From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3.0 — TEI-tagged view

Masafumi OizumipersName, Larissa AlbantakispersName, Giulio TononipersName (2014date). “From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3.0.” PLoS Computational Biologytitle·j.

Object of study — the phenomenological properties and physical mechanisms claimed to constitute consciousnessterm·dom

Research question — which intrinsic causal organization makes a system conscious, how much, and with what experiential content

Contribution — a formal identity between experience and a maximally irreducible conceptual structureterm·def generated by a complexterm·dom

Full text — tagged

From the Phenomenology to the Mechanisms of Consciousnessterm·dom: Integrated Information Theoryterm·dom 3.0 Abstract This paper presents Integrated Information Theoryterm·dom (IIT) of consciousnessterm·dom 3.0, which incorporates several advances over previous formulations. IIT starts from phenomenological axiomsterm·dom: information says that each experience is specific – it is what it is by how it differs from alternative experiences; integration says that it is unified – irreducible to non-interdependent components; exclusion says that it has unique borders and a particular spatio-temporal grainterm·var. These axiomsterm·def are formalized into postulates that prescribe how physical mechanisms, such as neurons or logic gates, must be configured to generate experience (phenomenology). The postulates are used to define intrinsic informationterm·mth as “differences that make a difference” within a system, and integrated informationterm·mth as information specified by a whole that cannot be reduced to that specified by its parts. By applying the postulates both at the level of individual mechanisms and at the level of systems of mechanisms, IIT arrives at an identity: an experience is a maximally irreducible conceptual structureterm·def ( MICSterm·dom , a constellation of conceptsterm·dom in qualia spaceterm·dom), and the set of elements that generates it constitutes a complexterm·dom . According to IIT, a MICSterm·dom specifies the quality of an experience and integrated informationterm·mth Φ Maxterm·var its quantity. From the theoryterm·mth follow several results, including: a system of mechanisms may condense into a major complexterm·dom and non-overlapping minor complexesterm·dom; the conceptsterm·dom that specify the quality of an experience are always about the complexterm·dom itself and relate only indirectly to the external environment; anatomical connectivityterm·var influences complexesterm·dom and associated MICSterm·dom; a complexterm·dom can generate a MICSterm·dom even if its elements are inactive; simple systems can be minimally conscious; complicated systems can be unconscious; there can be true “zombies” – unconscious feed-forward systems that are functionally equivalent to conscious complexesterm·dom.

Introduction Understanding consciousnessterm·dom requires not only empirical studies of its neural correlates, but also a principled theoretical approach that can provide explanatory, inferential, and predictive power. For example, why is consciousnessterm·dom generated by the corticothalamic system – or at least some parts of it, but not by the cerebellum, despite the latter having even more neurons? Why does consciousnessterm·dom fade early in sleep, although the brain remains active? Why is it lost during generalized seizures, when neural activity is intense and synchronous? And why is there no direct contribution to consciousnessterm·dom from neural activity within sensory and motor pathways, or within neural circuits looping out of the cortex into subcortical structures and back, despite their manifest ability to influence the content of experience? Explaining these facts in a parsimonious manner calls for a theoryterm·mth of consciousnessterm·dom. (Below, consciousnessterm·dom, experience, and phenomenology are taken as being synonymous).

A theoryterm·mth is also needed for making inferences in difficult or ambiguous cases. For example, is a newborn baby conscious, how much, and of what? Or an animal like a bat, a lizard, a fruit fly? In such cases, one cannot resort to verbal reports to establish the presence and nature of consciousnessterm·dom, or to the neural correlates of consciousnessterm·dom as established in healthy adults. The inadequacy of behavioral assessments of consciousnessterm·dom is also evident in many brain-damaged patients, who cannot communicate, and whose brain may be working in ways that are hard to interpret. Is a clinically vegetative patient showing an island of residual, near-normal brain activity in just one region of the cortex conscious, how much, and of what? Or is nobody home? Or again, consider machines, which are becoming more and more sophisticated at reproducing human cognitive abilities and at interacting profitably with us. Some machines can learn to categorize objects such as faces, places, animals, and so on, as well if not better than humans [1] , or can answer difficult questions better than humans [2] , [3] . Are such machines approaching our level of consciousnessterm·dom? If not, what are they missing, and what does it take to build a machine that is actually conscious? Clearly, only a theoryterm·mth - one that says what consciousnessterm·dom is and how it can be generated - can hope to offer a combination of explanatory, inferential, and predictive power starting from a few basic principles, and provide a way to quantify both the level of consciousnessterm·dom and its content.

Integrated information theoryterm·dom (IIT) is an attempt to characterize consciousnessterm·dom mathematically both in quantity and in quality [4] – [6] . IIT starts from the fundamental properties of the phenomenology of consciousnessterm·dom, which are identified as axiomsterm·def of consciousnessterm·dom. Then, IIT translates these axiomsterm·def into postulates , which specify which conditions must be satisfied by physical mechanisms, such as neurons and their connections, to account for the phenomenology of consciousnessterm·dom. It must be emphasized that taking the phenomenology of consciousnessterm·dom as primary, and asking how it can be implemented by physical mechanisms, is the opposite of the approach usually taken in neuroscience: start from neural mechanisms in the brain, and ask under what conditions they give rise to consciousnessterm·dom, as assessed by behavioral reports [7] – [10] . While identifying the “neural correlates of consciousnessterm·dom” is undoubtedly important [8] , it is hard to see how it could ever lead to a satisfactory explanation of what consciousnessterm·dom is and how it comes about [11] .

As will be illustrated below, IIT offers a way to analyze systems of mechanisms to determine if they are properly structured to give rise to consciousnessterm·dom, how much of it, and of which kind. As reviewed previously [4] , [5] , [12] , [13] , the fundamental principles of IIT, such as integration and differentiation, can provide a parsimonious explanation for many neuroanatomical, neurophysiological, and neuropsychological findings concerning the neural substrate of consciousnessterm·dom. Moreover, IIT leads to experimental predictions, for instance that the loss and recovery of consciousnessterm·dom should be associated with the breakdown and recovery of information integration. This prediction has been confirmed using transcranial magnetic stimulation in combination with high-density electroencephalography in several different conditions characterized by loss of consciousnessterm·dom, such as deep sleep, general anesthesia obtained with several different agents, and in brain damaged patients (vegetative, minimally conscious, emerging from minimal consciousnessterm·dom, locked-in [14] ). Furthermore, IIT has inspired theoretically motivated measures of the level of consciousnessterm·dom that have been applied to human and animal data (e.g. [14] , see also [15] for a related attempt to measure the level of consciousnessterm·dom based on symbolic mutual information).

While the central assumptions of IIT have remained the same, its theoretical apparatus has undergone various developments over the years. The original formulation, which may be called IIT 1.0, introduced the essential notions including causal measures of the quantity and quality of consciousnessterm·dom. However, to simplify the analysis, IIT 1.0 dealt exclusively with stationary systems [4] (see also [16] ). The next formulation, which will be called IIT 2.0 [5] , [17] , [18] applied the same notions on a state-dependent basis: it showed how integrated informationterm·mth could be calculated in a top-down manner for a system of mechanisms in a state [17] and suggested a way to characterize the quality of an experience by considering its sub-mechanisms [18] . The formulation presented below, and the new results that follow from it, represent a substantial advance at several different levels, hence IIT 3.0 (see also [6] ). Nevertheless, this article is presented independently of previous “releases” for readers new to IIT. For those readers who may have followed the evolution of IIT, the main advances are summarized in the Supplementary Material ( Text S1 ).

In what follows, we first present the axiomsterm·def and the postulates of IIT. We then provide the mathematical formalism and motivating examples for each of the postulates. The key constructs of IIT are introduced first at the level of individual mechanisms, which can be taken to represent physical objects such as logic gates or neurons, then at the level of systems of mechanisms, such as computers or neural architectures. The Models section ends by presenting the central identity proposed by IIT, according to which the quality and quantity of an experience is completely specified by a maximally irreducible conceptual structureterm·def (MICSterm·dom) and the associated value of integrated informationterm·mth Φ Maxterm·var . The Results/Discussion section presents several new results that follow directly from IIT, including the condensation of systems of mechanisms into main complexesterm·dom and minor complexesterm·dom; examples of simple systems that are minimally conscious and of complicated systems that are not; an example of an unconscious feed-forward system that is functionally equivalent to a conscious complexterm·dom; and finally, an example showing that conceptsterm·dom within a complexterm·dom are self-referential and relate only indirectly to the external environment.

Models Axiomsterm·def, postulates, and identities The main tenets of IIT can be presented as a set of phenomenological axiomsterm·dom, ontological postulatesterm·dom, and identities. While the terms “axiomsterm·def” and “postulates” are often used interchangeably, we follow the classical tradition according to which an “axiomterm·def” is a self-evident truth, whereas a “postulate” is an unproven assumption that can serve as the basis for logic or heuristics. Here the distinction takes on an even stronger meaning: axiomsterm·def are self-evident truths about consciousnessterm·dom – the only truths that, with Descartes, cannot be doubted and do not need proof (experience exists, it is irreducible etc.). Postulates instead are assumptions about the physical world and specifically about the physical substrates of consciousnessterm·dom (mechanisms must exist, be irreducible, etc.), which can be formalized and form the basis of the mathematical framework of IIT.

Axiomsterm·def The central axiomsterm·def, which are taken to be immediately evident, are as follows: E xistence : Consciousnessterm·dom exists – it is an undeniable aspect of reality. Paraphrasing Descartes, “I experience therefore I am”.

C omposition : Consciousnessterm·dom is compositional (structured): each experience consists of multiple aspects in various combinations. Within the same experience, one can see, for example, left and right, red and blue, a triangle and a square, a red triangle on the left, a blue square on the right, and so on.

I nformation : Consciousnessterm·dom is informative: each experience differs in its particular way from other possible experiences. Thus, an experience of pure darkness is what it is by differing, in its particular way, from an immense number of other possible experiences. A small subset of these possible experiences includes, for example, all the frames of all possible movies.

I ntegration : Consciousnessterm·dom is integrated: each experience is (strongly) irreducible to non-interdependent components. Thus, experiencing the word “SONO” written in the middle of a blank page is irreducible to an experience of the word “SO” at the right border of a half-page, plus an experience of the word “NO” on the left border of another half page – the experience is whole. Similarly, seeing a red triangle is irreducible to seeing a triangle but no red color, plus a red patch but no triangle.

E xclusion : Consciousnessterm·dom is exclusive: 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 – certain things can be experienced and others cannot; each experience has a particular spatial and temporal grain – it flows at a particular speed, and it has a certain resolution such that some distinctions are possible and finer or coarser distinctions are not.

Postulates To parallel the phenomenological axiomsterm·dom, IIT posits a set of postulates. These list the properties physical systems must satisfy in order to generate experience.

E xistence : Mechanisms in a state exist. A system is a set of mechanisms.

C omposition : Elementary mechanisms can be combined into higher order ones.

The next three postulates, information, integration, and exclusion, apply both to individual mechanisms and to systems of mechanisms.

Mechanisms I nformation : A mechanism can contribute to consciousnessterm·dom only if it specifies “differences that make a difference” within a system. That is, a mechanism in a state generates information only if it constrains the states of a system that can be its possible causes and effects – its cause-effect repertoireterm·mth . The more selective the possible causes and effects, the higher the cause-effect information cei specified by the mechanism.

I ntegration : A mechanism can contribute to consciousnessterm·dom only if it specifies a cause-effect repertoireterm·mth (information) that is irreducible to independent components. Integration/irreducibility φ is assessed by partitioning the mechanism and measuring what difference this makes to its cause-effect repertoireterm·mth.

