The machine that looks the same from outside

The ordinary intuition is functional: preserve the transformation from inputs to outputs and you preserve what matters. This intuition earns its place in engineering. A sorting routine can move from silicon to paper without ceasing to sort. A trained model can be copied to another compatible accelerator and preserve its benchmark performance. When reliability, cost or latency is the target, implementation details matter only through their effects on those targets.

IIT makes a stronger and more controversial proposal. It identifies an experience with the cause-effect structure specified by a maximal physical substrate. In IIT 4.0, the substrate must have cause-effect power that is intrinsic, specific, unitary, definite and structured. These are theory postulates derived from proposed properties of experience, not measurements that independently establish the theory.^[1]

The hidden assumption inside the functional intuition is therefore exposed: that the same realised computation carries the same intrinsic causal organisation. It need not. Two devices can implement one input-output map while their parts differ in what they can affect and be affected by. IIT treats that difference as constitutive, not incidental.

To see the shift, imagine labelling four voltages in a circuit as the symbols north, south, east and west. An observer can use the sequence as a compass code. That extrinsic interpretation may be perfectly useful, yet the voltages do not acquire new causal powers from the labels. IIT asks what each physical state rules out for the substrate itself, not what a human decoder can infer from it. A software-level node matters only when its proposed relations are realised by units that can be independently manipulated and that make the corresponding differences.

The present state matters too. One set of gates can be highly selective in one configuration and degenerate in another. A device therefore does not receive a timeless quantity merely because its wiring diagram is fixed. The assessment concerns this candidate, in this state, at this grain. This state-dependence is one reason a benchmark-level label such as “GPT-class model” is far too coarse to carry an IIT claim.

flowchart LR
  A["Two clocks that never disagree"] --> B["The machine that looks the<br/>same from outside"]
  B --> C["The mechanism IIT claims is<br/>decisive"]
  C --> D["Where an artificial system<br/>begins and ends"]
  D -. "re-test" .-> A
  classDef first fill:#0a1424,stroke:#007D68,stroke-width:2px,color:#e6f3ff
  classDef step fill:#0a1424,stroke:#3f7da0,stroke-width:1px,color:#e6f3ff
  class A first
  class B,C,D step

The mechanism IIT claims is decisive

IIT’s formalism is extensive, and successive versions have changed important definitions. The useful first-principles route is to hold one question steady: what would remain of this system’s causal constraint if we broke it at its weakest fault line?

Begin with physical units that can be set and observed. Choose a present state and a time step. For every possible starting state, intervene to set the units and record the probability of every next state. The result is a transition probability matrix, or TPM:

This equation compresses an experiment. If the candidate has two binary units, there are four possible present states and four possible next states. The TPM has four rows and four columns. If the hardware is stochastic, each row is a probability distribution. IIT 4.0 assumes a finite state space, discrete updates and a complete causal description at the chosen level, with conditional independence of unit updates given the preceding system state.^[1] Real devices rarely arrive in that form. Discretisation, hidden variables, asynchronous updates and measurement error are modelling debts, not clerical details.

Now vary one property at a time. Give a unit many possible effects but let an external controller choose them. The unit is informative to an observer, yet its apparent power is not intrinsic to the proposed candidate. Let two halves each constrain the future, but allow one directional cut to leave those constraints unchanged. The whole is not unitary under IIT because a part neither genuinely affects nor is affected by the rest. Enlarge the boundary to include everything in the laboratory and the result may cease to be definite, since overlapping subsets can compete for the maximal claim.

The fifth commitment, composition, prevents the theory from stopping at “the whole is irreducible”. Subsets of units in their current states can specify their own irreducible causes and effects. Those distinctions can overlap in their purviews and stand in causal relations. IIT 4.0 calls the resulting structured object a Phi-structure. Its overall structure-level quantity is not simply connectivity, entropy or the system-level irreducibility of one cut. Integration selects a whole; composition asks what causal structure that whole specifies.

This is also where a tempting shortcut fails. A computational graph displays dependencies required by an algorithm. An IIT causal graph must describe what physical units would do under interventions, including states the normal programme never visits. The two graphs may align in a carefully engineered circuit. They need not align in a compiler stack, shared accelerator, virtual machine or distributed service.

