intellecton/papers/references/Oizumi2014.txt

From the Phenomenology to the Mechanisms of
Consciousness: Integrated Information Theory 3.0

Masafumi Oizumi1,2., Larissa Albantakis1., Giulio Tononi1*

1 Department of Psychiatry, University of Wisconsin, Madison, Wisconsin, United States of America, 2 RIKEN Brain Science Institute, Wako-shi, Saitama, Japan

Abstract

This paper presents Integrated Information Theory (IIT) of consciousness 3.0, which incorporates several advances over
previous formulations. IIT starts from phenomenological axioms: 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 grain. These axioms
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 information as ‘‘differences that make
a difference’’ within a system, and integrated information 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 structure (MICS, a constellation
of concepts in qualia space), and the set of elements that generates it constitutes a complex. According to IIT, a MICS
specifies the quality of an experience and integrated information WMax its quantity. From the theory follow several results,
including: a system of mechanisms may condense into a major complex and non-overlapping minor complexes; the
concepts that specify the quality of an experience are always about the complex itself and relate only indirectly to the
external environment; anatomical connectivity influences complexes and associated MICS; a complex can generate a MICS
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 complexes.

Citation: Oizumi M, Albantakis L, Tononi G (2014) From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3.0. PLoS
Comput Biol 10(5): e1003588. doi:10.1371/journal.pcbi.1003588

Editor: Olaf Sporns, Indiana University, United States of America

Received November 18, 2013; Accepted March 11, 2014; Published May 8, 2014

Copyright: � 2014 Oizumi et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: 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.

Competing Interests: The authors have declared that no competing interests exist.

* E-mail: gtononi@wisc.edu

. These authors contributed equally to this work.

Introduction

Understanding consciousness 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 consciousness generated by the corticotha-
lamic system – or at least some parts of it, but not by the
cerebellum, despite the latter having even more neurons? Why
does consciousness 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 consciousness 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 theory of consciousness.
(Below, consciousness, experience, and phenomenology are taken
as being synonymous).
A theory 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 consciousness, or to the neural correlates of

consciousness as established in healthy adults. The inadequacy of
behavioral assessments of consciousness 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 consciousness? If not,
what are they missing, and what does it take to build a machine
that is actually conscious? Clearly, only a theory - one that says
what consciousness 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 consciousness and its content.
Integrated information theory (IIT) is an attempt to characterize
consciousness mathematically both in quantity and in quality [4–
6]. IIT starts from the fundamental properties of the phenome-
nology of consciousness, which are identified as axioms of

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consciousness. Then, IIT translates these axioms into postulates,
which specify which conditions must be satisfied by physical
mechanisms, such as neurons and their connections, to account for
the phenomenology of consciousness. It must be emphasized that
taking the phenomenology of consciousness 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 consciousness, as assessed by behavioral reports
[7–10]. While identifying the ‘‘neural correlates of consciousness’’
is undoubtedly important [8], it is hard to see how it could ever
lead to a satisfactory explanation of what consciousness 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 consciousness, 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
consciousness. Moreover, IIT leads to experimental predictions,
for instance that the loss and recovery of consciousness 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 electroen-
cephalography in several different conditions characterized by loss
of consciousness, such as deep sleep, general anesthesia obtained
with several different agents, and in brain damaged patients
(vegetative, minimally conscious, emerging from minimal con-
sciousness, locked-in [14]). Furthermore, IIT has inspired theo-
retically motivated measures of the level of consciousness that have
been applied to human and animal data (e.g. [14], see also [15] for
a related attempt to measure the level of consciousness 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 consciousness. 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 information 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 axioms 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 structure (MICS)
and the associated value of integrated information WMax. The
Results/Discussion section presents several new results that follow
directly from IIT, including the condensation of systems of
mechanisms into main complexes and minor complexes; 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 complex; and
finally, an example showing that concepts within a complex are
self-referential and relate only indirectly to the external environ-
ment.

Models

Axioms, postulates, and identities
The main tenets of IIT can be presented as a set of
phenomenological axioms, ontological postulates, and identities.
While the terms ‘‘axioms’’ and ‘‘postulates’’ are often used
interchangeably, we follow the classical tradition according to
which an ‘‘axiom’’ 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:
axioms are self-evident truths about consciousness – 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 consciousness (mechanisms must exist, be
irreducible, etc.), which can be formalized and form the basis of
the mathematical framework of IIT.
Axioms.
The central axioms, which are taken to be imme-
diately evident, are as follows:
N EXISTENCE: Consciousness exists – it is an undeniable aspect of
reality. Paraphrasing Descartes, ‘‘I experience therefore I am’’.