E xclusion : A mechanism can contribute to consciousnessterm·dom at most one cause-effect repertoireterm·mth, the one having the maximum value of integration/irreducibility φ Maxterm·var . This is its maximally irreducible cause-effect repertoireterm·mth (MICE, or qualeterm·def sensu stricto (in the narrow sense of the word, [5] )). If the MICE exists, the mechanism constitutes a conceptterm·dom .

Systems of mechanisms I nformation : A set of elements can be conscious only if its mechanisms specify a set of “differences that make a difference” to the set – i.e. a conceptual structureterm·dom . A conceptual structureterm·dom is a constellation of points in conceptterm·dom space, where each axis is a possible past/future state of the set of elements, and each point is a conceptterm·dom specifying differences that make a difference within the set. The higher the number of different conceptsterm·dom and their φ Maxterm·var value, the higher the conceptual information CI that specifies a particular constellation and distinguishes it from other possible constellations.

I ntegration : A set of elements can be conscious only if its mechanisms specify a conceptual structureterm·dom that is irreducible to non-interdependent components (strong integration). Strong integration/irreducibility Φ is assessed by partitioning the set of elements into subsets with unidirectional cuts.

E xclusion : Of all overlapping sets of elements, only one set can be conscious – the one whose mechanisms specify a conceptual structureterm·dom that is maximally irreducible (MICSterm·dom) to independent components. A local maximum of integrated informationterm·mth Φ Maxterm·var (over elements, space, and time) is called a complexterm·dom .

Identities Finally, according to IIT, there is an identity between phenomenological properties of experience and informational/causal properties of physical systems (see [11] and [19] for the importance of identities for the mind-body problem). The central identity is the following: The maximally irreducible conceptual structureterm·def ( MICSterm·dom ) generated by a complexterm·dom of elements is identical to its experience. The constellation of conceptsterm·dom of the MICSterm·dom completely specifies the quality of the experience (its qualeterm·def “sensu lato” (in the broad sense of the term [5] )). Its irreducibility Φ Maxterm·var specifies its quantity. The maximally irreducible cause-effect repertoireterm·mth (MICE) of each conceptterm·dom within a MICSterm·dom specifies what the conceptterm·dom is about (what it contributes to the quality of the experience, i.e. its qualeterm·def sensu stricto (in the narrow sense of the term)), while its value of irreducibility φ Maxterm·var specifies how much the conceptterm·dom is present in the experience. An experience is thus an intrinsic property of a complexterm·dom of mechanisms in a state. In other words, the maximally irreducible conceptual structureterm·def specified by a complexterm·dom exists intrinsically (from its own intrinsic perspective), without the need for an external observer.

Mechanisms In what follows, we consider simple systems that can be used to illustrate the postulates of IIT. In the first part, we apply the postulates of IIT at the level of individual mechanisms . We show that an individual mechanism generates information by specifying both selective causes and effects (information), that it needs to be irreducible to independent components (integration), and that only the most irreducible cause-effect repertoireterm·mth of each mechanism should be considered (exclusion). This allows us to introduce the notion of a conceptterm·dom : the maximally irreducible cause-effect repertoireterm·mth of a mechanism.

In the next part, we consider the postulates of IIT at the level of systems of mechanisms , and show how the requirements for information, integration, and exclusion can be satisfied at the system level. This allows us to introduce the notion of a complexterm·dom – a maximally integrated set of elements – and of a qualeterm·def – the maximally irreducible conceptual structureterm·def (MICSterm·dom) it generates. Altogether, these two sections show how to assess in a step-by-step, bottom up manner, whether a system generates a maximally integrated conceptual structureterm·dom and how the latter can be characterized in full. A summary of the key conceptsterm·dom and associated measures is provided as a reference in Table 1 and Box 1 .

Key conceptsterm·dom and measures of IIT.

Box 1. Glossary Axiomterm·def: Self-evident truth about consciousnessterm·dom (experience exists, it is irreducible etc.). The only truths that, with Descartes, cannot be doubted and do not need proof. They are existence, composition, information, integration, and exclusion (see text).

Background conditions: Fixed external constrains on a candidate set of elements. Past and current stateterm·var of the elements outside the candidate set are fixed to their actual values.

Candidate set: The set of elements under consideration. Elements inside the candidate set are perturbed into all their possible states to obtain the TPM of the candidate set.

Cause-effect repertoireterm·mth: The probability distribution of potential past and future states of a system as constrained by a mechanism in its current stateterm·var.

Cause-effect information ( cei ): The amount of information specified by a mechanism in a state, measured as the minimum of cause information ( ci ) and effect information ( ei ).

Cause information ( ci ) and effect information ( ei ): Information about the past and the future, which is measured as the distance between the cause repertoire and the unconstrained cause repertoire (same on the effect side).

Complexterm·dom: A set of elements within a system that generates a local maximum of integrated conceptual informationterm·def Φ Maxterm·var . Only a complexterm·dom exists as an entity from its own intrinsic perspective.

Conceptterm·dom: A set of elements within a system and the maximally irreducible cause-effect repertoireterm·mth it specifies, with its associated value of integrated informationterm·mth φ Maxterm·var . The conceptterm·dom expresses the causal role of a mechanism within a complexterm·dom.

Conceptual structureterm·dom, constellation of conceptsterm·dom ( C ): A conceptual structureterm·dom is the set of all conceptsterm·dom specified by a candidate set with their respective φ Maxterm·var values, which can be plotted as a constellation in conceptterm·dom space.

Conceptual information ( CI ): A measure of how many different conceptsterm·dom are generated by a system of elements. CI is quantified by the distance D between the constellation of conceptsterm·dom and the “null” conceptterm·dom, the unconstrained cause-effect repertoireterm·mth p uc .

Conceptterm·dom space: Conceptterm·dom space is a high dimensional space with one axis for each possible past and future state of the system in which a conceptual structureterm·dom can be represented.

Distance (D): In IIT 3.0, the Wasserstein distance, also known as earth mover's distance (EMD). It specifies the metric of conceptterm·dom space and thus the distance between probability distributions ( φ ) and between constellations of conceptsterm·dom (Φ).

Integrated conceptual informationterm·def (Φ): Conceptual information that is generated by a system above and beyond the conceptual information generated by its (minimal) parts. Φ measures the integration or irreducibility of a constellation of conceptsterm·dom (integration at the system level).

Integrated informationterm·mth ( φ ): Information that is generated by a mechanism above and beyond the information generated by its (minimal) parts. φ measures the integration or irreducibility of mechanisms (integration at the mechanism level).

Intrinsic informationterm·mth: Differences that make a difference within a system.

Mechanism: Any subsystem of a system, including the system itself, that has a causal role within the system, for example, a neuron in the brain, or a logic gate in a computer.

MICE (maximally irreducible cause-effect repertoireterm·mth): The cause-effect repertoireterm·mth of a conceptterm·dom, i.e., the cause-effect repertoireterm·mth that generates a maximum of integrated informationterm·mth φ among all possible purviews.

MICSterm·dom (maximally irreducible conceptual structureterm·def): The conceptual structureterm·dom generated by a complexterm·dom in a state that corresponds to a local maximum of integrated conceptual informationterm·def Φ Maxterm·var (synonymous with “qualeterm·def” or “constellation” in “qualia spaceterm·dom”).

MIP (minimum information partitionterm·mth): The partition that makes the least difference (in other words, the minimum “difference” partition).

Null conceptterm·dom: The unconstrained cause-effect repertoireterm·mth p uc of the candidate set, with φ = 0.

Partition: Division of a set of elements into causally/informationally independent parts, performed by noising the connections between the parts.

Power set: The set of all subsets of a candidate set of elements.

Postulates: Assumptions, derived from axiomsterm·def, about the physical substrates of consciousnessterm·dom (mechanisms must have causal power, be irreducible, etc.), which can be formalized and form the basis of the mathematical framework of IIT. They are existence, composition, information, integration, and exclusion (see text).

Purview: Any set of elements of a candidate set over which the cause and effect repertoires of a mechanism in a state are calculated.

Qualeterm·def: The conceptual structureterm·dom generated by a complexterm·dom in a state that corresponds to a local maximum of integrated conceptual informationterm·def Φ Maxterm·var (synonymous with “MICSterm·dom” or “constellation” in “qualia spaceterm·dom”).

Qualia spaceterm·dom: If a set of elements forms a complexterm·dom, its conceptterm·dom space is called qualia spaceterm·dom.

System: A set of elements/mechanisms.

TPM (transition probability matrix): A matrix that specifies the probability with which any state of a system transitions to any other system state. The TPM is determined by the mechanisms of a system and obtained by perturbing the system into all its possible states.

Unconstrained repertoire ( p uc ) : The probability distribution of potential past and future system states without constraints due to any mechanism in a state. The unconstrained cause repertoire is the uniform distribution of system states. The unconstrained effect repertoire is obtained by assuming unconstrained inputs to all system elements.

Existence The existence postulate, the “zeroth” postulate of IIT, claims that mechanisms in a state exist. Within the present framework, “mechanism” simply denotes anything having a causal role within a system, for example, a neuron in the brain, or a logic gate in a computer. In principle, mechanisms might be characterized at various spatio-temporal scales, down to the micro-physical level, although for any given system there will be a scale at which causal interactions are strongest [20] . In what follows, we consider systems in which the elementary mechanisms are discrete logic gates or linear threshold units ( Text S2 ) and assume that these mechanisms are the ones mediating the strongest causal interactions.

Figure 1A shows the example system ABCDEF , which includes three logic gate mechanisms, OR, AND, XOR, which will be used to illustrate the postulates of IIT throughout the Model section. The dotted circle indicates that the particular set of elements ABC is going to be considered as a “candidate set” for IIT analysis, whereas the remaining elements D , E , F are considered external and treated as background conditions ( Text S2 ).

Existence: Mechanisms in a state having causal power. (A) The dotted circle indicates elements ABC as the candidate set of mechanisms. Elements outside the candidate set ( D , E , F ) are taken as background conditions (external constraints). The logic gates A , B , and C are represented as is customary in neural circuits rather than electronic circuits. The arrows indicate directed connections between the elements. (B) The set's mechanisms ABC determine the transition probability matrix (TPM) of the set under the background conditions of DEF (here DEF ( t −1 ) = DEF ( t 0 ) = 010). With element D fixed to D = 0, element A , for instance, receives inputs from B and C and outputs to B and C . The OR gate A is on (1) if either B , or C , or both were on at the last time step, and off (0) if BC was 00. Filled circles denote that the state of an element is ‘1’, open circles indicate that the state of an element is ‘0’. The current stateterm·var of ABC is 100.

The mechanisms of ABC determine the transition probability matrix (TPM) of the candidate set, which specifies the probability with which any state of the set ABC transitions into any other state under the background conditions of elements DEF, here ( Figure 1B ). In this case, since the system is deterministic, the values in the TPM are 0 or 1, but non-deterministic systems can also be considered. In this example, at the current time step , the mechanisms are in state . The TPM specifies which past states could have led to the current stateterm·var (the shaded column in Figure 1B ) and which future states it could go to (shaded row in Figure 1B ), out of all possible states of the set.

Composition The composition postulate states that elementary mechanisms can be structured, forming higher order mechanisms in various combinations. In Figure 2 , A , B , and C are the elementary (first-order) mechanisms. By combining them, higher order mechanisms can be constructed. Pairs of elements form second-order mechanisms ( AB , AC , BC ), and all elements together form the third-order mechanism ABC . A red area highlights the respective mechanisms in Figure 2 . The elements inside the candidate set, but outside the mechanism under consideration, are treated as independent noise sources ( Text S2 ). Altogether, the elementary mechanisms and their combinations form the power set of possible mechanisms.

