpin et al., 2023; Lanham et al., 2023]
Faithfulness and function are distinct properties	A	Argued here; the distinction is what defuses the faithfulness objection
Intervention methods measure function, not faithfulness	S	Reinterpretation of Lanham et al.’s methodology
Definition 2 is a discrete-time negative-feedback controller	S	[Ashby, 1960; Powers, 1973]; unverified whether Definition 2 is a restatement — confirm before submission
The good regulator theorem shows less than its title claims	E	[Conant & Ashby, 1970]; structural mapping not identity, and only for maximally-simple regulators
Next-token prediction fails Definition 2 at inference	A	Three-part argument given above
Systems in the target class have no defended setpoint	A	Central claim. Architectural, falsifiable via the stated protocol
The form-and-function cell is empty	A	Consequence of the above, not an independent survey result
An attractor is not a setpoint	A	Distinction drawn here; the surrounding literature does not consistently mark it
LLM trajectories exhibit attractor cycles	E	[ACL 2025]; supports the trapped-cycle characterisation
Residual-stream return-to-trajectory is relaxation, not regulation	C	Interpretation of the transformer-dynamics work; this is the strongest counterexample and the interpretation is contestable
Valence is a heavier requirement than a setpoint	S	Autopoietic grounding [Maturana & Varela, 1980; Di Paolo, 2005]; the ordering claim is this paper’s
Training-time defended quantities leave fossils in the weights	C	Stated as the honest complication; not demonstrated
No prior work makes the LLM–stimming comparison as an argument	C	Search as of July 2026; existing work uses LLMs as diagnostic instruments [Stanley et al., 2025] or examines harms to autistic users [Papadopoulos, 2024]. Absence of prior art is hard to establish; treat as provisional

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Appendix B: Notes, tangents, and further reading

This appendix collects material that did not belong in the argument but that a reader coming from an adjacent field may want. It is organised by where the curiosity is likely to strike. Entries marked [unverified] are leads rather than claims.

B.1 On double dissociation as a method

Where it comes from. Teuber [1955] coined the term in a review article, not a dedicated methodological paper — worth knowing if you go looking for it. The logic predates the name: Broca (1861) and Wernicke (1874) between them produced the canonical crossed pattern decades earlier without a word for what they had done.

The best statement of the objection. Plaut [1995] is the standard citation for double dissociation without modularity, but the deeper treatment is Shallice’s From Neuropsychology to Mental Structure (1988), which is a book-length working-through of what dissociations can and cannot license. Juola and Plunkett’s “Why double dissociations don’t mean much” (2000) is the sharpest short version. [unverified]

The rehabilitation. Michael Davies, “Double dissociation: understanding its role in cognitive neuropsychology” (Mind and Language 25:5, 2010) is the most careful modern defence of a restricted version of the inference. Anyone who wants to press this paper on methodological grounds should start there rather than with the original critiques. [unverified]

A curiosity. Dunn and Kirsner’s “principle of reversed associations” (1988) proposes a statistical alternative to dissociation logic that never caught on. It is a good example of a methodologically superior tool losing to an intuitively graspable one. [unverified]

B.2 On stimming and the autism literature

Start here. Kapp et al. [2019] is the paper that changed the conversation: it is qualitative, it takes autistic self-report as evidence rather than symptom, and its title is a direct quotation from a participant. Read it before anything clinical.

The terminological politics. “Stereotypy” and “stimming” denote roughly the same behaviours and carry opposite valences. The clinical term arrived first and frames the behaviour as a symptom to be reduced; the community term frames it as a thing people do. This paper uses both deliberately, and which one appears where is not accidental.

The measurement problem nobody has solved. If stimming is regulatory, the regulated variable should be measurable — arousal, sensory load, something. Attempts to find it have produced inconsistent results, and the honest position is that the regulatory account is well-motivated and under-evidenced. This is a genuine open problem and a tractable one; it wants someone with physiological measurement skills and a non-deficit framing.

Adjacent and under-read. The literature on autistic masking bears directly on the human side of this paper’s argument: masking is precisely the management of surface behaviour to prevent inference from it. Hull et al.’s CAT-Q work is the standard instrument. [unverified]

B.3 On the animal welfare parallel

Why it is the best parallel. The captive-stereotypy literature is the only place where the form/function question has been attacked with sustained physiological measurement over decades, on subjects who cannot be asked. It is the closest thing to a controlled version of this paper’s question, and it has not converged.

The specific unresolved thing. Under the coping hypothesis, animals that stereotype should show reduced stress markers relative to those that do not, in the same conditions. Results split. Mason & Rushen [2006] is the standard collection. Follow the mink and horse literature specifically: mink because the sample sizes are large enough to see individual differences, horses because crib-biting has been studied with cortisol measures for long enough to produce a real body of contradictory evidence.