N COMPOSITION: Consciousness 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.

N INFORMATION: Consciousness 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,

Author Summary

Integrated information theory (IIT) approaches the rela-
tionship between consciousness and its physical substrate
by first identifying the fundamental properties of experi-
ence itself: existence, composition, information, integra-
tion, and exclusion. IIT then postulates that the physical
substrate of consciousness must satisfy these very prop-
erties. We develop a detailed mathematical framework in
which composition, information, integration, and exclusion
are defined precisely and made operational. This allows us
to establish to what extent simple systems of mechanisms,
such as logic gates or neuron-like elements, can form
complexes that can account for the fundamental proper-
ties of consciousness. Based on this principled approach,
we show that IIT can explain many known facts about
consciousness and the brain, leads to specific predictions,
and allows us to infer, at least in principle, both the
quantity and quality of consciousness for systems whose
causal structure is known. For example, we show that
some simple systems can be minimally conscious, some
complicated
systems
can
be
unconscious,
and
two
different systems can be functionally equivalent, yet one
is conscious and the other one is not.

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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.

N INTEGRATION: Consciousness 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.

N EXCLUSION: Consciousness 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 axioms, IIT
posits a set of postulates. These list the properties physical systems
must satisfy in order to generate experience.
N EXISTENCE: Mechanisms in a state exist. A system is a set of
mechanisms.

N COMPOSITION: 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
N INFORMATION: A mechanism can contribute to consciousness
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 repertoire. The more selective
the possible causes and effects, the higher the cause-effect
information cei specified by the mechanism.

N INTEGRATION: A mechanism can contribute to consciousness
only if it specifies a cause-effect repertoire (information) that is
irreducible to independent components. Integration/irreducibility Q
is assessed by partitioning the mechanism and measuring what
difference this makes to its cause-effect repertoire.

N EXCLUSION: A mechanism can contribute to consciousness at
most one cause-effect repertoire, the one having the maximum
value of integration/irreducibility QMax. This is its maximally
irreducible cause-effect repertoire (MICE, or quale sensu stricto
(in the narrow sense of the word, [5])). If the MICE exists, the
mechanism constitutes a concept.

Systems of mechanisms
N INFORMATION: 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 structure. A conceptual
structure is a constellation of points in concept space, where each
axis is a possible past/future state of the set of elements, and
each point is a concept specifying differences that make a
difference within the set. The higher the number of different

concepts and their QMax value, the higher the conceptual
information CI that specifies a particular constellation and
distinguishes it from other possible constellations.

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

N EXCLUSION: Of all overlapping sets of elements, only one set
can be conscious – the one whose mechanisms specify a
conceptual structure that is maximally irreducible (MICS) to
independent components. A local maximum of integrated
information WMax (over elements, space, and time) is called a
complex.

Identities.
Finally, according to IIT, there is an identity
between phenomenological properties of experience and informa-
tional/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 structure (MICS) gener-
ated by a complex of elements is identical to its experience. The
constellation of concepts of the MICS completely specifies the
quality of the experience (its quale ‘‘sensu lato’’ (in the broad sense of
the term [5])). Its irreducibility WMax specifies its quantity. The
maximally irreducible cause-effect repertoire (MICE) of each
concept within a MICS specifies what the concept is about (what it
contributes to the quality of the experience, i.e. its quale sensu stricto
(in the narrow sense of the term)), while its value of irreducibility
QMax specifies how much the concept is present in the experience.
An experience is thus an intrinsic property of a complex of
mechanisms in a state. In other words, the maximally irreducible
conceptual structure specified by a complex 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 repertoire of each mechanism
should be considered (exclusion). This allows us to introduce the
notion
of
a
concept:
the
maximally
irreducible
cause-effect
repertoire 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 complex – a
maximally integrated set of elements – and of a quale – the
maximally irreducible conceptual structure (MICS) 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 structure and how the latter can be
characterized in full. A summary of the key concepts and
associated measures is provided as a reference in Table 1 and
Box 1.
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,

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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.