Composition: Higher order mechanisms can be composed by combining elementary mechanisms. The set ABC has 3 elementary mechanisms A , B , and C (at the bottom). Second-order mechanisms AB , AC , and BC are shown in the middle row and the third-order mechanism ABC (corresponding to the full set) is shown at the top. Altogether, the figure indicates the power set of possible mechanisms in set ABC . In the figure, each mechanism is highlighted by a red shaded area. The current stateterm·var of the elements inside the candidate set but outside of a mechanism is undetermined for the mechanism under consideration.

Information: Cause-effect repertoiresterm·mth and cause-effect information ( cei ) In IIT, information is meant to capture the “differences that make a difference” from the perspective of the system itself – and is therefore both causal and intrinsic. These and other features distinguish this “intrinsic” notion of information from the “extrinsic”, Shannon notion (see Text S3 ; cf. [21] – [23] for related approaches to information and causation in networks).

Information as “differences that make a difference” to a system from its intrinsic perspective can be quantified by considering how a mechanism in its current stateterm·var constrains the system's potential past and future states. Figure 3 illustrates how a mechanism A constrains the past states of more or less selectively depending on its input/output function and state. is an AND gate of the inputs from . The constrained distribution of past states is called A 's cause repertoire . In Figure 3A the connections between and BCD are substituted by noise. Therefore, the current stateterm·var of A cannot specify anything about the past state of BCD , the cause repertoire is identical to the unconstrained distribution (unselective), and A generates no information. By contrast, when the connections between A and BCD are deterministic and A is on ( A = 1), the past state of BCD is fully constrained, since the only compatible past state is BCD = 111 ( Figure 3B ). In this case, the cause repertoire is maximally selective, corresponding to high information. On the other hand, when is off ( , Figure 3C ), the cause repertoire is less selective, because only is ruled out, corresponding to less information.

Information requires selectivity. A mechanism generates information to the extent that it selectively constrains a system's past states. Element constrains the past states of depending on its mechanism (AND gate) and its current stateterm·var. The constrained distribution of past states is called A 's cause repertoire . (A) The connections between and are noisy. A 's cause repertoire is thus unselective, since could have followed from any state of with equal probability. (B) In the case of deterministic connections and current stateterm·var , A 's cause repertoire is maximally selective, because all states except are ruled out as possible causes of . (C) In the case of deterministic connections and current stateterm·var , A 's cause repertoire is much less selective than for , because only state is ruled out as a possible cause of .

Figure 4 illustrates how element in state 1 constrains the past states (left) and future states (right) of the candidate set . The probability distribution of past states that could have been potential causes of is its cause repertoire . The probability distribution of future states that could be potential effects of is called effect repertoire . Here, the superscripts p , c , and f stand for past, current, and future, respectively. The set of elements over which the cause and effect repertoires of a mechanism are calculated is called its purview . Figure 4 shows the cause and effect repertoire of mechanism over its purview (the full set) in the past and future, labeled and . If the purview is not over the full set, the elements outside of the purview are unconstrained (see Text S2 for details on the calculation).

Information: “Differences that make a difference to a system from its own intrinsic perspective.” A mechanism generates information by constraining the system's past and future states. (Top) The candidate set consisting of OR, AND, and XOR gates is shown in its current stateterm·var 100. We consider the purview of mechanism , highlighted in red, over the set in the past (blue) and in the future (green). (Bottom center) The same network is displayed unfolded over three time steps, from (past), (current) to (future). Gray-filled circles are undetermined states. The current stateterm·var of mechanism A constrains the possible past and future system states compared to the unconstrained past and future distributions . For example, rules out the two states where as potential causes. The constrained distribution of past states is A 's cause repertoire (left). The constrained distribution of future states is A 's effect repertoire (right). Cause information ( ci ) is quantified by measuring the distance D between the cause repertoire and the unconstrained past repertoire ; effect information ( ei ) is quantified by measuring the distance D between the effect repertoire and the unconstrained future repertoire . Note that the unconstrained future repertoire is not simply the uniform distribution, but corresponds to the distribution of future system states with unconstrained inputs to each element. Cause-effect information ( cei ) is then defined as the minimum of ci and ei .

The amount of information that specifies about the past, its cause information ( ci ), is measured as the distance D between the cause repertoire and the unconstrained past repertoire . For the purview : corresponds to the cause repertoire in the absence of any constraints on the set's output states due to its mechanisms, which is the uniform distribution.

Just like cause information ( ci ), effect information ( ei ) of A = 1 is quantified as the distance between the effect repertoire of A and the unconstrained future repertoire : As can be seen in Figure 4 (right), the unconstrained future repertoire is not simply the uniform distribution of future system states. While corresponds to the distribution of past system states with unconstrained outputs, corresponds to the distribution of future system states with unconstrained inputs. Therefore, is obtained by perturbing the inputs to each element into all possible states. As an example, the unconstrained future repertoire of element A , being an OR gate, is and , which is obtained by perturbing the inputs of A into all possible states .

To quantify differences that make a difference, the distance D between two probability distributions is evaluated using the earth mover's distance (EMD) [24] , which quantifies how much two distributions differ by taking into account the distance between system states. This is important because, from the intrinsic perspective of the system, it should make a difference if two system elements, rather than just one, differ in their state (see Text S2 for details on the EMD and a discussion of EMD as the current distance measure of choice).

Finally, having calculated and , the total amount of cause-effect information ( cei ) specified by A = 1 over the purview is the minimum of its ci and ei : The motivation for choosing the minimum is illustrated in Figure 5 . First, consider an element that receives inputs from the system but sends no output to it (element A in Figure 5A ). In this case, the state of element A constrains the past states of the system – A has selective causes within the system ( ), but not the future states of the system – A has no selective effects on the system ( , what A does makes no difference to the system). Put differently, while the state of element A does convey information about the system's past states from the perspective of an external observer, it does not do so from the intrinsic perspective of the system itself, because the system is not affected by A (the system cannot “observe” A and thus has no access to A 's cause information).

A mechanism generates information only if it has both selective causes and selective effects within the system. (A) Element A receives input from the system and specifies a selective cause repertoire. However, since it has no outputs to the system it does not specify a selective effect repertoire. (B) Element A receives no input from the system and therefore it does not specify a selective cause repertoire. In both cases the cause-effect information cei generated by mechanism A is zero (the minimum between cause and effect information).

Similarly, consider an element that only outputs to the system but does not receive inputs from it, being controlled exclusively by external causes (element A in Figure 5B ). In this case, the state of element A constrains the future states of the system – A has selective effects on the system ( ), but not the past states of the system – A has no selective causes within the system ( , what the system might have done makes no difference to A ). Put differently, while the state of element A does convey information about the system's future states from the perspective of an external observer, it does not do so from the intrinsic perspective of the system, because the system cannot affect the state of A (the system cannot “control” A and thus has no access to A 's effect information).

As illustrated by these two limiting cases, each mechanism in the system acts as an information bottleneck from the intrinsic perspective: its cause information only exists for the system to the extent that it also specifies effect information and vice versa. While other ways of measuring a mechanism's cei may also be compatible with the examples shown in Figure 5 , the “intrinsic informationterm·mth bottleneck principle” is best captured by defining a mechanism's cei as the minimum between its cause and effect information.

Integration: Irreducible cause-effect repertoiresterm·mth and integrated informationterm·mth ( φ ) At the level of an individual mechanism, the integration postulate says that only mechanisms that specify integrated informationterm·mth can contribute to consciousnessterm·dom. Integrated informationterm·mth is information that is generated by the whole mechanism above and beyond the information generated by its parts. This means that, with respect to information, the mechanism is irreducible. Similar to cause-effect information, integrated informationterm·mth φ (“small phi”) is calculated as the distance D between two probability distributions: the cause-effect repertoireterm·mth specified by the whole mechanism is compared against the cause-effect repertoireterm·mth of the partitioned mechanism. Of the many possible ways to partition a mechanism, integrated informationterm·mth is evaluated across the minimum information partitionterm·mth (MIP), the partition that makes the least difference to the cause and effect repertoires (in other words, the minimum “difference” partition). In Figure 6 this is demonstrated for the order mechanism ABC . The MIP for the purview is in the past and in the future, where [] denotes the empty set. The cause and effect repertoire specified by the partitioned mechanisms can be calculated as: and where the connections between the parts are “injected” with independent noise ( Text S2 ).

Integrated informationterm·mth: The information generated by the whole that is irreducible to the information generated by its parts. Integrated informationterm·mth is quantified by measuring the distance between the cause repertoire specified by the whole mechanism and the partitioned mechanism (the same for the effect repertoire). MIP is the minimum information partitionterm·mth – the partition of the mechanism that makes the least difference to the cause and effect repertoires (indicated by dashed lines in the unfolded system). Partitions are performed by noising connections between the parts (those that cross the dashed lines, see Text S2 ).

The distance D between the cause-effect repertoireterm·mth specified by the whole mechanism and its MIP is quantified again using the EMD, taken separately for the past and the future (cause and effect repertoires): As with information, the total amount of integrated informationterm·mth of mechanism ABC in its current stateterm·var 100 over the purview is the minimum of its past and future integrated informationterm·mth: In what follows, integrated informationterm·mth φ is always evaluated for the MIP, so the MIP superscript is dropped for readability.

According to IIT, mechanisms that do not generate integrated informationterm·mth do not exist from the intrinsic perspective of a system, as illustrated in Figure 7 . Suppose that A is a non-parity gate ( A turns on when the inputs are even) and B is a majority gate ( B turns on when the majority of its inputs are on). If A and B have independent causes and independent effects as shown in Figure 7A , a higher order mechanism AB cannot generate integrated informationterm·mth, since it is possible to partition AB 's causes and effects without any loss of information. In this case, AB does not exist intrinsically.

A mechanism generates integrated informationterm·mth only if it has both integrated causes and integrated effects. (A) The mechanisms of element A and B are independent, having separate causes and effects. From the intrinsic perspective of the system, the joint mechanism AB does not exist, since it can be partitioned (red dashed line) without making any difference to the system. (B) The mechanism AB generates integrated informationterm·mth both in the past and in the future. Since it cannot be partitioned without loss, it exists intrinsically. (C) The mechanism AB generates integrated informationterm·mth in the past but not in the future. (D) The mechanism AB generates integrated informationterm·mth in the future but not in the past. In both cases, the joint mechanism does not exist intrinsically.

Consider instead Figure 7B . Here, specifies that all inputs had to be on in the past (‘All ON’), which goes above and beyond what is specified separately by (an even number of inputs was on) and by (the majority of inputs was on). On the effect side, there is an AND gate that takes inputs from both A and B , so the effect of goes above and beyond the separate effects of and . Therefore, mechanism AB exists from the intrinsic perspective of the system, in the sense that it plays an irreducible causal role: it picks up a difference that makes a difference to the system in a way that cannot be accounted for by its parts.

By contrast, in Figure 7C mechanism AB does not exist from the intrinsic perspective of the system, because the information ‘All ON’ as such does not make any difference to the future state of the system. Similarly, in Figure 7D , and do not specify an irreducible past cause for the irreducible future effect that the AND gate will be ON.

Exclusion: A maximally irreducible cause-effect repertoireterm·mth (MICE) specified by a subset of elements (a conceptterm·dom) The exclusion postulate at the level of a mechanism says that a mechanism can have only one cause and one effect, those that are maximally irreducible; other causes and effects are excluded. The core cause of a mechanism from the intrinsic perspective is its maximally irreducible cause repertoire ( one cause thus means a probability distribution over the past states of one particular set of inputs of the mechanism). Consider for example mechanism in Figure 8 . To find the core cause of BC , one needs to evaluate for all past purviews of the power set . In this case, the purview has the highest value of . The corresponding maximally irreducible cause repertoire is thus the core cause of . The core effect is assessed in the same way: it is the maximally irreducible effect repertoire of a mechanism with , where F denotes the power set of future purviews. A mechanism that specifies a maximally irreducible cause and effect (MICE) constitutes a conceptterm·dom or, for emphasis, a core conceptterm·dom .