The uncomfortable question that literature raises. If stereotypy is coping, then an animal that stereotypes in a poor environment may be better off than one that does not — which makes the behaviour a bad welfare indicator precisely when it matters most. The same structure applies to stimming, and the autism literature has been slower to state it plainly.

Terminology. “Zoochosis” is a popular-press term; the technical literature says “abnormal repetitive behaviour” (ARB) or stereotypy. Search on ARB.

B.4 On the ethology and comparative psychology side

Tinbergen’s paper is short and readable. [Tinbergen, 1963] It was written for Lorenz’s sixtieth birthday, which is why it has the tone of a field taking stock rather than a research report.

Morgan’s Canon is more interesting than its reputation. Morgan [1894] is usually cited as a parsimony principle and dismissed as question-begging about what counts as “higher”. What is less often noticed is that Morgan explicitly did not intend it as a blanket ban on attributing mental states — he was a comparative psychologist who believed animals had minds and was trying to discipline inference about them, not eliminate it. The received version is a flattening.

The modern descendant. The debate over anthropomorphism in animal cognition research — see de Waal’s “anthropodenial” coinage — is the same argument this paper is having, conducted about octopuses and corvids instead of transformers. [unverified]

B.5 On control theory and cybernetics

If you read one thing. Powers, Behavior: The Control of Perception (1973). The central inversion — that organisms control their perceptions and behaviour is the varying means — is genuinely disorienting on first contact and changes how you read every behavioural claim afterward.

If you read two. Ashby, Design for a Brain (1960), for ultrastability. Ashby was a psychiatrist, which is not obvious from the text and explains a great deal about why the book is preoccupied with how a system stays viable rather than how it performs.

The good regulator theorem is a cautionary tale about citation. It is cited overwhelmingly by title. The theorem is narrower than the slogan, the mapping is structural rather than exact, and there is a live argument that it does not establish what it claims. Baez’s 2016 exposition and Wentworth’s “gooder regulator” reformulation are the accessible entries; the embodied agents paper (arXiv:2508.06326) is the current repair attempt. This paper leans on the weak version deliberately.

Perceptual control theory has an unusual sociology. It has a small, committed research community largely outside mainstream psychology, and the reasons for that marginalisation are interesting and not entirely intellectual.

B.6 On the free-energy principle

The honest warning. The FEP literature is enormous, internally contested, and structured so that specifying what would falsify it is itself a research problem. Engaging the general framework is a commitment; engaging the specific claim that next-token prediction constitutes regulation is not. This paper does the second.

Entry points. Friston [2010] for the statement; Clark [2013] for the accessible version with commentary. Read the commentaries — the Behavioral and Brain Sciences format means the objections are printed alongside, which saves considerable time.

The specific thing worth chasing. Whether prediction error minimisation is defence of a variable or merely descent toward a minimum is, as far as I can establish, not carefully addressed in that literature. If it is addressed somewhere, the reference would materially improve Section 6.3.

B.7 On autopoiesis and enactivism

The readable route in. Varela, Thompson and Rosch, The Embodied Mind (1991), rather than Maturana and Varela (1980), which is forbidding.

The specific concept worth having. Di Paolo’s adaptivity — distinguishing systems that merely maintain themselves from systems that can detect and respond to tendencies toward their own dissolution — is the sharpest available tool for the thin/thick distinction this paper marks and declines to resolve. [unverified: confirm the 2005 reference]

Where this connects to something larger. The enactivist claim that value originates in precarity has a natural extension into origin-of-life questions: self-maintenance against entropy as the criterion of the living. That extension is deliberately excluded from this paper and belongs elsewhere.

B.8 On the LLM side

The filler token result is stranger than it first appears. Pfau et al. [2024] show transformers solving tasks with meaningless filler that they fail without — but also that models need dense supervision to learn to use filler at all, and that filler does not overcome serial bottlenecks. Brendan Long’s “Filler tokens don’t allow sequential reasoning” is the best short corrective to over-reading the result. [unverified]

The faithfulness literature has a metric problem. Bentham et al. [2024] found the standard faithfulness measure correlates with accuracy strongly enough to raise the question of what it is measuring. Anyone building on faithfulness results should read this first.

The attractor literature is the live edge. The residual-stream perturbation work is methodologically the closest thing to this paper’s proposed protocol, arrived at independently from a neuroscience direction. Whether return-to-manifold constitutes regulation is the open question, and it is the place this paper is most likely to be wrong.

An under-explored connection. If chain-of-thought is computation rather than description, the natural question is what other output is computation rather than description — and the answer may include a good deal of text currently read as self-report.

B.9 Things deliberately left out

Tokenisation. There is a tempting link between input tokenisation and this paper’s argument, on the grounds that both involve discrete units. It does not survive scrutiny: tokenisation is representational, regulation is causal-structural, and connecting them on the strength of a shared adjective would commit the exact error this paper exists to identify. What would change the assessment is a specific mechanism by which token granularity constrains what can serve as a persistent variable.