IIT then searches for the partition that makes the least difference, the candidate’s weakest fault line. If some directional partition changes neither the relevant cause nor effect probability, the system is reducible at that boundary. If every admissible partition loses causal information, the candidate has system-level irreducibility in its present state. IIT further selects maxima over overlapping candidates and possible grains, then unfolds distinctions and relations that compose a Phi-structure.

A scalar is therefore the end of a long chain of choices, not the beginning. Before one can quote it, one has committed to units, state variables, interventions, boundary, update interval, partition set, causal model, distance or intrinsic-information definition, and a version of IIT. Two papers that both say “integrated information” may compute different objects. Comparative work has found marked disagreement among proposed measures even on simple networks.^[6]

A useful report should show the object beneath the scalar. For a small candidate, publish the TPM, current state, intact cause-effect state, tested directional partitions and the minimum partition. For a structure-level claim, publish the distinctions and relations or a machine-readable representation of them. This lets another team ask whether the numerical result came from a genuine causal constraint, a state convention, a tie-breaking rule or an implementation detail.

That transparency also separates two questions often collapsed by the Greek letter. System-level irreducibility asks whether the candidate exists as one causal whole under the theory. Structure-level integrated information concerns how much irreducible structured cause-effect power the selected whole specifies. A system can share a system-level value with another while differing in its distinctions and relations. Treating one number as the complete phenomenological prediction discards the structure the theory says is decisive.

Where an artificial system begins and ends

Ask for “the integrated information of a language model” and the first problem is grammatical. A model can mean a file of numerical parameters, an abstract function, a running process, a configured service, a cluster of accelerators or an agent connected to tools and people. Only some of these are candidates for physical cause-effect analysis. None is selected merely by the product name.

Consider one response from a transformer service. The weights shape computations but do not update during ordinary inference. Tokens enter a runtime. Activations and a key-value cache occupy volatile hardware. Kernels execute across accelerator cores under clocks, schedulers, memory controllers and network fabrics. A CPU orchestrates work. A tool call may leave the machine, alter a database and return evidence. Which units form the candidate substrate? Which states recur? At what interval? What is inside the candidate’s causal closure, and what is merely an input?

“The model” is usually an engineering abstraction that crosses several possible IIT boundaries. Treating its attention matrix, loss, parameter count or computational graph as intrinsic causal structure skips the physical question the theory makes decisive.

Even the status of a weight is not obvious. A stored parameter affects currents when read, but during ordinary inference the activation may not write back to that memory cell. At one boundary the weight bank is a one-way condition on a recurrent compute core. IIT’s integration postulate requires parts of one candidate to be able to affect and be affected by the rest. A read-only store may therefore act as background conditions rather than as a member of the same maximal complex. Change the hardware to in-memory computing or rapid online learning and that conclusion may change.

Virtualisation adds another trap. Two logical units can be time-multiplexed on one physical core, while one logical unit can be distributed across many cores. Software adjacency does not establish physical adjacency, and a message edge does not reveal whether causal influence is reciprocal at the relevant time scale. An assessment needs a mapping from each proposed unit and state to a reproducible physical intervention. Without that mapping, the boundary is a diagram of our description rather than a candidate’s own causal border.

In practice, state preparation is often the hardest step. Clamping one latch group can disturb power, timing or neighbouring units. Some nominal states may be physically unreachable. Repeated interventions may heat the device and change transition probabilities. The dossier should therefore distinguish ideal interventions in a causal model from realised hardware manipulations, and quantify the gap between them. An estimated TPM without intervention fidelity is evidence about the experiment as configured, not a transparent window onto intrinsic powers.

Uncertainty must propagate forward. Confidence intervals on transition probabilities can alter which partition is minimal, which subset wins and whether a small positive result is distinguishable from zero. Reporting only the value from a point-estimate TPM hides this instability. A robust claim shows how often the same qualitative causal portrait appears under resampled TPMs and nearby modelling choices.

The practical ceiling arrives early. Exact full analysis nests searches over candidate subsets, partitions, states, mechanisms, purviews and relations. PyPhi made formal analyses of small discrete systems reproducible, and current work on upper bounds can prune some calculations.^[2][3] Neither converts a modern accelerator or distributed model service into a routine exact calculation.