The maximally integrated cause repertoire over the power set of purviews is the “core cause” specified by a mechanism. All purviews of mechanism BC for the past are considered. Only the purview that generates the maximal value of integrated informationterm·mth, φ Maxterm·var , exists intrinsically as the core cause of the mechanism (or effect when considering the future). In this case, the core cause is .

To understand the motivation behind the exclusion postulate as applied to a mechanism, consider a neuron with several strong synapses and many weak synapses ( Figure S1 ). From the intrinsic perspective of the neuron, any combination of synapses could be a potential cause of firing, including “strong synapses”, “strong synapses plus some weak synapses”, and so on, eventually including the potential cause “all synapses”, “all synapses plus stray glutamate receptors”, “all synapses plus stray glutamate receptors plus cosmic rays affecting membrane channels”, and so on, rapidly escalating to infinite regress. The exclusion postulate requires, first, that only one cause exists. This requirement 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 [6] . In the present context this means that only one set of synapses can be the cause for the neuron's firing and not, for example, both “strong synapses S1,S2” and “all synapses”, or an average or integral over all possible causes. Second, the exclusion postulate requires that, from the intrinsic perspective of a mechanism in a system, the only cause be the maximally irreducible one. Recall that IIT's information postulate is based on the intuition that, for something to exist, it must make a difference. By extension, something exists all the more, the more of a difference it makes. The integration postulate further requires that, for a whole to exist, it must make a difference above and beyond its partition, i.e. it must be irreducible. Since, according to the exclusion postulate, only one cause can exist, it must be the cause that makes the most difference to the neuron's output if it is eliminated by a partition – that is, the cause that is maximally irreducible. In Figure S1 , for example, the maximally irreducible cause turns out to be “the strong synapses S1,S2”. Note that the exclusion postulate appears to fit with phenomenology also at the level of mechanisms. Thus, invariant conceptsterm·dom such as “chair”, or “apple” seem to exclude the accidental details of particular apples and chairs, but only reflect the “core” conceptterm·dom. In neural terms, this would imply that the maximally irreducible cause-effect repertoireterm·mth of the neurons underlying such invariant conceptsterm·dom is similarly restricted to their core causes and effects.

The notion of a conceptterm·dom is illustrated in Figure 9 for mechanism A of the candidate set ABC . The core cause of A is the cause repertoire of purview ; the core effect is the effect repertoire of . These purviews generate the maximal amount of integrated informationterm·mth over the whole power set of purviews in the past ( P ) and future ( F ), respectively. The amount of integrated informationterm·mth generated by conceptterm·dom is again the minimum between past and future: Each conceptterm·dom of a mechanism in a state is thus endowed with a maximally irreducible cause-effect repertoireterm·mth (MICE), which specifies what the conceptterm·dom is about (its qualeterm·def “sensu stricto” ), and its particular value, which quantifies its amount of integration or irreducibility. Finally note that the exclusion postulate is applied to the possible cause-effect repertoiresterm·mth of a single mechanism (elementary or higher order). Exclusion does not apply across mechanisms within a set of elements, since elementary and higher order mechanisms can have different causal roles (conceptsterm·dom) in the set, as emphasized by the composition postulate.

A conceptterm·dom: A mechanism that specifies a maximally irreducible cause-effect repertoireterm·mth. The core cause and effect of mechanism A are and , respectively. Together, they specify “what” the conceptterm·dom of A is about. The value of the conceptterm·dom specifies “how much” the conceptterm·dom exists intrinsically.

Systems of mechanisms We now turn from the level of mechanisms to the level of a system of mechanisms, and apply the postulates of IIT with the objective of deriving the experience or qualeterm·def generated by a system in a bottom up manner, from the set of all its conceptsterm·dom.

Information: Conceptual structureterm·dom (constellation of conceptsterm·dom in conceptterm·dom space) and conceptual information ( CI ) At the system level, the information postulate says that only sets of “differences that make a difference” (i.e. a constellations of conceptsterm·dom) matter for consciousnessterm·dom. Figure 10 shows all the conceptsterm·dom specified by the candidate set ABC ( Figure 10A,B ). Of all the possible mechanisms of the power set of ABC , only AC does not give rise to a conceptterm·dom, since its integrated informationterm·mth ( Figure 10B ). All other mechanisms generate non-zero integrated informationterm·mth and thus specify conceptsterm·dom ( Figure 10C ). The set of all conceptsterm·dom of a candidate set constitutes its conceptual structureterm·dom , which can be represented in conceptterm·dom space .

Information: A conceptual structureterm·dom C (constellation of conceptsterm·dom) is the set of all conceptsterm·dom generated by a set of elements in a state. (A) The candidate set ABC – a system composed of mechanisms in a state. (B) The power set of ABC 's mechanisms. (C) The conceptsterm·dom generated by the candidate set. Core causes are plotted on the left, core effects on the right. values are shown in blue fonts in the middle of the cause and effect repertoires of each mechanism. Note that all mechanisms in the power set are conceptsterm·dom, with the exception of mechanism AC , which can be fully reduced . (D) The conceptsterm·dom generated by the candidate set plotted in conceptterm·dom space, where each axis corresponds to a possible state of ABC . For ease of representation past and future subspaces are plotted separately, with only three axes each. The “null” conceptterm·dom p uc is indicated by the small black crosses in conceptterm·dom space.

Conceptterm·dom space is a high dimensional space, with one axis for each possible past and future state of the system. In this space, each conceptterm·dom is symbolized as a point, or “star”: its coordinates are given by the probability of past and future states in its cause-effect repertoireterm·mth, and its size is given by its value. If is zero, the conceptterm·dom simply does not exist, and if its is small, it exists to a minimal amount.

In the case of the candidate set ABC , the dimension of conceptterm·dom space is 16 (8 axes for the past states and 8 for the future states). For ease of representation, in the figures past and future subspaces are plotted separately, with only three axes each (corresponding to the states at which the conceptsterm·dom have the highest variance in probability). Therefore the 6 conceptsterm·dom in Figure 10D are displayed twice, once in the past subspace and once in the future subspace. In the full 16-dimensional conceptterm·dom space, however, each conceptterm·dom is a single star.

At the system level, the equivalent of the cause-effect information ( cei ) at the level of mechanisms is called conceptual information ( CI ). Just like cei , CI is quantified by the distance D from the unconstrained repertoire of past and future states p uc , which corresponds to the “null” conceptterm·dom (a conceptterm·dom that specifies nothing): The distance D from a constellation C to the “null” conceptterm·dom can be measured using an extension of the EMD (see Text S2 ), which can be understood as the cost of transporting the amount of of each conceptterm·dom from its location in conceptterm·dom space to . CI is thus the sum of the distances between the cause-effect repertoireterm·mth of each conceptterm·dom and , multiplied by the conceptterm·dom's value ( Figure 11 ). Thus, a rich constellation with many different elementary and higher order conceptsterm·dom generates a high amount of conceptual information CI ( Figure 11A ). By contrast, a system comprised of a single elementary mechanism generates a minimal amount of conceptual information ( Figure 11B ).

Assessing the conceptual information CI of a conceptual structureterm·dom (constellation of conceptsterm·dom). CI is quantified by measuring the distance in conceptterm·dom space between C , the constellation of conceptsterm·dom generated by a set of elements, and , the unconstrained past and future repertoire, which can be termed the “null” conceptterm·dom (in the absence of a mechanism, every state is equally likely). This can be done using an extended version of the earth mover's distance (EMD) that corresponds to the sum of the standard EMD for distributions between the cause-effect repertoiresterm·mth of all conceptsterm·dom and , weighted by their values. (A) Therefore, a system with many different elementary and higher order conceptsterm·dom has high CI , as shown here for the candidate set ABC . (B) By contrast, a system comprised of a single mechanism can only have one conceptterm·dom and thus has low CI .

In sum, conceptsterm·dom are considered (metaphorically) as stars in conceptterm·dom space. The conceptual structureterm·dom C generated by a set of mechanisms is thus a constellation of conceptsterm·dom – a particular shape in conceptterm·dom space spanned by the set's conceptsterm·dom. The more stars, the further away they are from the “null” conceptterm·dom, and the larger their size, the greater the conceptual information CI generated by the constellation C .

Integration: Irreducible conceptual structureterm·dom and integrated conceptual informationterm·def (Φ) At the system level, the integration postulate says that only conceptual structuresterm·dom that are integrated can give rise to consciousnessterm·dom. As for mechanisms, the integration or irreducibility of the constellation of conceptsterm·dom C specified by a set of mechanisms can be assessed by partitioning a set of elements and measuring integrated conceptual informationterm·def Φ as the difference made by the partition (“big phi”, as opposed to “small phi” φ at the level of mechanisms).

Partitioning at the system level amounts to noising the connections from one subset of S to its complement . As for mechanisms, whether and how much the constellation of conceptsterm·dom generated by a set of mechanisms is irreducible can be assessed with respect to the minimum information partitionterm·mth (MIP) of the set of elements S . This corresponds to the unidirectional partition that makes the least difference to the constellation of conceptsterm·dom (in other words, the minimum “difference” partition; Figure 12 ). To find the unidirectional MIP, for each subset one must evaluate both the connections from to and the connections from to and take the minimum MIP. This corresponds, at the level of mechanisms, to finding the minimum of the MIPs with respect to the cause and the effect repertoires. Therefore a set of elements S and its associated constellation is integrated if and only if each subset of elements specifies both selective causes and selective effects about its complement in S . Similar to integrated informationterm·mth φ for a mechanism, integrated conceptual informationterm·def Φ for a set of elements is defined as the distance D between the constellation of the whole set and that of the partitioned set: where denotes the constellation of the unidirectionally partitioned set of elements.

Assessing the integrated conceptual informationterm·def Φ of a constellation C . Φ (“big phi”) is quantified by measuring the distance C between the constellation of conceptsterm·dom of the whole set of elements C and that of the partitioned set , using an extended version of the earth mover's distance (EMD). The set is partitioned unidirectionally (see text for the motivation) until the partition is found that yields the least difference between the constellations (MIP, the minimum information i.e. minimum difference partition). In this case, the MIP corresponds to “noising” the connections from AB to C . This partition leaves 2 conceptsterm·dom intact ( A and B , with zero distance to A and B from constellation C , indicated by the red stars), while the other conceptsterm·dom are destroyed by the partition (gray stars). The distance between the whole and partitioned constellations thus amounts to the sum of the EMD between the cause-effect repertoiresterm·mth of the destroyed conceptsterm·dom and the “null” conceptterm·dom , weighted by their values (see Text S2 ).

The extended EMD between the whole and the partitioned constellation corresponds to the minimal cost of transforming C into in conceptterm·dom space. Through the partition, conceptsterm·dom of C may change location, lose , or disappear. Their has to be allocated to fill the conceptsterm·dom in with an associated cost of transportation that is proportional to the distance in conceptterm·dom space and the amount of that is moved. Any residual is transported to the “null” conceptterm·dom ( ) under the same cost of transportation.

Figure 12 shows the conceptual structureterm·dom for the candidate system ABC and its MIP (see Text S2 for a calculation of ). In this case, 4 of the 6 conceptsterm·dom of ABC are lost through the partition; their is thus transported to the location of the “null” conceptterm·dom ( ). Since Φ is always evaluated over the MIP, in what follows the superscript MIP is dropped, as it was for φ .