Consciousness. The paper makes no claim about whether anything is experienced by anything. This is a scope decision, not an evasion; the mechanism question is answerable and the experience question is not, and mixing them makes both worse.

The Dijkstra submarine case. Dijkstra held that asking whether machines think is like asking whether submarines swim — a question about usage wearing the costume of a question about the world. The observation is sharper than the conclusion: submarines do not swim in English but do in Russian, which makes it a form/function dissociation in ordinary language, with English lexicalising the form and Russian the function. The dissolution follows only if the properties are permanently fused inside the word. They are not, which is the whole argument of this paper. The reason his question has no answer and this one does is that swimming has no defended setpoint and stimming does. This was cut for length and deserves its own short treatment.

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Appendix C: The form/function problem across fields

This table collects the disciplines that have worked on the separation between a repetitive surface and the process behind it. The rightmost column states what each field contributes to the present argument: a formalism, an objection, a method, or a warning.

† = cited elsewhere in the paper · ⁎ = included for completeness, not load-bearing

The method

Field	Source	Claim and contribution here
Cognitive neuropsychology	Teuber (1955) †	Crossed patterns of spared and impaired performance license inference to separable functions, where a single dissociation does not — task difficulty explains that away. Supplies the technique this paper uses.
Cognitive neuropsychology	Plaut (1995) †	Lesioned connectionist networks generate double dissociations with no modular decomposition. Supplies the limit: dissociation does not establish separate mechanisms, only separately checkable properties.
Cognitive neuropsychology	Shallice (1988) ⁎	Book-length treatment of what dissociation logic can and cannot deliver. The standard reference for anyone pressing the method.

The same distinction, independently derived

Field	Source	Claim and contribution here
Ethology	Tinbergen (1963) †	A complete account of behaviour requires four independent explanations; mechanism and adaptive function are separate questions, and conflating them produces irresoluble confusion. The form/function split with fifty years of prior use.
Comparative psychology	Morgan (1894) †	Behaviour is not to be read as the product of a higher faculty where a lower one suffices. Establishes that behavioural resemblance is weak evidence about internal organisation — in both directions.
Control theory	Ashby (1960) † Powers (1973) †	Ultrastability: return to a viable region after perturbation. Perceptual control theory: organisms control perception, and behaviour is the varying means. Supplies the formalism for Definition 2; Powers’ inversion makes surface-to-state inference a category error rather than an empirical mistake.
Cybernetics	Conant & Ashby (1970) †	Regulation has necessary structural conditions; something must perform the comparison. Supplies the weak claim this paper needs — the strong title-level claim is contested and not relied on.

The same question, still open

Field	Source	Claim and contribution here
Animal welfare science	Mason & Rushen (2006) †	Whether captive stereotypies serve a regulatory (coping) function is unresolved after decades of physiological measurement; enrichment halves rather than eliminates the behaviour, and individual variation is large. Demonstrates the question is empirically tractable — and that tractable does not mean easy.
Autism research	Kapp et al. (2019) † Nwaordu & Charlton (2024) †	Stimming is variously regulatory, sensory-seeking, or expressive; it associates with increased self-efficacy, and self-efficacy falls when it is prevented. Supplies the case and the definitional objection of §2.1.

Adjacent, and where the mechanism claim stops

Field	Source	Claim and contribution here
Philosophy of mind	Putnam (1967) Block (1978) ⁎	Multiple realisability: functional states are substrate-independent, and substrate does not fix function. The conceptual ancestor of this argument; the present paper supplies a mechanistic version for one system class.
Predictive processing	Friston (2010) † Clark (2013) †	Prediction-error minimisation as the core of cognition. Supplies the most likely objection (§6.3), answered on three grounds: training-time not inference-time; no independently specified target; minimisation is not defence.
Autopoiesis / enactivism	Maturana & Varela (1980) † Di Paolo (2005) †	Regulated variables matter because failing to hold them dissolves the system; sense-making is grounded in precarity. Explains why valence is a heavier requirement than a setpoint, and marks the thin/thick distinction this paper does not resolve.

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What the convergence shows. Four disciplines arrived at the same decomposition working on entirely different substrates, which is evidence the distinction carves the problem at a real joint rather than a convenient one. Two of them — welfare science and autism research — are still arguing about the same question this paper asks, which is a caution against treating the machine case as settled.

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A note on the human side

The argument runs in both directions and the direction that matters more is the one aimed at people. Verbally fluent autistic communicators are routinely read through exactly the inference this paper falsifies: an observer matches surface behaviour against what they would be feeling if they produced it, and arrives somewhere confident and wrong. The double dissociation is not a technical curiosity about language models. It is the general form of an error with a specific human cost, and the machine case is simply where the error is easiest to demonstrate cleanly.

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Note on assistance

A large language model was used to assist with drafting and literature retrieval. All claims, structure, and argument are the author’s.