NOTE-365: Integrated Information Theory 3.0

Contribution

IIT 3.0 sets out the theory’s axioms and postulates explicitly and applies each postulate twice, once to single mechanisms and once to systems of mechanisms. Text S1 lists the changes from IIT 2.0. Information becomes “a difference that makes a difference”, requiring both causes and effects within the system. The elements are mechanisms in a state, not connections. A complex is found by partitioning its whole conceptual structure, not only its top-order concept. The distance used is the earth mover’s distance, not KL divergence. And, item 8, “the exclusion postulate is applied not only to systems of mechanisms but also to causes and effects specified by individual mechanisms”. The result is a definite recipe that, for a small discrete system with a known transition probability matrix, says which sets of elements are conscious, how much, and with what quality.

Key insight

Consciousness is a property of whichever set of elements is most irreducible, judged against every set it overlaps. A set of elements has a whole-level causal structure that partitioning destroys, measured by Φ. Of any family of overlapping sets, only the one at a local maximum of Φ “exists intrinsically”. So the boundary of a conscious entity is fixed by competition between overlapping candidates. A conscious system can have no conscious parts and be part of no conscious whole, because its parts and its wholes are exactly the sets it beats or loses to.

Assumptions

• The axioms are self-evident and “do not need proof”. The exclusion axiom reads: “each experience excludes all others – at any given time there is only one experience having its full content, rather than a superposition of multiple partial experiences; each experience has definite borders …; each experience has a particular spatial and temporal grain.”
• The postulates are “unproven assumption[s]” about physical substrates, chosen to mirror the axioms. The paper’s definition of “postulate” says so.
• The identity: the MICS of a complex “is identical to its experience”. It is asserted, not derived.
• The setting. Systems are discrete in time and state, with a known transition probability matrix (TPM) obtained by perturbing the system into all its states. Elements outside the candidate set are background conditions, fixed at their actual values (Text S1, item 9).
• The grain. The examples assume that the binary elements and unit time steps are the grain at which Φ peaks. The theory says the grain should be searched over as well (refs 20, Hoel et al. 2013).
• The distance is the earth mover’s distance, called “the current distance measure of choice”. The extended EMD between constellations is defined in Text S2, which was not read.

Key results

All results are either definitions or are computed on small logic-gate networks with the authors’ software. Nothing is computed for a brain.

• Exclusion within a mechanism (Fig. 8, Fig. S1). A mechanism’s “core cause” is the purview with maximal φ, and “other causes and effects are excluded”. The motivation is an infinite regress: strong synapses, plus weak synapses, plus stray glutamate receptors, plus cosmic rays. The exclusion postulate “represents a causal version of Occam’s razor, saying in essence that ‘causes should not be multiplied beyond necessity’, i.e. that causal superposition is not allowed”. Only the most irreducible cause is kept, because “something exists all the more, the more of a difference it makes”. Ties go to the larger purview (Fig. S1 caption). “Exclusion does not apply across mechanisms within a set of elements.”
• Exclusion between systems (Fig. 14). “Of all overlapping sets of elements, only one set can be conscious.” A complex is “a local maximum of integrated conceptual information ΦMax (meaning that it has maximal Φ as compared to all overlapping sets of elements)”. “Because of exclusion, complexes cannot overlap and at each point in time, an element/mechanism can belong to one complex only.” In the example, ABC is the complex, so “no subset or superset of ABC can form another complex”. No separate argument is given for this level beyond the axiom. The Occam’s-razor passage is attached to the mechanism level. No tie rule is stated for systems.
• Integration requires two-way causation (Figs. 5, 7, 13). An element with inputs but no outputs to the set, or the reverse, contributes no intrinsic information. A set is a whole only if every subset has both causes and effects in the rest. A one-way connected subset is an “appendix”, like a minute-taker who cannot answer back to the board.
• Condensation (Fig. 16). A larger network condenses into a major complex ABC, a minor complex DE and an isolated minor complex FG. ABCDE is integrated but “excluded from forming a complex, since it overlaps with ABC”. Extrapolated, not computed: the human brain has a dynamic main cortical complex and many “minimally conscious” minor complexes. After split-brain surgery there are two main complexes. Some unconscious semantic processing may be “paraconscious” minor complexes.
• Architecture (Fig. 17). A modular network of three COPY–AND pairs is not one complex but three, “each generat[ing] more Φ than the whole system”. A homogeneous all-to-all network of OR gates has low Φ. A specialised network of majority gates has high Φ. The cerebellum and slow-wave sleep are offered as the neural analogues.
• Inactive systems (Fig. 18). Four COPY gates all off form a complex. An inactive but responsive main complex would be conscious, and no “broadcast” or “ignition” is needed.
• Minimally conscious photodiode (Fig. 19). A detector and a predictor feeding back to each other form a complex with ΦMax = 1 and two concepts. A thermistor with the same internal mechanism has the same experience.
• Feed-forward zombies (Figs. 20–21). A purely feed-forward system has no complex, by recursion on its input and output layers. A recurrent network (ΦMax = 0.76, 17 concepts in the depicted state) is matched over at least four time steps by an unfolded feed-forward network with no complex. “Whether a system is conscious or not cannot be decided based on its input-output behavior only.”
• Self-referential concepts (Fig. 22). In a ten-element segment/dot network, every concept’s purview lies inside the complex. Concepts are “self-generated, self-referential, and holistic”, and experience is “an ‘awake dream’ selected by the environment”.