Box 1. Glossary

Axiom: Self-evident truth about consciousness (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 state 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 repertoire: The probability distribution of
potential past and future states of a system as constrained
by a mechanism in its current state.
Cause-effect information (cei): The amount of informa-
tion 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).
Complex: A set of elements within a system that generates
a local maximum of integrated conceptual information WMax.
Only a complex exists as an entity from its own intrinsic
perspective.
Concept: A set of elements within a system and the
maximally irreducible cause-effect repertoire it specifies, with
its associated value of integrated information QMax. The
concept expresses the causal role of a mechanism within a
complex.
Conceptual structure, constellation of concepts (C): A
conceptual structure is the set of all concepts specified by a
candidate set with their respective QMax values, which can be
plotted as a constellation in concept space.
Conceptual information (CI): A measure of how many
different concepts are generated by a system of elements. CI
is quantified by the distance D between the constellation of
concepts and the ‘‘null’’ concept, the unconstrained cause-
effect repertoire puc.
Concept space: Concept space is a high dimensional space
with one axis for each possible past and future state of the
system in which a conceptual structure 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 concept space and thus the distance between
probability distributions (Q) and between constellations of
concepts (W).
Integrated conceptual information (W): Conceptual
information that is generated by a system above and
beyond
the
conceptual
information
generated
by
its
(minimal) parts. W measures the integration or irreducibility
of a constellation of concepts (integration at the system
level).
Integrated information (Q): Information that is generated

by a mechanism above and beyond the information
generated by its (minimal) parts. Q measures the integration
or irreducibility of mechanisms (integration at the mecha-
nism level).
Intrinsic information: 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 repertoire):
The cause-effect repertoire of a concept, i.e., the cause-effect
repertoire that generates a maximum of integrated informa-
tion Q among all possible purviews.
MICS (maximally irreducible conceptual structure):
The conceptual structure generated by a complex in a state
that corresponds to a local maximum of integrated concep-
tual information WMax (synonymous with ‘‘quale’’ or ‘‘con-
stellation’’ in ‘‘qualia space’’).
MIP (minimum information partition): The partition that
makes the least difference (in other words, the minimum
‘‘difference’’ partition).
Null concept: The unconstrained cause-effect repertoire puc

of the candidate set, with Q = 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 axioms, about the
physical substrates of consciousness (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.
Quale: The conceptual structure generated by a complex in
a state that corresponds to a local maximum of integrated
conceptual information WMax (synonymous with ‘‘MICS’’ or
‘‘constellation’’ in ‘‘qualia space’’).
Qualia space: If a set of elements forms a complex, its
concept space is called qualia space.
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 (puc): The probability distribu-
tion of potential past and future system states without
constraints due to any mechanism in a state. The uncon-
strained cause repertoire is the uniform distribution of
system
states.
The
unconstrained
effect
repertoire
is
obtained by assuming unconstrained inputs to all system
elements.

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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).
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

DEF(t{1)~DEF(t0)~010 (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 t0, the mechanisms are in state ABC~100.
The TPM specifies which past states could have led to the current
state ABC~100 (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 elemen-
tary mechanisms can be structured, forming higher order
mechanisms in various combinations. In Figure 2, A, B, and C

Table 1. Key concepts and measures of IIT.

MECHANISM
SYSTEM OF MECHANISMS

Information

Only mechanisms that specify differences that make a difference within a system count

Cause-effect information (cei): How a mechanism
in a state specifies the probability of past and future states
of a set of elements (cause-effect repertoires)

Conceptual information (CI): How a set of mechanisms
specifies the probability of past and future states of the set
(conceptual structure)

Integration

Only information that is irreducible to independent components counts

Integrated information (Q, ‘‘small phi’’): How irreducible
the cause-effect repertoire specified by a mechanism is compared to its
minimum information partition (MIP)

Integrated conceptual information (W, ‘‘big phi’’): How
irreducible the conceptual structure specified by a set of mechanism is
compared to its minimum information partition (MIP)

Exclusion

Only maxima of integrated information count (over elements, space, time)

Concept (QMax): A mechanism that specifies a
maximally irreducible cause-effect repertoire (MICE or quale ‘‘
sensu stricto’’)

