The Tononi Lab and the Phi Structure at the Centre of IIT 4.0
Integrated information theory is usually discussed as though it produces a number. IIT 4.0, published by Larissa Albantakis and fifteen colleagues from Giulio Tononi’s group, makes clear that the number was never the point. The theory specifies an entire cause and effect structure, called the Phi-structure, and the scalar phi is a summary of it. That distinction matters because most criticism of the theory, and most attempted applications of it to artificial systems, target the summary rather than the thing being summarised.
| What people usually discuss | What IIT 4.0 actually specifies |
|---|---|
| A single scalar, phi | A Phi-structure, the full set of causal distinctions and relations |
| Whether a system passes a threshold | What the system’s experience is structured like |
| Integration as a quantity | Which specific causes and effects are irreducible and how they overlap |
The Paper and the Group
Integrated information theory (IIT) 4.0 appeared in PLOS Computational Biology in 2023, volume 19, article e1011465. The author list is the working membership of the field’s most productive lab: Larissa Albantakis, Leonardo Barbosa, Graham Findlay, Matteo Grasso, Andrew Haun, William Marshall, William Mayner, Alireza Zaeemzadeh, Melanie Boly, Bjorn Juel, Shuntaro Sasai, Keiko Fujii, Isaac David, Jeremiah Hendren, Jonathan Lang and Tononi.
Naming them together is deliberate here. The individual contributions are real, Albantakis on causal analysis, Grasso on the structure of experience, Haun on spatial phenomenology, Marshall and Mayner on the formalism, but the work is a single programme and reading any one of them in isolation misrepresents it. This is one theory being built by a group over two decades, not a set of competing proposals.
What Changed in Version Four
Three things, and the third is the substantive one.
The axioms are restated as postulates more carefully, tightening the move from claims about what experience is like to claims about what a physical substrate must be.
A new measure, intrinsic difference, replaces the earlier distance functions. The argument is that it is the only measure satisfying the theory’s own requirements, which matters because previous versions used metrics chosen partly for tractability, and critics reasonably asked why those and not others.
Then the Phi-structure is characterised completely for the first time, including the causal relations between distinctions rather than only the distinctions themselves. Earlier formulations described which parts of a system make an irreducible difference. This one describes how those parts overlap and bind, which is the part that is supposed to correspond to the structure of an experience rather than its mere quantity.
Why the Shift From Quantity to Structure Matters
If the theory only claimed that consciousness scales with a number, it would be easy to test and easy to refute. Almost every objection takes that form, including the strongest one, that simple highly connected systems score higher than brains, set out in Scott Aaronson and the expander graph objection to integrated information theory.
The structural claim is different and harder to attack. It says that the geometry of the cause and effect structure corresponds to the geometry of experience, so that a visual field being extended and continuous is not a fact about what the system reports but a fact about how its causal distinctions relate. Haun and Tononi have pursued exactly that for spatial experience.
That is a much more ambitious claim than a threshold, and it is falsifiable in a way a scalar is not, because a mismatch between the structure and the reported phenomenology would count against it. It is also further from anything currently measurable, since computing a full Phi-structure is harder than computing phi, and computing phi is already intractable for systems of any size.
What It Says About Artificial Systems
The verdict on current AI is unchanged and the reasoning is now more explicit. A feedforward network has no irreducible cause and effect structure to speak of, because unrolling it in time shows each layer depends only on the previous one. There is nothing that makes a difference to itself.
The stronger consequence, which the structural formulation sharpens, concerns simulation. A digital computer simulating a conscious system does not inherit that system’s Phi-structure, because the causal structure that exists physically is the computer’s, transistors switching in sequence, not the structure being represented. On IIT this is not a limitation of current hardware. It is a claim that simulation of consciousness and instantiation of consciousness come apart in principle.
That is the sharpest point of disagreement between IIT and the functionalist position this project works from, described on the functionalist emergentism page. If IIT is right, substrate independence is false and the whole programme is misconceived. The disagreement is stated cleanly enough on both sides that it should eventually be decidable, which is more than can be said for most disputes in the field. The full set of positions is in the index of consciousness theories and what each predicts about AI.
The Objection That Survives
Making the theory structural does not make it computable. A Phi-structure for even a modest system requires evaluating every possible partition and every possible subset, and the cost grows super-exponentially. Every published value for a real system uses an approximation, and the approximations do not agree with one another.
Work on decomposing integrated information into redundant and synergistic components, covered in Pedro Mediano and Integrated Information Decomposition, takes a different route to a related goal and does produce quantities computable on real recordings. Whether that counts as a friendly extension of IIT or a replacement for it depends on who is asked.
Comparison to The Consciousness AI
This project’s architecture, described on the architecture page, is one IIT would score poorly and for an interesting reason.
The Global Workspace layer has genuine recurrence. Broadcast is fed back to the specialist modules that produced the bids, across five to ten reentrant cycles, so the system is not feedforward and does have loops that make a difference to themselves. On the crude version of the criterion it does better than a transformer.
It runs on a digital computer, which on IIT 4.0 settles the matter regardless. The Phi-structure that physically exists belongs to the hardware, and the architecture is a description the hardware is representing rather than a causal structure in its own right. No amount of recurrence in the simulated design changes what is physically the case at the level IIT cares about.
Stating that plainly is more useful than working around it. This project proceeds on the functionalist assumption, and IIT is the position under which that assumption fails. Which is right is not settled by either side asserting it.
What Follows
IIT 4.0 is the most complete formal statement of any theory of consciousness, and completeness has made its commitments harder to evade. It says what experience is made of, why simulation does not suffice, and what would have to be measured.
What it has not done is make any of it measurable. The theory is now precise about a quantity nobody can compute for anything larger than a toy, which leaves it in the unusual position of being simultaneously the most rigorous and the least applicable framework in the field.