Infeasibility is not permission to substitute an easier statistic without changing the claim. Compression complexity, spectral connectivity, perturbational complexity, mutual information and neural synchrony may be useful observables. They can test particular predictions or act as pragmatic complexity measures. They are not automatically IIT 4.0 system irreducibility or Phi-structure.

stateDiagram-v2
  [*] --> Claim
  state "The recurrent twin and the<br/>replay twin" as Claim
  state "Cross-copy versus independent hold" as Test
  state "Cause and effect repertoires" as Revision
  Claim --> Test: expose mechanism
  Test --> Decision: evidence survives
  Test --> Revision: rival survives
  Revision --> Claim: narrow or rebuild
  Decision --> [*]

Build a causal dossier, not a consciousness meter

The engineering temptation is to reduce uncertainty to one number. That is exactly what this problem does not permit. A responsible artificial-system assessment needs a sequence of gates that fail visibly. The proposed causal dossier keeps three questions separate: can the physical candidate be analysed, is the result robust to reasonable modelling choices, and what conclusion follows if IIT is assumed?

The dossier is versioned because each layer can change independently. A firmware update can alter the physical transition model while leaving task accuracy fixed. A new intervention technique can reveal hidden state. A revised IIT formalism can change the computed quantity without changing the hardware. A new empirical study can lower confidence in the theory bridge while leaving the substrate analysis intact. Versioning prevents these changes from being compressed into the sentence “the system became more conscious”.

Its conclusion field has four allowed forms. Eligible and robust means the substrate-specific causal finding survived the declared tests. Eligible but sensitive means the finding depends materially on boundary, grain or uncertainty. Ineligible means the required causal object could not be constructed. Theory-conditional implication records what IIT would infer if its identity claim is accepted. These are not four levels on one scale. They are different epistemic outcomes.

What the lab tests

The lab creates a complete four-by-four TPM from one of three two-bit update rules. Each next bit can flip independently with the selected noise probability. For the A|B partition, the missing input from the other side is replaced by a fair random bit. The intact and cut effect repertoires are compared for the selected current state. Cause repertoires are computed by Bayes’ rule under a uniform prior over past states.

A positive result permits a narrow claim: the chosen transition model contains cross-part causal dependence that is lost under the specified partition. A negative result means the lab found none for this state and cut. It does not rule out other states, boundaries, grains or partitions. Neither result establishes experience.

The “common-clock observations only” preset refuses to calculate. That refusal is part of the artefact. A trace in which two bits move together does not supply the unobserved interventional rows needed for a causal TPM.

The artefact also reveals how noise changes interpretation. In the deterministic cross-copy case, the cut erases a sharp constraint. As independent output noise approaches one half, intact and cut repertoires both approach uniformity and the distance shrinks. The wiring has not disappeared, but the present state makes progressively less reliable difference to the future. This is why topological connectivity alone is insufficient. Causal power depends on transition probabilities in the state being assessed.

const states = [[0,0],[0,1],[1,0],[1,1]];
const tv = (p,q) => 0.5 * p.reduce((s,x,i) => s + Math.abs(x-q[i]), 0);
const norm = xs => {
  const z = xs.reduce((a,b) => a+b, 0);
  return z ? xs.map(x => x/z) : xs.map(() => 1/xs.length);
};

function rule(name, [a,b]) {
  if (name === "cross") return [b,a];
  if (name === "hold")  return [a,b];
  if (name === "xor")   return [a ^ b,a];
  throw new Error("Unknown rule");
}

function row(name, past, eps=0) {
  const target = rule(name, past);
  return states.map(next => next.reduce((p,bit,k) =>
    p * (bit === target[k] ? 1-eps : eps), 1));
}

function cutRow(name, past, eps=0) {
  const [a,b] = past;
  const pA1 = [0,1].reduce((s,missingB) =>
    s + row(name,[a,missingB],eps)
      .reduce((u,p,i) => u + p*states[i][0],0),0)/2;
  const pB1 = [0,1].reduce((s,missingA) =>
    s + row(name,[missingA,b],eps)
      .reduce((u,p,i) => u + p*states[i][1],0),0)/2;
  return states.map(([x,y]) =>
    (x ? pA1 : 1-pA1) * (y ? pB1 : 1-pB1));
}