Complex (WMax): A set of elements whose mechanisms specify
a maximally irreducible conceptual structure (MICS or quale ‘‘sensu lato’’)

doi:10.1371/journal.pcbi.1003588.t001

Figure 1. 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(t21) = DEF(t0) = 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 state of ABC is 100.
doi:10.1371/journal.pcbi.1003588.g001

Figure 2. 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 state of the elements inside the
candidate set but outside of a mechanism is undetermined for the
mechanism under consideration.
doi:10.1371/journal.pcbi.1003588.g002

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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 combina-
tions form the power set of possible mechanisms.
Information: Cause-effect repertoires 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 state s0 constrains the system’s potential
past and future states. Figure 3 illustrates how a mechanism A
constrains the past states of BCD more or less selectively depending
on its input/output function and state. A is an AND gate of the
inputs from BCD. The constrained distribution of past states is
called A’s cause repertoire. In Figure 3A the connections between A
and BCD are substituted by noise. Therefore, the current state of A
cannot specify anything about the past state of BCD, the cause
repertoire is identical to the unconstrained distribution (unselec-
tive), 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 A is off (A~0, Figure 3C),
the cause repertoire is less selective, because only BCD~111 is
ruled out, corresponding to less information.
Figure 4 illustrates how element A in state 1 constrains the past
states (left) and future states (right) of the candidate set ABC. The

probability distribution of past states that could have been
potential causes of A~1 is its cause repertoire p(ABCpDAc~1).
The probability distribution of future states that could be potential
effects of A~1 is called effect repertoire p(ABCf DAc~1). 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 A~1
over its purview ABC (the full set) in the past and future, labeled
Ac=ABCp and Ac=ABCf . 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).
The amount of information that A~1 specifies about the past,
its cause information (ci), is measured as the distance D between
the cause repertoire p(ABCpDAc~1) and the unconstrained past
repertoire puc. For the purview ABCp:

ci(ABCpDAc~1)~D(p(ABCpDAc~1)DDpuc(ABCp))~0:33:
ð1Þ

puc(ABCp) 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 puc(ABCf ):

ei(ABCf DAc~1)~D(p(ABCf DAc~1)DDpuc(ABCf ))~0:25:
ð2Þ

As can be seen in Figure 4 (right), the unconstrained future
repertoire puc(ABCf ) is not simply the uniform distribution of
future system states. While puc(ABCp) corresponds to the
distribution of past system states with unconstrained outputs,
puc(ABCf ) corresponds to the distribution of future system states
with unconstrained inputs. Therefore, puc(ABCf ) is obtained by
perturbing the inputs to each element into all possible states. As an

Figure 3. Information requires selectivity. A mechanism generates information to the extent that it selectively constrains a system’s past states.
Element A constrains the past states of BCD depending on its mechanism (AND gate) and its current state. The constrained distribution of past
states is called A’s cause repertoire. (A) The connections between A and BCD are noisy. A’s cause repertoire is thus unselective, since A~1 could have
followed from any state of BCD with equal probability. (B) In the case of deterministic connections and current state A~1, A’s cause repertoire is
maximally selective, because all states except BCD~111 are ruled out as possible causes of A~1. (C) In the case of deterministic connections and
current state A~0, A’s cause repertoire is much less selective than for A~1, because only state BCD~111 is ruled out as a possible cause of A~0.
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example, the unconstrained future repertoire of element A, being
an OR gate, is p(A~0)~0:25 and p(A~1)~0:75, which is
obtained by perturbing the inputs of A into all possible states
½00,10,01,11�.
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 ci(ABCpDA~1) and ei(ABCf DA~1),
the total amount of cause-effect information (cei) specified by A = 1 over
the purview A=ABCp,f is the minimum of its ci and ei:

cei(ABCp,f jAc~1)~

min½ci(ABCpjA~1),ei(ABCf jA~1)�~0:25:
ð3Þ

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

Figure 4. 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 ABC consisting of OR, AND, and XOR gates is shown in its
current state 100. We consider the purview of mechanism A, highlighted in red, over the set ABC in the past (blue) and in the future (green). (Bottom
center) The same network is displayed unfolded over three time steps, from t{1 (past), t0 (current) to tz1 (future). Gray-filled circles are undetermined
states. The current state of mechanism A constrains the possible past and future system states compared to the unconstrained past and future
distributions puc(ABCp=f ). For example, A~1 rules out the two states where BC~00 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 puc(ABCp); effect information (ei) is quantified by
measuring the distance D between the effect repertoire and the unconstrained future repertoire puc(ABCf ). Note that the unconstrained future
repertoire puc(ABCf ) 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.
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– A has selective causes within the system (ciw0), but not the
future states of the system – A has no selective effects on the system
(ei~0, 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).
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 (eiw0), but not the past states of the
system – A has no selective causes within the system (ci~0, 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
information bottleneck principle’’ is best captured by defining a
mechanism’s cei as the minimum between its cause and effect
information.
Integration:
Irreducible
cause-effect
repertoires
and
integrated information (Q).
At the level of an individual
mechanism, the integration postulate says that only mechanisms
that specify integrated information can contribute to conscious-
ness. Integrated information 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 information Q (‘‘small phi’’) is calculated as the distance
D between two probability distributions: the cause-effect repertoire
specified by the whole mechanism is compared against the cause-
effect repertoire of the partitioned mechanism. Of the many
possible ways to partition a mechanism, integrated information is
evaluated across the minimum information partition (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 3r�d order mechanism
ABC.
The
MIP
for
the
purview
ABCc=ABCp,ABCf
is
ABCc=ABCp?(ABc=Cp)|(Cc=ABp)
in
the
past
and
ABCc=ABCf ?(ABCc=ACf )|(½�=Bf ) in the future, where []
denotes the empty set. The cause and effect repertoire specified by
the partitioned mechanisms can be calculated as:

p(ABCpjABCc~100=MIP)~

p(CpjABc~10)|p(ABpjCc~0),
ð4Þ

and

p(ABCf DABCc~100=MIP)~p(ACf DABCc~100)|p(Bf ),
ð5Þ

where the connections between the parts are ‘‘injected’’ with
independent noise (Text S2).
The distance D between the cause-effect repertoire 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):

QMIP
cause(ABCpjABCc~100)~

D(p(ABCpjABCc~100)jjp(ABCpjABCc~100=MIP))~0:5,
ð6Þ

QMIP
effect(ABCf jABCc~100)~

D(p(ABCf jABCc~100)jjp(ABCf jABCc~100=MIP))~0:25,
ð7Þ

As with information, the total amount of integrated information
of mechanism ABC in its current state 100 over the purview
ABCc=ABCp,f is the minimum of its past and future integrated
information:

QMIP(ABCp,f jABCc~100)~min½QMIP
cause(ABCpjABCc~100),

QMIP
effect(ABCf jABCc~100)�~0:25,
ð8Þ

In what follows, integrated information Q is always evaluated for
the MIP, so the MIP superscript is dropped for readability.
According to IIT, mechanisms that do not generate integrated
information 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
information, since it is possible to partition AB’s causes and effects

Figure 5. 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).
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without any loss of information. In this case, AB does not exist
intrinsically.
Consider instead Figure 7B. Here, AB~11 specifies that all
inputs had to be on in the past (‘All ON’), which goes above and
beyond what is specified separately by A~1 (an even number of
inputs was on) and by B~1 (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 AB~11 goes above and beyond the separate
effects of A~1 and B~1. 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, A~1 and B~1 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
repertoire (MICE) specified by a subset of elements (a
concept).
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 BC~00 in Figure 8. To find the core cause of BC,
one needs to evaluate Qcause for all past purviews of the power set
P~ Ap,Bp,Cp,ABp,ACp,BCp,ABCp
f
g. In this case, the purview
BCc=ABp has the highest value of QMax
cause(PDBCc~00)~0:33. The
corresponding maximally irreducible cause repertoire is thus the
core cause of BC~00. The core effect is assessed in the same way:
it is the maximally irreducible effect repertoire of a mechanism
with QMax
effect(FDBCc~00), where F denotes the power set of future
purviews. A mechanism that specifies a maximally irreducible cause
and effect (MICE) constitutes a concept or, for emphasis, a core concept.
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