The motivation for integration at the system level is illustrated in Figure 13 (as was done for mechanisms in Figure 6 ). The set of 6 elements shown in Figure 13A can be subdivided into two independent subsets of 3 elements, each with its independent set of conceptsterm·dom. Therefore, a minimum partition between the two subsets makes no difference and integrated conceptual informationterm·def . Since the set is reducible without any loss, it does not exist intrinsically – it can only be treated as “one” system from the extrinsic perspective of an observer. By contrast, the set in Figure 13B is irreducible because each part specifies both causes and effects in the other part. Two other possibilities are that a subset specifies causes, but not effects, in the rest of the set ( Figure 13C ), or only effects, but not causes ( Figure 13D ). In the case of unidirectional connections the subset is integrated “weakly” rather than “strongly” (in analogy with weak and strong connectedness in graph theoryterm·mth, e.g. [25] ), which means that the subset is not really an “integral” part of the set, but merely an “appendix”. As an analogy, take the executive board of a company. An employee who transcribes the recording of a board meeting is obviously affected by the board, but if he has no way to provide any feed-back, he should not be considered an “integral” part of the board, which has no way of knowing that he exists and what he does. The same obtains for an employee who prints the agenda for the board meeting, if the board has no way of giving him feedback about the agenda.

A set of elements generates integrated conceptual informationterm·def Φ only if each subset has both causes and effects in the rest of the set. (A) A set of 6 elements is composed of two subsets that are not interconnected. The set reduces to 2 independent subsets of 3 elements each that can be partitioned without loss (dashed red line). The 6 element set does not exist intrinsically (dashed black oval). (B) All subsets of the 6 node set have causes and effects in the rest of the set. The 6 node set generates an integrated conceptual structureterm·dom since it cannot be unidirectionally partitioned without loss of conceptual information. (C,D) A set of 6 elements divides into 2 subsets of 3 elements that are connected unidirectionally. (C) The left subset has causes in the rest of the set, but no effects. (D) The left subset has effects on the rest of the set, but no causes. In both cases, the set reduces to 2 subsystems of 3 elements each that can be unidirectionally partitioned without loss (dashed red line with directional arrow). The 6 element set does not exist intrinsically.

Exclusion: A maximally irreducible conceptual structureterm·def (MICSterm·dom) specified by a set of elements (a complexterm·dom) The exclusion postulate at the level of systems of mechanisms says that only a conceptual structureterm·dom that is maximally irreducible can give rise to consciousnessterm·dom – other constellations generated by overlapping elements are excluded. A complexterm·dom is thus defined as a set of elements within a system that generates a local maximum of integrated conceptual informationterm·def Φ Maxterm·var (meaning that it has maximal Φ as compared to all overlapping sets of elements). Only a complexterm·dom exists as an entity from the intrinsic perspective. Because of exclusion, complexesterm·dom cannot overlap and at each point in time, an element/mechanism can belong to one complexterm·dom only (complexesterm·dom should be evaluated as maxima of integrated informationterm·mth not only over elements, but also over spatial and temporal grains [20] , but here it is assumed that the binary elements and time intervals considered in the examples are optimal). Once a complexterm·dom has been identified, conceptterm·dom space can be called “ qualia spaceterm·dom ,” and the constellation of conceptsterm·dom can be called a “ qualeterm·def ‘sensu lato’ ”. A qualeterm·def in the broad sense of the word is therefore a maximally irreducible conceptual structureterm·def (MICSterm·dom) or, alternatively, an integrated informationterm·mth structure .

To determine whether an integrated set of elements is a complexterm·dom, Φ must be evaluated for all possible candidate sets (subsets of the system) ( Figure 14 ). As mentioned above, when a set of elements within the system is assessed, the other elements are treated as background conditions (see Text S2 ). Figure 14 shows the values of for all possible candidate sets that are subsets of ( , , , ) and for one superset ( ). The latter, and all other sets that include elements D , E , or F , have Φ = 0. This is because D , E , and F are not strongly integrated with the rest of the system. Single elements are not taken into account as candidate sets since they cannot be partitioned and thus cannot be complexesterm·dom by definition. In this example, the set of elements ABC generates the highest value of Φ Maxterm·var and is therefore the complexterm·dom. By the exclusion postulate (“of all overlapping sets of elements, only one set can be conscious”), only ABC “exists” intrinsically, and other overlapping sets of elements within the system cannot “exist” intrinsically at the same time (they are excluded).

A complexterm·dom: A local maximum of integrated conceptual informationterm·def Φ. Integrated conceptual informationterm·def Φ is computed for the power set of elements of system ABCDEF (all possible candidate sets). By the exclusion postulate, among overlapping candidate sets, only one set of elements forms a complexterm·dom, the one that generates the maximum amount of integrated conceptual informationterm·def Φ Maxterm·var . In the example system the set of elements ABC form the complexterm·dom. Therefore, no subset or superset of ABC can form another complexterm·dom. Note that all candidate sets that include D , E , or F are not strongly integrated and thus have Φ = 0 (only one example is shown).

Identity between an experience and a maximally irreducible conceptual structureterm·def (MICSterm·dom or qualeterm·def “sensu lato”) generated by a complexterm·dom The notions and measures related to the information, integration, and exclusion postulates, both at the level of mechanisms and at the level of systems of mechanisms, are summarized in Table 1 . On this basis, it is possible to formulate the central identity proposed by IIT: an experience is identical with the maximally irreducible conceptual structureterm·def (MICSterm·dom, integrated informationterm·mth structure, or qualeterm·def “sensu lato”) specified by the mechanisms of a complexterm·dom in a state . Subsets of elements within the complexterm·dom constitute the conceptsterm·dom that make up the MICSterm·dom. The maximally irreducible cause-effect repertoireterm·mth (MICE) of each conceptterm·dom specifies what the conceptterm·dom is about (what it contributes to the quality of the experience, i.e. its qualeterm·def “sensu stricto” (in the narrow sense of the term)). The value of irreducibility φ Maxterm·var of a conceptterm·dom specifies how much the conceptterm·dom is present in the experience. An experience (i.e. consciousnessterm·dom) is thus an intrinsic property of a complexterm·dom of elements in a state: how they constrain – in a compositional manner – its space of possibilities, in the past and in the future.

In Figure 15 , this identity is illustrated by showing an isolated system of physical mechanisms ABC in a particular state (bottom left). The above analysis allows one to determine that in this case the system does constitute a complexterm·dom, and that it specifies a MICSterm·dom or qualeterm·def (top right). As before, the constellation of conceptsterm·dom in qualia spaceterm·dom is plotted over 3 representative axes separately for past and future states of the system. For clarity, the conceptsterm·dom are also represented as probability distributions over all 16 past and future states (cause-effect repertoiresterm·mth, bottom right).

A qualeterm·def: The maximally irreducible conceptual structureterm·def (MICSterm·dom) generated by a complexterm·dom. An experience is identical with the constellation of conceptsterm·dom specified by the mechanisms of the complexterm·dom. The Φ Maxterm·var value of the complexterm·dom corresponds to the quantity of the experience, the “shape” of the constellation of conceptsterm·dom in qualia spaceterm·dom completely specifies the quality of a particular experience and distinguishes it from other experiences.

The central identity of IIT can also be formulated to express the classic distinction between level and content of consciousnessterm·dom [26] : the quantity or level of consciousnessterm·dom corresponds to the Φ Maxterm·var value of the qualeterm·def; the quality or content of the experience corresponds to the particular constellation of conceptsterm·dom that constitutes the qualeterm·def – a particular shape in qualia spaceterm·dom. Note that, by specifying the quality of an experience, the particular shape of each constellation also distinguishes it from other possible experiences, just like the particular shape of a tetrahedron is what makes it a tetrahedron and distinguishes it from a cube, an icosahedron, and so on.

s indicated by the figure, once a phenomenological analysis of the essential properties (axiomsterm·def) of consciousnessterm·dom has been translated into a set of postulates that the physical mechanisms generating consciousnessterm·dom must satisfy, it becomes possible to invert the process: One can now ask, for any set of physical mechanisms, whether it is associated with phenomenology (is there “something it is like to be it,” from its own intrinsic perspective), how much of it (the quantity or level of consciousnessterm·dom), and of which kind (the quality or content of the experience). As also indicated by the figure, these phenomenological properties should be considered as intrinsic properties of physical mechanisms arranged in a certain way, meaning that a complexterm·dom of physical mechanisms in a certain state is necessarily associated with its qualeterm·def.

Results/Discussion The Models section presented a way of constructing the experience or qualeterm·def generated by a system of mechanisms in a state in a step-by-step, bottom up manner. The next section explores several implications of the postulates and conceptsterm·dom introduced above using example systems of mechanisms and the conceptual structuresterm·dom they generate.

A system may condense into a major complexterm·dom and several minor complexesterm·dom In Figure 16 , the previous example system ABC has been embedded within a larger network. In the larger system, elements I , J , and L cannot be a part of the complexterm·dom because they lack either inputs or outputs, or both. H and K also cannot be part of the complexterm·dom, since they are connected to the rest of the system in a strictly feed-forward manner. Nevertheless, elements H and K act as background conditions for the rest of the system. The remaining elements cannot form a complexterm·dom as a whole, since the subset of elements FG is not connected to the rest of the system. The subset of elements does generate a small amount of integrated conceptual informationterm·def Φ and could thus potentially form a complexterm·dom. Among the power set of elements , however, it is the smaller subset that generates the local maximum of Φ Maxterm·var . This excludes from being a complexterm·dom, since an element can participate in only one complexterm·dom at each point in time. The remaining elements DE , however, can still form a minor complexterm·dom , with lower Φ Maxterm·var than ABC . Thus, condenses down to the major complexterm·dom ABC , the minor complexterm·dom DE , and their residual interactions. Finally, FG forms a minor complexterm·dom that does not interact with the rest of the system.

A system can condense into a major complexterm·dom and minor complexesterm·dom that may or may not interact with it. The set of elements ABC specifies the local maximum of integrated informationterm·mth Φ Maxterm·var and thus forms the major complexterm·dom of the system. The sets of elements DE and FG also specify local maxima of integrated informationterm·mth albeit with lower Φ Maxterm·var than the main complexterm·dom. DE and FG thus form minor complexesterm·dom. The set of elements ABCDE is strongly integrated, but is excluded from forming a complexterm·dom, since it overlaps with ABC , which is a local maximum of integrated informationterm·mth. The elements I , J , and L cannot be part of any complexterm·dom since they do not have both causes and effects in the rest of the system. Neither can H and K , since they are part of a strictly feed-forward chain.

This simple example of “condensation” into major and minor complexesterm·dom may be relevant also for much more complicated systems of interconnected elements. For example, IIT predicts that in the human brain there should be a dominant “main” complexterm·dom of high Φ Maxterm·var , constituted of neural elements within the cortical system, which satisfies the postulates described above and generates the changing qualia of waking consciousnessterm·dom [12] . The set of neuronal elements constituting this main complexterm·dom is likely to be dynamic [27] , at times including and at times excluding particular subsets of neurons. Through its interface elements (called “ports-in” and “ports-out”), this main complexterm·dom receives inputs and provides outputs to a vast number of smaller systems involved in parsing inputs and planning and executing outputs. While interacting with the main complexterm·dom in both directions, many of these smaller systems may constitute minor complexesterm·dom specifying little more than a few conceptsterm·dom, which would qualify them as “minimally conscious” (see below). In the healthy, adult human brain the qualia and Φ Maxterm·var generated by the dominant main complexterm·dom are likely to dwarf those specified by the minimally conscious minor complexesterm·dom. In addition to the fully conscious main complexterm·dom and minimally conscious minor complexesterm·dom, there will be a multitude of unconscious processes mediated by purely feed-forward systems (see below) or by the residual interactions between main complexterm·dom and minor complexesterm·dom, as in Figure 16 .