function analyse(name, current=[0,1], eps=0) {
  const tpm = states.map(s => row(name,s,eps));
  const cut = states.map(s => cutRow(name,s,eps));
  const index = states.findIndex(s => s[0]===current[0] && s[1]===current[1]);
  const effect = tpm[index], cutEffect = cut[index];
  const cause = norm(tpm.map(r => r[index]));
  const cutCause = norm(cut.map(r => r[index]));
  const effectTV = tv(effect,cutEffect), causeTV = tv(cause,cutCause);
  return {effectTV,causeTV,cutSensitivity:Math.min(effectTV,causeTV)};
}

console.log(analyse("cross", [0,1], 0));

What would strengthen or weaken the dossier

The proposal gains force if independent teams recover similar interventional models and cut-sensitive results across defensible boundaries and grains, while matched behavioural mimics diverge in the predicted direction. It weakens if small changes in discretisation, hidden-variable treatment or intervention semantics reverse the result, or if observational proxies fail to predict actual perturbations.

A rival explanation can reproduce apparent irreducibility through common input, synchronisation, aggregation or an imposed state representation. The smallest useful implementation is therefore modest: two to four physical units, a complete intervention table, one explicit partition, uncertainty intervals and a record of prohibited inferences. Do not begin with a billion-parameter system whose causal units cannot be set.

The instrument should not be applied to rank humans, patients or animals. Their moral and scientific assessment rests on converging biological, behavioural, interpersonal and first-person evidence. The dossier is designed to stop overclaiming where artificial-system internals are inspectable and alterable.

sequenceDiagram
  participant Q as Question
  participant M as Mechanism
  participant E as Evidence
  participant D as Decision
  Q->>M: Two clocks that never disagree
  M->>E: The recurrent twin and the replay twin
  E-->>M: compare rival explanations
  E->>D: Fund interventions before interpretations
  D-->>Q: revise scope or act

Fund interventions before interpretations

When someone asks whether an artificial model has high integrated information, do not search first for a library function. Ask which physical units are the candidate, which present state is being analysed, which interventions identify the TPM, which update grain is justified, and which wider or narrower boundary has been ruled out. If those questions have no answer, the correct scientific response is abstention.

If the candidate is small enough to analyse, report the exact formal quantity and its version. Show the intact and partitioned causal repertoires, not only a scalar. Publish the weakest cut, the winning boundary and grain, uncertainty, alternative models and matched implementations. Keep theory evidence separate from substrate evidence.

The most discriminating artificial-system experiment is therefore not a leaderboard. Construct two physical implementations that match the same task-level computation and observable history but differ in a pre-registered causal property. Intervene on the candidate units rather than prompting the software. IIT should predict a different causal portrait, and rival theories should state whether that difference bears on experience. A null result can then weaken a substrate model, an intervention bridge or a theory prediction instead of dissolving into argument about definitions.

The strongest objection must remain in view. The unfolding argument contends that recurrent and feed-forward systems can be functionally equivalent, challenging theories that assign different consciousness on causal-structure grounds.^[7] Replies dispute whether input-output equivalence exhausts empirical evidence, and recent work shows that rapid plasticity can break the static equivalence on which an unfolding construction relies.^[8][9] None of this makes recurrence sufficient for experience. It identifies what an experiment must preserve and what a rival implementation must match.

IIT itself remains contested. Critics question whether its phenomenal axioms are complete or constraining, and work on IIT 3.0 identified non-uniqueness in its Phi calculation.^[13][12] IIT 4.0 revises the formalism, so older criticisms must be reapplied rather than assumed unchanged. A large adversarial collaboration found results consistent with some predictions of IIT and global neuronal workspace theory while challenging central claims of both.^[11] The lesson is not that theory testing failed. It is that serious theories earn progress by exposing divergent predictions and absorbing negative evidence.

This changes the practical decision from “Which AI system has more consciousness?” to “Which configured physical candidates permit discriminating causal tests, and what would those tests establish under rival theories?” That question is slower, smaller and more useful. It turns an ungrounded ranking exercise into a research programme.