Claims

id	claim	strength	support
C1	Experience is identical to the MICS of a complex; ΦMax is its quantity and the constellation’s shape its quality	assertion (the central identity)	stated as an identity; motivated by the axiom–postulate parallel
C2	Of all overlapping sets of elements only the local maximum of Φ is conscious: no subset or superset of a complex is conscious	postulate	the exclusion axiom (“definite borders”, one experience at a time); no argument specific to the system level
C3	A mechanism has exactly one cause and one effect, the maximally irreducible	postulate with an informal argument	infinite-regress example and “causal Occam’s razor” (Fig. S1)
C4	A system can condense into one major and several non-overlapping minor complexes; the brain has a main complex plus paraconscious minor ones	strong for the toy network (Fig. 16); assertion for the brain	computed example; neural extrapolation
C5	Modular networks split into small complexes, which may explain why the cerebellum does not contribute to consciousness	moderate for the toy; suggestive for the cerebellum	Fig. 17 computation; anatomical analogy
C6	Inactive but responsive systems can be conscious	strong within the formalism	Fig. 18 computation
C7	Feed-forward systems are never conscious, and a conscious system can have an unconscious functional equivalent	strong within the formalism	recursion argument; Fig. 21 computation
C8	Integrated architectures are favoured by evolution and are “autonomous, since [they] can act and react based on [their] internal states and goals”	assertion	listed benefits, no analysis
C9	Ant colonies, octopuses and computers have definite IIT answers that are “in principle testable”	assertion	none; computing them is “not practically feasible”

Concepts

• Mechanism — “anything having a causal role within a system”, for example a neuron or a logic gate, including higher-order combinations.
• Cause-effect repertoire; cei — the distributions over past and future states a mechanism in a state constrains; cause–effect information is the smaller of the two distances from the unconstrained repertoire.
• φ (small phi) — how far a mechanism’s cause–effect repertoire is from that of its minimum information partition.
• Concept (core concept) — a mechanism with its maximally irreducible cause–effect repertoire (MICE), weighted by φMax.
• Φ (big phi) — how far a set’s constellation of concepts is from that of its unidirectional minimum information partition.
• Complex — a set of elements at a local maximum of Φ against all overlapping sets. “Only a complex exists as an entity from its own intrinsic perspective.”
• MICS, quale sensu lato — the constellation of concepts a complex specifies, identified with its experience.
• Major and minor complexes; paraconscious — non-overlapping complexes of high and low ΦMax in one system; a minor complex is “conscious ‘on the side’”.
• Background conditions — elements outside the candidate set, held at their actual states.