Under special circumstances, such as after split brain surgery, the main complexterm·dom may split into two main complexesterm·dom, both having high Φ Maxterm·var . There is solid evidence that in such cases consciousnessterm·dom itself splits in two individual consciousnessesterm·dom that are unaware of each other [28] . A similar situation may occur in dissociative and conversion disorders, where splits of the main complexterm·dom may be functional and reversible rather than structural and permanent [29] .

An intriguing dilemma is posed by behaviors that would seem to require a substantial amount of cognitive integration, such as semantic judgments (e.g. [30] , [31] ). Such behaviors are usually assumed to be mediated by neural systems that are unconscious, because they can be shown to occur under experimental conditions, such as continuous flash suppression, where the speaking subject is not aware of them and cannot report about them. If such behaviors were carried out in a purely feed-forward manner, they would indeed qualify as unconscious in IIT (see below). However, at least some of these behaviors may constitute the output of minor complexesterm·dom separated from the main one. According to IIT such minor complexesterm·dom, if endowed with non-trivial values of Φ Maxterm·var , should be considered paraconscious (i.e. conscious “on the side” of the conscious subject) rather than unconscious. In principle, the presence of paraconscious minor complexesterm·dom could be demonstrated by developing experimental paradigms of dual report.

In brains substantially different from ours many other scenarios may occur. For example, the nervous system of highly intelligent invertebrates such as the octopus contains a central brain as well as large populations of neurons distributed in the nerve cords of its arms. It is an open question whether such a brain would give rise to a large, distributed main complexterm·dom, or to multiple major complexesterm·dom that generate separate consciousnessesterm·dom. Similar issues apply to systems composed of non-neural elements, such as ant colonies, computer architectures, and so on. While determining rigorously how such systems condense in terms of major and minor complexesterm·dom, and what kind of MICSterm·dom they may generate, is not practically feasible, the predictions of IIT are in principle testable and should lead to definite answers.

Consciousnessterm·dom and connectivityterm·var: Modular, homogeneous, and specialized networks Whether a set of elements as a whole constitutes a complexterm·dom or decomposes into several complexesterm·dom depends first of all on the connectivityterm·var among its elementary mechanisms. In Figure 17 we show the complexesterm·dom and the associated MICSterm·dom of three simple networks, representative of a modular, homogeneous, and specialized system architecture.

Qualia generated by modular, homogeneous and specialized networks. (A) The modular network decomposes into three small complexesterm·dom and their residual interactions. (B) The homogenous system forms a complexterm·dom, but it has low Φ Maxterm·var and only 5 identical conceptsterm·dom. (C) The specialized network also forms a complexterm·dom, with all but one conceptsterm·dom of its power set and a high Φ Maxterm·var value. In the middle row, the respective conceptsterm·dom of each system are listed. The bottom row shows the constellation of the respective complexesterm·dom in qualia spaceterm·dom (projected into 3 dimensions for the past and the future subspaces).

Figure 17A (top) shows a “modular” network of 3 COPY ( ACE ) and 3 AND ( BDF ) logic gates. In this network, the system as a whole is not a complexterm·dom, despite being integrated due to the presence of inter-connections among all elements. Instead, each of the three modules ( AB , CD , and EF ) that consist of 1 COPY and 1 AND gate constitutes a complexterm·dom, because each generates more Φ than the whole system, although each module has just two conceptsterm·dom. The purviews of module AB 's conceptsterm·dom are shown in Figure 17A (middle), and their representation in qualia spaceterm·dom is displayed in Figure 17A (bottom).

Figure 17B shows a “homogeneous” network of 5 OR gates ( ABCDE ), in which every element is connected to every other element including itself. Since all elements in the network specify the same cause-effect repertoireterm·mth, their 5 first order (elementary) conceptsterm·dom are identical. Moreover, there are no higher order conceptsterm·dom, since combining elements yields nothing above the elementary mechanisms. In qualia spaceterm·dom, the 5 identical conceptsterm·dom are concentrated on a single point ( Figure 17B , bottom). Accordingly, the homogeneous network has a low value of CI and Φ Maxterm·var .

Figure 17C shows a “specialized” network consisting of 5 majority gates, which turn on when the majority of inputs is on. However, each gate has only 3 afferent and efferent connections, which differ for every element. Therefore, each elementary conceptterm·dom specifies a different cause-effect repertoireterm·mth. For the same reason, there are many higher order conceptsterm·dom (all but the highest order conceptterm·dom of the power set). The specialized network thus gives rise to a rich constellation in qualia spaceterm·dom ( Figure 17C , bottom) with a high value of CI and Φ Maxterm·var .

The example in Figure 17A , which shows that a network can be interconnected, either directly or indirectly, yet condense into a number of mini-complexes of low Φ Maxterm·var if its architecture is primarily modular, is potentially consistent with neuropsychological evidence. As mentioned in the Introduction , the cerebellum is a paramount example of a complicated neuronal network, comprising even more neurons than the cerebral cortex, that does not give rise to consciousnessterm·dom or contribute to it [32] – [34] . This paradox could be explained by its anatomical and physiological organization, which seems to be such that small cerebellar modules process inputs and produce outputs largely independent of each other [35] , [36] . By contrast, a prominent feature of the cerebral cortex, which instead can generate consciousnessterm·dom, is that it is comprised of elements that are functionally specialized and at the same time can interact rapidly and effectively [4] , [37] , [38] . This is the kind of organization that yields a comparatively high value of Φ Maxterm·var in the simple example of Figure 17C . Finally, the example in Figure 17B , where connections are abundant but are organized in a homogeneous manner, may also have neurobiological counterparts. For instance, during deep slow wave sleep or in certain states of general anesthesia, the interactions among different cortical regions become highly stereotypical. Due to the characteristic bistability between on and off states of most neurons in the cerebral cortex, even though the anatomical connectivityterm·var is unchanged, functional and effective connectivityterm·var become virtually homogeneous [39] , [40] . Under such conditions, consciousnessterm·dom invariably fades [14] . The examples of Figure 17B and C also suggest that both the richness of conceptsterm·dom and the level of consciousnessterm·dom should increase with the refinement of cortical connections during neural development and the associate increase in functional specializationterm·var (e.g. [41] ).

Consciousnessterm·dom and activity: Inactive systems can be conscious The conceptual structureterm·dom generated by a complexterm·dom depends not only on the connectivityterm·var among its elements and the input/output function they perform, but also on their current stateterm·var. An important corollary of IIT is that both active and inactive elements can contribute to its conceptual structureterm·dom. Moreover, high-order conceptsterm·dom will often be specified by subsets including both active and inactive elements.

In Figure 18 , the system ABCD, comprised of 4 COPY gates, illustrates that a set of elements can form a complexterm·dom and specify a MICSterm·dom even though all of its elements are in state ‘0’ (off). This is because inactive elements, too, can selectively constrain past and future states of the system (as opposed to “inactivated” or non-functional elements, which cannot change state and thus cannot generate information). For example, element specifies an irreducible cause ( D had to be off at ) and an irreducible effect ( B will be on at ) within the complexterm·dom. Thus, IIT predicts that, even if all the neurons in a main complexterm·dom were inactive (or active at a low baseline rate), they would still generate consciousnessterm·dom as long as they are ready to respond to incoming spikes. An intriguing possibility is that a neurophysiological state of near-silence may be approximated through certain meditative practices that aim at reaching a state of “pure” awareness without content [18] , [42] . This corollary of IIT contrasts with the common assumption that neurons can only contribute to consciousnessterm·dom if they are active in such a way that they can “signal” or “broadcast” the information they represent and “ignite” fronto-parietal networks [7] , [10] . This is because, in IIT, information is not in the message that is broadcasted by an element, but in the shape of the MICSterm·dom that is specified by a complexterm·dom.

Qualeterm·def generated by an inactive system. Neural activity is not necessary to generate experience, nor does it need to be “broadcasted” globally. Although all the elements in the system are off (0), the system still forms a complexterm·dom and specifies a MICSterm·dom. Moreover, an element can contribute to experience as long as it affects the shape of the MICSterm·dom, without the need to “broadcast” its activity globally to affect every other element. This is because information is not in the message that is broadcasted by an element, but it is the shape of the MICSterm·dom that is specified by a complexterm·dom.

Another corollary of IIT that is relevant to neuroscience is that it is not necessary for the firing state of neurons to percolate or be “broadcasted” globally through the entire main complexterm·dom for it to contribute to experience. For example, in the system in Figure 18 , element A does not connect directly to element C . As a consequence, the activity (or inactivity) of A cannot affect C , and vice versa, within one time step. Nevertheless, ABCD still forms a complexterm·dom and gives rise to a MICSterm·dom at time . Thus, according to IIT, the activation or deactivation of a neuron (over the time scale at which integrated informationterm·mth reaches a maximum [20] ) can modify an experience as long as it affects the shape of the MICSterm·dom specified by the complexterm·dom to which the neuron belongs, without requiring any global “broadcast” of signals.

Simple systems can be conscious: A “minimally conscious” photodiode The previous section showed that activations and direct interactions between elements are not necessary to generate a MICSterm·dom. Taking into account the axiomsterm·def and postulates of IIT, we can now summarize what it takes to be conscious and give an example of a “minimally conscious system,” which will be called a “minimally conscious” photodiode.

The “photodiode” in Figure 19A consists of two elements: the detector D and the predictor P . D receives two external light inputs (and is thus a port-in) and one internal input from P , all with strength 1. As illustrated in Figure 19B , D turns on if it receives at least two inputs from internal and/or external sources. If D has switched on due to sufficiently strong external inputs, it activates element P , which serves as a “memory”. At the next time step, P acts as a “predictor” of the next external input to D by increasing its sensitivity to light.

Quantity and quality of experience of a “minimally conscious” photodiode. (A) The minimally conscious photodiodeterm·dom DP consists of detector element D and predictor element P . D receives two external inputs and has a threshold ≥2. All connections have weight 1. (B) P serves as a memory for the previous state of D and its feed-back to D serves as a predictor of the next external input by effectively decreasing the threshold of D . (C) The MICSterm·dom specified by the minimally conscious photodiodeterm·dom. D and P both specify a first order conceptterm·dom about the other element. (D) A minimally conscious thermistor or a minimally conscious blue detector with the same internal mechanisms as the minimally conscious photodiodeterm·dom generate the same MICSterm·dom and therefore have the same minimal experience.

Simple as it is, the photodiode system satisfies the postulates of IIT: both of its elements specify selective causes and effects within the system (each element about the other one), their cause-effect repertoiresterm·mth are maximally irreducible, and the conceptual structureterm·dom specified by the two elements is also maximally irreducible. Consequently, the system forms a complexterm·dom that gives rise to a MICSterm·dom, albeit one having just two conceptsterm·dom and a Φ Maxterm·var value of 1 ( Figure 19C ). DP is therefore conscious, albeit minimally so.

It is instructive to consider the quality of experience specified by such a minimally conscious photodiodeterm·dom. From an observer's perspective, the photodiode detects light, but from the intrinsic perspective, the experience is only minimally specified, and in no way can convey the meaning “light”: D says something about P 's past and future, and P about D 's, and that is all. Accordingly, the shape in qualia spaceterm·dom is a constellation having just two stars, and is thus minimally specific. This aspect is further emphasized if one considers that different physical systems, say a photodiode activated by blue light (a “blue” detector), or even a binary thermistor (a “temperature” detector) would generate the exact same MICSterm·dom ( Figure 19D ) and thus the same minimal experience. Moreover, the symmetry of the MICSterm·dom implies that the quality of the experience would be the same regardless of the system's state: the photodiode in state , 01, or 10, receiving one external input, generates exactly the same MICSterm·dom as . In all the above cases, the experience might be described roughly as “it is like this rather than not like this”, with no further qualifications. The photodiode's experience is thus both quantitatively and qualitatively minimal. Only additional mechanisms that create new conceptsterm·dom and break the symmetries in the shape of the MICSterm·dom can generate additional meaning. Ultimately, only a set of conceptsterm·dom comparable to that of our main complexterm·dom can specify the shape of the experience “light” as it appears to us, and distinguish it from countless other shapes corresponding to different experiences [6] .