It also leaves metaphysics open. A functionalist may regard the right causal organisation as sufficient across substrates. A biological naturalist may require specifically biological powers. Emergentist, panpsychist, neutral-monist, dual-aspect, process and idealist positions can treat organisation as producing, selecting, structuring or expressing experience in different ways. The causal dossier does not settle those views. It gives each of them a better specified object to disagree about.

The decision is therefore to fund interventions before interpretations. Build a small substrate whose units, states and cuts can be controlled. Compare causal twins that behave alike. Publish negative results. Only then scale the question.

Glossary

Candidate substrate

The declared physical units, state and time scale proposed for causal analysis.

Cause-effect power

A system’s ability to be affected and to affect its own possible states under intervention.

Transition probability matrix

A table of probabilities for every next state under every imposed present state.

Cause or effect repertoire

A probability distribution over possible past or future states constrained by the current state.

Partition

A counterfactual cut that replaces selected cross-part causal influences with independent noise.

Minimum information partition

The admissible partition that exposes the candidate’s weakest causal fault line under the chosen IIT formulation.

Phi-structure

In IIT 4.0, the maximally irreducible cause-effect structure comprising distinctions and relations.

Boundary sensitivity

Change in a result under defensible alternatives for units, border, state description or spatiotemporal grain.

References

1. Albantakis, L. et al. (2023). “Integrated information theory (IIT) 4.0: Formulating the properties of phenomenal existence in physical terms.” PLOS Computational Biology, 19(10), e1011465. doi:10.1371/journal.pcbi.1011465.
2. Mayner, W. G. P. et al. (2018). “PyPhi: A toolbox for integrated information theory.” PLOS Computational Biology, 14(7), e1006343. doi:10.1371/journal.pcbi.1006343.
3. Zaeemzadeh, A. and Tononi, G. (2024). “Upper bounds for integrated information.” PLOS Computational Biology, 20(8), e1012323. doi:10.1371/journal.pcbi.1012323.
4. Albantakis, L. and Tononi, G. (2019). “Causal composition: Structural differences among dynamically equivalent systems.” Entropy, 21(10), 989. doi:10.3390/e21100989.
5. Hoel, E. P., Albantakis, L., Marshall, W. and Tononi, G. (2016). “Can the macro beat the micro? Integrated information across spatiotemporal scales.” Neuroscience of Consciousness, 2016(1), niw012. doi:10.1093/nc/niw012.
6. Mediano, P. A. M., Seth, A. K. and Barrett, A. B. (2019). “Measuring integrated information: Comparison of candidate measures in theory and simulation.” Entropy, 21(1), 17. doi:10.3390/e21010017.
7. Doerig, A., Schurger, A. and Herzog, M. H. (2019). “Hard criteria for empirical theories of consciousness.” Consciousness and Cognition, 72, 49–59. doi:10.1016/j.concog.2019.04.002.
8. Kleiner, J. (2020). “Brain states matter. A reply to the unfolding argument.” Consciousness and Cognition, 85, 102981. doi:10.1016/j.concog.2020.102981.
9. O’Reilly-Shah, V. N., Selvitella, A. and Schurger, A. (2026). “A caveat regarding the unfolding argument: implications of plasticity.” Neuroscience of Consciousness, 2026(1), niag027. doi:10.1093/nc/niag027.
10. Leung, A., Cohen, D., van Swinderen, B. and Tsuchiya, N. (2021). “Integrated information structure collapses with anesthetic loss of conscious arousal in Drosophila melanogaster.” PLOS Computational Biology, 17(2), e1008722. doi:10.1371/journal.pcbi.1008722.
11. Cogitate Consortium et al. (2025). “Adversarial testing of global neuronal workspace and integrated information theories of consciousness.” Nature, 642, 133–142. doi:10.1038/s41586-025-08888-1.
12. Hanson, J. R. and Walker, S. I. (2023). “On the non-uniqueness problem in integrated information theory.” Neuroscience of Consciousness, 2023(1), niad014. doi:10.1093/nc/niad014.
13. Bayne, T. (2018). “On the axiomatic foundations of the integrated information theory of consciousness.” Neuroscience of Consciousness, 2018(1), niy007. doi:10.1093/nc/niy007.