Connections

• Schwitzgebel (LIT-159, NOTE-131; book version LIT-216, NOTE-188). NOTE-131 records that the 2014 manuscript’s §2 cites this paper with Tononi 2008–2012 and Tononi & Koch 2014. What it attacks matches this paper’s system-level exclusion. The strict local-maximum comparison is what makes the one-ballot threshold sharp, and the “local maximum against all overlapping sets” wording does nothing to soften it. But the defence Schwitzgebel attributes to Tononi, Occam’s razor plus the absurdity of a two-person group consciousness, is not this paper’s system-level defence. Here Occam’s razor appears only at the mechanism level, and groups of people are not discussed. NOTE-131 sources the threshold passage to Tononi 2010 (n. 9) and Tononi & Koch 2014 (n. xii); which Tononi text supplies the two-person example it does not say. The grain clause here (“the macro may emerge over the micro”) is the hook the book version later uses, via this paper’s ref. 20, to argue that a polity could out-integrate its citizens.
• The IIT line in the record. LIT-185 (NOTE-122) reads IIT 4.0, which keeps exclusion as one of six axioms. It turns this paper’s non-overlapping complexes into a gapless “tiling” of space-time by non-overlapping substrates. That sharpens the anti-nesting reading without changing it, and NOTE-122 notes that it does not engage Schwitzgebel either. This paper’s own limitations (discrete states, full TPM, a dozen elements, grain assumed) are the ones LIT-185 presses in their later form.
• Putnam. Not cited. The system-level postulate does formally what Putnam’s stipulation did by fiat: it rules out a pain-feeler with pain-feeling parts. The difference is that here which level wins is decided by a quantity, Φ. Putnam’s stipulation says only that whole and part cannot both feel pain, and his stated motive, ruling out swarms of bees (NOTE-131), favours the parts.
• Group agency. The paper says nothing about groups of people. Its zombie result is what lets an IIT theorist grant that a group is an agent while denying that it experiences anything. That is the move group-agency accounts make when they use IIT against group consciousness.
• Minsky, Brooks, Levin. Minsky’s mindless agents (LIT-429), Brooks’s behaviour layers (LIT-436) and Levin’s nested Selves (LIT-439) are all architectures of parts. Under this paper, none of them is conscious or unconscious by virtue of how it behaves. Two of its own conditions bear on them. A part with one-way causal links to the rest is only an “appendix”. And the environment counts only as background condition, so feedback that runs through the world does not integrate a system. That second point is my observation, not the paper’s, but it bears directly on Brooks’s design, whose layers “interface directly to the world through perception and action, rather than interface to each other particularly much”.

Bearing on the record

For the Minsky–Schwitzgebel bridge, this is the anti-nesting principle itself, in its most formal statement. Against NOTE-131’s numbering:

• C3: contests, for any whole that overlaps a conscious part with higher Φ, and symmetrically for any part of a higher-Φ whole.
• C4: neutral. Putnam is not cited, though this is the formal heir of his stipulation.
• C5: the target. Nothing here answers the reductio. The strict local-maximum rule is what produces the sharp threshold. The grain clause is the one resource the paper offers for a whole to out-integrate its parts.

A THEORY drawing the bridge should cite it for three things: the statement of exclusion, the fact that its system-level form is postulated from the axiom, not argued, and the zombie result. The zombie result says that agency composed from parts does not bring experience with it on IIT, and that is the clearest answer any work on this list gives to the brief’s second question. A THEORY should not cite this paper for the Occam’s-razor or two-person-group defence of system-level exclusion, which are not in it.

It carries no instruction for machine-learning practice.

Limitations

• Toy systems only. “The present analysis is unfeasible for systems of more than a dozen elements or so.” The brain, cerebellum, split-brain and octopus claims are extrapolations.
• The grain is assumed, not found. The authors say the optimal spatio-temporal grain “needs to be established”. Every example assumes it.
• Exclusion at the system level is unargued. It is the axiom restated as a postulate. Why the maximum and not, say, every integrated set is not addressed, and no tie rule for systems is given.
• The identity is not tested by anything in the paper. The empirical support mentioned (TMS–EEG in sleep, anaesthesia and brain damage) concerns integration as a correlate of the level of consciousness, not exclusion.
• Incomplete by the authors’ account. The relation of the MICS to modalities and “feel”, the origin of meaning, and “matching” to the environment are left to future work.

Open questions

• Is there an argument for system-level exclusion that does not reduce to the axiom “each experience has definite borders”? The axiom is about one experience. It does not obviously forbid a second, larger experience that includes the first subject as a part. That is the gap Schwitzgebel exploits.
• What does the grain search do to a nested system? If a coarse-grained whole can beat its fine-grained parts, exclusion could favour the collective, as the book version of Schwitzgebel’s argument suggests via Hoel et al. 2013. No calculation for a social system exists.
• Does feedback through a shared environment ever count as integration? It does not under the background-condition rule here. That matters for every behaviour-based or swarm architecture.