Complexterm·dom systems can be unconscious: A “zombie” feed-forward networkterm·dom Another corollary of IIT is that certain structures do not give rise to consciousnessterm·dom even though they may perform complicated functions. Consider first an “unconscious” photodiode ( Figure 20A ), comprising again two elements: a detector D and output O . In this case, however, whether D is on or off is determined by external inputs only, and the output of O does not feed back into the system. Therefore, D 's response to light is just passed through the system, but never comes back to it. Although an observer may describe the two elements DO as a system, D and O do not have both causes and effects within the system DO , which is thus not a complexterm·dom, and generates no qualeterm·def.

Feed-forward “zombie” systems do not generate consciousnessterm·dom. (A) An unconscious photodiode DO without recurrent connections. The detector element D affects output element O , but has no cause within the system DO . O is caused by D , but has no effect on the photodiode DO . Therefore, the elements do not form a complexterm·dom and generate no qualeterm·def. (B) Even complicated systems cannot form a complexterm·dom if they have a strictly feed-forward architecture. This can be understood in the following way: for any system background imposed by an observer, the system's input layer has no causes within the system and the output layer has no effects on it, regardless of the elements' (logic) functions. Consequently, the system cannot form a complexterm·dom and it remains unconscious, just like the unconscious photodiode DO .

The same lack of feed-back that disqualifies the unconscious photodiode can be extended, by recursion, to any feed-forward system, no matter how numerous its elements and complicated its connectivityterm·var ( Figure 20B ). From the viewpoint of an extrinsic observer, the system's borders can be set arbitrarily. However, the input layer is always determined entirely by external inputs and the output layer does not affect the rest of the system. Consequently, from the intrinsic perspective, both input and output layer cannot be part of the complexterm·dom. Drawing the system boundaries closer and closer together in a recursive manner, one eventually ends up with just one input and output layer, made up of many “unconscious photodiodes”, and thus generating no qualeterm·def. Therefore, systems with a purely feed-forward architecture cannot generate consciousnessterm·dom.

The idea that “feed-back”, “reentry”, or “recursion” of some kind may be an essential ingredient of consciousnessterm·dom has many proponents [27] , [43] – [45] . Recently, it has been suggested that the presence or absence of feed-back could be directly equated with the presence or absence of consciousnessterm·dom [46] . Moreover, several recent studies indicate that an impairment of reentrant interactions over feed-back connections is associated with loss of consciousnessterm·dom during anesthesia [47] – [49] and in brain-damaged patients [50] . However, it has been pointed out that the brain (and many other systems) is full of reentrant circuits, many of which do not seem to contribute to consciousnessterm·dom [51] . IIT offers some specific insights with respect to these issues. First, the need for reciprocal interactions within a complexterm·dom is not merely an empirical observation, but it has theoretical validity because it is derived directly from the phenomenological axiomterm·dom of (strong) integration. Second, (strong) integration is by no means the only requirement for consciousnessterm·dom, but must be complemented by information and exclusion. Third, for IIT it is the potential for interactions among the parts of a complexterm·dom that matters and not the actual occurrence of “feed-back” or “reentrant” signaling, as is usually assumed. As was discussed above, a complexterm·dom can be conscious, at least in principle, even though none of its neurons may be firing, no feed-back or reentrant loop may be activated, and no “ignition” may have occurred.

Conscious complexesterm·dom and unconscious “zombie” systems can be functionally equivalent The last section showed that according to IIT feed-forward systems cannot give rise to a qualeterm·def. However, without restrictions on the number of nodes, feed-forward networksterm·dom with multiple layers can in principle approximate almost any given function to an arbitrary (but finite) degree [52] , [53] . Therefore, it is conceivable that an unconscious system could show the same input-output behavior as a “conscious” system.

An example is shown in Figure 21A . A strongly integrated system is compared to a feed-forward networkterm·dom that produces the same input-output behavior over at least 4 time steps (9 4 input states, Figure 21B ). To achieve a memory of x past time steps in the feed-forward system, the relevant elements were unfolded over time: the state of each element is passed on through a chain of x nodes, one node for each of the x time steps [54] , [55] . In this way, the states of upstream elements in previous time steps can be combined (converge) in a feed-forward manner to determine the state of elements downstream, but can never feed back on elements upstream. As illustrated in the figure, while the recurrent system gives rise to a complexterm·dom with Φ Maxterm·var >0 in every state, and would therefore be conscious, the feed-forward system does not constitute a complexterm·dom and is thus unconscious.

Functionally equivalent conscious and unconscious systems. (A) A strongly integrated system gives rise to a complexterm·dom in every network state. In the depicted state (yellow: 1, white: 0), elements form a complexterm·dom with Φ Maxterm·var = 0.76 and 17 conceptsterm·dom. (B) Given many more elements and connections, it is possible to construct a feed-forward networkterm·dom implementing the same input-output function as the strongly integrated system in (A) for a certain number of time steps (here at least 4). This is done by unfolding the elements over time, keeping the memory of their past state in a feed-forward chain. The transition from the first layer to the second hidden layer in the feed-forward system is assumed to be faster than in the integrated system ( ) to compensate for the additional layers ( ). Despite the functional equivalence, the feed-forward system is unconscious, a “zombie” without phenomenological experience, since its elements do not form a complexterm·dom.

This comparison highlights an important corollary of IIT: whether a system is conscious or not cannot be decided based on its input-output behavior only. In neuroscience, the ability to report is usually considered as the gold standard for assessing the presence of consciousnessterm·dom. Behavior and reportability can be reliable guides under ordinary conditions (typically adult awake humans) and can be employed to evaluate neural correlates of consciousnessterm·dom [9] and to validate theoretical constructs [14] . However, behavior and reportability become problematic for evaluating consciousnessterm·dom in pathological conditions, during development, in animals very different from us, and in machines that may perform sophisticated behaviors [6] . For example, programs running on powerful computers can not only play chess better than humans, but win in difficult question games such as “Jeopardy” [3] . Moreover, recent advances in machine learning have made it possible to construct simulated networks, primarily feed-forward, that can learn to recognize natural categories such as cats, dogs [1] , pedestrians [56] , [57] , and/or faces [58] – [60] . Hence, if behavior is the gold standard, it is not clear on what grounds we should deny consciousnessterm·dom to a phone “assistant” program that can answer many difficult questions, and can even be made to report about her internal feelings, or to a chip that recognizes thousands of different objects as well or better than we do, while granting it to a human who can barely follow an object with his eyes. IIT claims, by contrast, that input-output behavior is not always a reliable guide: one needs to investigate not just “what” functions are being performed by a system, but also “how” they are performed within the system. Thus, IIT admits the possibility of true “zombies”, which may behave more and more like us while lacking subjective experience [11] .

The examples of Figure 21 also suggest that, while it may be possible to build unconscious systems that perform many complexterm·dom functions, there is an evident evolutionary advantage towards the selection of integrated architectures that can perform the same functions consciously. Among the benefits of integrated architectures are economy of units and wiring, speed, compositionality, context-dependency, memory, and the ability to learn adaptive functions rapidly, flexibly, and building upon previous knowledge [6] . Moreover, in a feed-forward networkterm·dom all system elements are entirely determined by the momentary external input passing through the system. By contrast, a (strongly) integrated system is autonomous, since it can act and react based on its internal states and goals.

The conceptsterm·dom within a complexterm·dom are self-generated, self-referential, and holistic The final example ( Figure 22A ) considers a simple perceptual system – a recurrent segment/dot system. The segment/dot system consists of 10 heavily interconnected elements that, in their current stateterm·var, form a complexterm·dom ( Figure 22A , blue circle). Elements , and C are the ports-in of the complexterm·dom: they each receive 2 inputs from an external source in addition to feed-back inputs from within the complexterm·dom. Elements F and J are the ports-out of the complexterm·dom: they output to the external elements O 1 and O 2, respectively, in addition to their outputs within the complexterm·dom. In this example, the ports-out are XOR logic gates. All other elements inside the segment/dot system are linear threshold units (LTUs). Connections within the complexterm·dom are excitatory (+1, black) or inhibitory (−1, red).

A complexterm·dom can have ports-in and ports-out from and to the external environment, but its qualia are solipsistic: Self-generated, self-referential, and holistic. (A) A recurrent segment/dot system consisting of 10 elements (8 linear threshold units, and 2 XOR logic gates) that are linked by excitatory and inhibitory connections (black +1, red −1). and C are the ports-in of the complexterm·dom. They receive external inputs of strength 0, 1, or 2. Elements F and J are the ports-out of the complexterm·dom. They output to the external elements O 1 and O 2. The current stateterm·var of the system corresponds to a sustained input with value 2-2-0. From an extrinsic perspective, the different layers of the complexterm·dom can be interpreted as feature detectors having increasingly invariant selectivities (e.g. D indicates “two contiguous left elements”, F “invariant segment”, and J “invariant dot”). (B) Since the segment/dot system is highly interconnected with specialized mechanisms, all first order conceptsterm·dom and many higher order conceptsterm·dom exist. (C) Both, elementary mechanisms that are “on” (1) and those that are “off” (0) constitute conceptsterm·dom. Note that the cause repertoire of is the mirror image of the cause repertoire of (highlighted in blue). (C,D,E) From the intrinsic perspective, the function of a mechanism is given by its cause-effect repertoireterm·mth. The purview of a conceptterm·dom can only contain elements within the complexterm·dom. The conceptsterm·dom that constitute the MICSterm·dom generated by the complexterm·dom are self-generated (specified exclusively by elements belonging to the complexterm·dom); self-referential (specified exclusively over elements belonging to the complexterm·dom); and holistic (their meaning is constructed in the context of the other conceptsterm·dom in the MICSterm·dom).

The elementary mechanisms comprising the segment/dot system have specialized functions and generate elementary conceptsterm·dom. In the segment/dot system, the conceptsterm·dom of mechanisms in the “off” state (0) tend to have lower φ Maxterm·var values, because the mechanisms tend to be more selective in their “on” state (1) (see also Figure 3 ). As listed in Figure 22B , in addition to first order conceptsterm·dom, the segment-dot system gives rise to many higher order conceptsterm·dom. Dependent on the state of the system, certain higher order conceptsterm·dom may or may not exist. For instance, in the current stateterm·var of the segment/dot system, the second order conceptterm·dom DI exists, while EG does not because it is reducible ( ). If the segment/dot system were presented instead with a “right”-segment (inputs 022), DI would disappear and EG would emerge.

From the perspective of an external observer (e.g. a neuroscientist recording the activity of “neurons” ), the function of a mechanism is typically described with respect to external inputs (e.g. a “segment” detector). In the segment/dot system, mechanisms at different hierarchical levels correspond to increasing levels of invariance: element D , for example, turns on if the two contiguous pixels on the left have been on persistently (with inputs of strength 2); higher up in the system, element F turns on if two contiguous pixels have been on either on the left or on the right, thus indicating the presence of the invariant “segment”. Element J , on the other hand, detects the invariant “dot”, either left, right, or center. The excitatory and inhibitory feed-back connections in the segment/dot system serve a predictive function: they temporarily increase/decrease the sensitivity to similar/opposed stimuli, allowing weaker inputs (with a value of 1) to be detected as segments and dots if the weaker external input is in accordance with the feed-back from within the complexterm·dom.

From the intrinsic perspective of the system, instead, the function of each mechanism is given by its conceptterm·dom. Each conceptterm·dom is self-generated , because it must be specified exclusively by a subset of elements belonging to the complexterm·dom. It is also self-referential , because its cause-effect repertoireterm·mth refers exclusively to elements within the complexterm·dom, and therefore only indirectly to external inputs. For example, the conceptterm·dom of D , in its current stateterm·var 1, is about the purview . From the intrinsic perspective, the function of is thus to constrain the possible past states of and J , and to constrain the possible future state of A ( Figure 22C ). Therefore, D = 1 specifies a conceptterm·dom that is exclusively self-referential to the complexterm·dom to which D belongs (note that, in this simple version of a recurrent segment/dot system, feed-forward and feed-back connections have the same absolute strength of 1. In a more realistic neural network, in which the function of the recurrent connections is mostly modulatory, a conceptterm·dom's past and future purviews would be modified accordingly). Nevertheless, in this case there is a good correspondence between the intrinsic and the extrinsic perspective, since the cause repertoire of specifies as potential causes those states in which both ports-in A and B are 1, which happens when two contiguous pixels on the left are on. Importantly, the conceptterm·dom of additionally takes into account the internal context (blue shaded states in Figure 22C ). However, the correspondence between intrinsic and extrinsic perspective breaks down for the ports-in : even though their state is partly determined by the external inputs, their conceptterm·dom specifies constraints about past and future states of elements higher up in the system, rather than about the environment ( Figure 22D ).

The self-referential property of the conceptsterm·dom specified by ports-in may have some implications with respect to the role of primary areas in consciousnessterm·dom. An influential hypothesis by Crick and Koch [61] suggests that primary visual cortex (V1) and perhaps other primary cortical areas may not contribute directly to consciousnessterm·dom, a hypothesis that is now supported by a large number of experimental results. For example, during binocular rivalry neurons in V1 may fire selectively to horizontal bars that are shown to one eye, even though the subject does not see them and is conscious of a different stimulus presented to the other eye [62] . On the other hand, the firing of units higher up in the visual system correlates tightly with the experience. While these results are compelling, other interpretations are possible if, as illustrated in the segment/dot system, V1 neurons were to constitute ports-in of the main complexterm·dom. Under this assumption, V1 units would have to specify conceptsterm·dom about other units in the complexterm·dom – either other V1 units or units in higher areas – rather than about their feed-forward inputs, which would remain outside the complexterm·dom. V1 conceptsterm·dom could relate for example to Gestalt properties such as spatial continuity, rather than to oriented bars. In that case, what V1 contributes to consciousnessterm·dom during binocular rivalry – namely spatial continuity – would not change substantially between the two rivalrous percepts. Instead, conceptsterm·dom corresponding to oriented bars would be specified by units in higher areas, whose firing is sensitive to perceptual rivalry, over units in V1. In sum, V1 units would contribute to consciousnessterm·dom not only by generating their own conceptsterm·dom (such as spatial continuity), but also by providing the cause repertoire for conceptsterm·dom specified by units higher up (such as oriented bars). While this possibility may be far-fetched and counterintuitive, it would not be inconsistent with lesion studies that highlight the importance of V1 for most aspects of visual consciousnessterm·dom [63] , [64] .

The self-referential nature of conceptsterm·dom within a complexterm·dom has implications with respect to how conceptsterm·dom obtain their meaning . As mentioned above, a (conscious) external observer “knows” that element F in Figure 22E turns on whenever there is a “segment” in the input from the environment. However, from the intrinsic perspective of the complexterm·dom, that meaning cannot be specified by F = 1 in isolation. This is because, while the cause repertoire of F = 1 specifies that either D or E must have been on, by itself it cannot specify what D and E mean in turn. In fact, the full meaning of “segment” can only be synthesized through the interlocking of cause-effect repertoiresterm·mth of multiple conceptsterm·dom within a MICSterm·dom (such as that of element F interlocked with those of elements D , E , and so on). In this view, the meaning of a conceptterm·dom depends on the context provided by the entire MICSterm·dom to which it belongs, and corresponds to how it constrains the overall “shape” of the MICSterm·dom. Meaning is thus both self-referential (internalistic) and holistic . A proper treatment of how the conceptual structureterm·dom of a complexterm·dom of mechanisms can give rise to meaning from the intrinsic perspective is beyond the scope of the present work and will be addressed in more detail elsewhere.

While emphasizing the self-referential nature of conceptsterm·dom and meaning, IIT naturally recognizes that in the end most conceptsterm·dom owe their origin to the presence of regularities in the environment, to which they ultimately must refer, albeit only indirectly. This is because the mechanisms specifying the conceptsterm·dom have themselves been honed under selective pressure from the environment during evolution, development, and learning [65] – [67] . Nevertheless, at any given time, environmental input can only act as a background condition, helping to “select” which particular conceptsterm·dom within the MICSterm·dom will be “on” or “off”, and their meaning will be defined entirely within the qualeterm·def. Every waking experience should then be seen as an “awake dream” selected by the environment. And indeed, once the architecture of the brain has been built and refined, having an experience – with its full complement of intrinsic meaning – does not require the environment at all, as demonstrated every night by the dreams that occur when we are asleep and disconnected from the world.

Limitations and future directions In finishing, we point out some limitations and unfinished business. IIT 3.0 starts from key properties of consciousnessterm·dom – the phenomenological axiomsterm·dom – and translates them into postulates that lay out how a system of mechanisms must be constructed to satisfy those axiomsterm·def and thus generate consciousnessterm·dom. To be able to formulate the postulates in explicit, computable terms, we considered small systems of interconnected mechanisms that are fully characterized by their transition probability matrix (TPM). For each system, mechanisms are discrete in time and space (see also Text S2 ) and transition probabilities are available for every possible state. Directly applying this approach to physical systems of interest, such as brains, is unfeasible for several reasons: i) One would need either to discretize the variables of interest or to extend the theoretical treatment to continuous variables. ii) For biological systems, one is usually limited to observable system states, and the exhaustive perturbation of a system as the brain across all its possible states is unfeasible. Nevertheless, systematic perturbations of brain states using naturalistic stimuli such as movies can provide useful approximations. Also, circumscribed regions of the cerebral cortex could be perturbed systematically using optogenetic methods coupled with calcium imaging. Moreover, discrete, analytically tractable brain models based on neuroanatomical connectivityterm·var such as [68] could provide a suitable approximation of large-scale neural mechanisms yet permit the rigorous measurement of integrated informationterm·mth. iii) Variables recorded in most neurophysiological experiments may not correspond to the spatial and temporal grain at which integrated informationterm·mth reaches a maximum, which is the appropriate level of analysis [20] . iv) The present analysis is unfeasible for systems of more than a dozen elements or so. This is because, to calculate Φ Maxterm·var exhaustively, all possible partitions of every mechanism and of every system of mechanisms should be evaluated, which leads to a combinatorial explosion, not to mention that the analysis should be performed at every spatio-temporal grainterm·var. For these reasons, the primary aim of IIT 3.0 is simply to begin characterizing, in a self-consistent and explicit manner, the fundamental properties of consciousnessterm·dom and of the physical systems that can support it. Hopefully, heuristic measures and experimental approaches inspired by this theoretical framework will make it possible to test some of the predictions of the theoryterm·mth [14] , [69] . Deriving bounded approximations to the explicit formalism of IIT 3.0 is also crucial for establishing in more complexterm·dom networks how some of the properties described here scale with system size and as a function of system architecture.

The above formulation of IIT 3.0 is also incomplete: i) We did not discuss the relationship between MICSterm·dom and specific aspects of phenomenology, such as the clustering into modalities and submodalities, and the characteristic “feel” of different aspects of experience (space, shape, color and so on; but see [4] – [6] , [18] ). ii) In the examples above, we assumed that the “micro” spatio-temporal grainterm·var size of elementary logic gates updating every time step was optimal. In general, however, for any given system the optimal grain size needs to be established by examining at which spatio-temporal level integrated informationterm·mth reaches a maximum [20] . In terms of integrated informationterm·mth, then, the macro may emerge over the micro, just like the whole may emerge above the parts. iii) While emphasizing that meaning is always internal to a complexterm·dom (it is self-generated and self-referential), we did not discuss in any detail how meaning originates through the nesting of conceptsterm·dom within MICSterm·dom (its holistic nature). iv) In IIT, the relationship between the MICSterm·dom generated by a complexterm·dom of mechanisms, such as a brain, and the environment to which it is adapted, is not one of “information processing”, but rather one of “matching” between internal and external causal structures [4] , [6] . Matching can be quantified as the distance between the set of MICSterm·dom generated when a system interacts with its typical environment and those generated when it is exposed to a structureless (“scrambled”) version of it [6] , [70] . The notion of matching, and the prediction that adaptation to an environment should lead to an increase in matching and thereby to an increase in consciousnessterm·dom, will be investigated in future work, both by evolving simulated agents in virtual environments (“animats” [71] – [73] ), and through neurophysiological experiments. v) IIT 3.0 explicitly treats integrated informationterm·mth and causation as one and the same thing, but the many implications of this approach need to be explored in depth in future work. For example, IIT implies that each individual consciousnessterm·dom is a local maximum of causal power. Hence, if having causal power is a requirement for existence, then consciousnessterm·dom is maximally real. Moreover, it is real in and of itself – from its own intrinsic perspective – without the need for an external observer to come into being.

Supporting Information Motivation for exclusion at the level of mechanisms. Core cause: only one cause exists intrinsically – the most irreducible one. A neuron that receives two strong inputs from and four weak inputs . The core cause is with (in the case of identical values, the largest purview is chosen because it specifies information about more system elements for the same value of irreducibility). This example illustrates that a core cause is not the most comprehensive set of possible causes of a particular state (in this case ), but the subset that is most affected by a partition.

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Main differences between IIT 3.0 and earlier versions.

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Supplementary methods.

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Some differences between integrated informationterm·mth and Shannon information.

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Acknowledgments We thank Chiara Cirelli, Lice Ghilardi, Melanie Boly, Christof Koch, and Marcello Massimini for many invaluable discussions concerning the conceptsterm·dom presented here. We also thank Brad Postle, Barry van Veen, Virgil Griffiths, Atif Hashmi, Erik Hoel, Matteo Mainetti, Andy Nere, Umberto Olcese, and Puneet Rana. We are especially grateful to V. Griffith for his contribution to characterizing the conceptterm·dom of synergy and its relation to integrated informationterm·mth; to M. Mainetti for his help in characterizing the proper metric for conceptual spaces. For developing the software used to compute maximally irreducible integrated conceptual structuresterm·dom we are indebted to B. Shababo, A. Nere, A. Hashmi, U. Olcese, and P. Rana.

Funding Statement This work was supported by a Paul G. Allen Family Foundation grant, by the McDonnell Foundation, and by the Templeton World Charities Foundation (Grant #TWCF 0067/AB41). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

References Associated Data Supplementary Materials Motivation for exclusion at the level of mechanisms. Core cause: only one cause exists intrinsically – the most irreducible one. A neuron that receives two strong inputs from and four weak inputs . The core cause is with (in the case of identical values, the largest purview is chosen because it specifies information about more system elements for the same value of irreducibility). This example illustrates that a core cause is not the most comprehensive set of possible causes of a particular state (in this case ), but the subset that is most affected by a partition.

(PDF) Click here for additional data file.

Main differences between IIT 3.0 and earlier versions.

(PDF) Click here for additional data file.

Supplementary methods.

(PDF) Click here for additional data file.

Some differences between integrated informationterm·mth and Shannon information.

(PDF) Click here for additional data file.