Figure 6. Integrated information: The information generated by the whole that is irreducible to the information generated by its
parts. Integrated information 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 partition – 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).
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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 concepts such as ‘‘chair’’, or
‘‘apple’’ seem to exclude the accidental details of particular apples
and chairs, but only reflect the ‘‘core’’ concept. In neural terms,
this would imply that the maximally irreducible cause-effect
repertoire of the neurons underlying such invariant concepts is
similarly restricted to their core causes and effects.
The notion of a concept is illustrated in Figure 9 for mechanism
A of the candidate set ABC. The core cause of A is the cause
repertoire of purview Ac=BCp; the core effect is the effect
repertoire of Ac=Bf . These purviews generate the maximal
amount of integrated information over the whole power set of

purviews in the past (P) and future (F), respectively. The amount of
integrated information generated by concept Ac=BCp,Bf is again
the minimum between past and future:

QMax(Ac~1)~min½QMax
cause(PDAc~1),QMax
effect(FDAc~1)�~0:17: ð9Þ

Each concept of a mechanism in a state is thus endowed with a
maximally irreducible cause-effect repertoire (MICE), which
specifies what the concept is about (its quale ‘‘sensu stricto’’), and
its
particular
QMax
value,
which
quantifies
its
amount
of
integration or irreducibility. Finally note that the exclusion
postulate is applied to the possible cause-effect repertoires 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 (concepts) in the set, as emphasized by the composition
postulate.

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 quale generated by a system
in a bottom up manner, from the set of all its concepts.
Information:
Conceptual
structure
(constellation
of
concepts in concept 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
concepts) matter for consciousness. Figure 10 shows all the
concepts 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 concept, since its integrated information QMax~0
(Figure 10B). All other mechanisms generate non-zero integrated
information and thus specify concepts (Figure 10C). The set of all
concepts of a candidate set constitutes its conceptual structure, which
can be represented in concept space.
Concept space is a high dimensional space, with one axis for
each possible past and future state of the system. In this space,
each concept is symbolized as a point, or ‘‘star’’: its coordinates are
given by the probability of past and future states in its cause-effect
repertoire, and its size is given by its QMax(P,FDs0) value. If QMax is
zero, the concept simply does not exist, and if its QMax is small, it
exists to a minimal amount.
In the case of the candidate set ABC, the dimension of concept
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

Figure 7. A mechanism generates integrated information 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 information both in the past and in
the future. Since it cannot be partitioned without loss, it exists
intrinsically. (C) The mechanism AB generates integrated information in
the past but not in the future. (D) The mechanism AB generates
integrated information in the future but not in the past. In both cases,
the joint mechanism does not exist intrinsically.
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Figure 8. 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 information, QMax, exists intrinsically as the core cause of the
mechanism (or effect when considering the future). In this case, the
core cause is BCc=ABf .
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are plotted separately, with only three axes each (corresponding to
the states at which the concepts have the highest variance in
probability). Therefore the 6 concepts in Figure 10D are displayed
twice, once in the past subspace and once in the future subspace.
In the full 16-dimensional concept space, however, each concept 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 puc,
which corresponds to the ‘‘null’’ concept (a concept that specifies
nothing):

CI(CjABCc~100)~

D((CjABCc~100)Epuc(ABCp,f ))~2:11:
ð10Þ

The distance D from a constellation C to the ‘‘null’’ concept
can be measured using an extension of the EMD (see Text S2),
which can be understood as the cost of transporting the
amount of QMax of each concept from its location in concept
space to puc. CI is thus the sum of the distances between the
cause-effect repertoire of each concept and puc, multiplied by
the concept’s QMax value (Figure 11). Thus, a rich constellation
with many different elementary and higher order concepts
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).

In sum, concepts are considered (metaphorically) as stars in
concept space. The conceptual structure C generated by a set of
mechanisms is thus a constellation of concepts – a particular shape
in concept space spanned by the set’s concepts. The more stars,
the further away they are from the ‘‘null’’ concept, and the larger
their size, the greater the conceptual information CI generated by
the constellation C.
Integration:
Irreducible
conceptual
structure
and
integrated conceptual information (W).
At the system level,
the integration postulate says that only conceptual structures that
are integrated can give rise to consciousness. As for mechanisms,
the integration or irreducibility of the constellation of concepts C
specified by a set of mechanisms can be assessed by partitioning a
set of elements and measuring integrated conceptual information W as
the difference made by the partition (‘‘big phi’’, as opposed to
‘‘small phi’’ Q at the level of mechanisms).
Partitioning at the system level amounts to noising the
connections from one subset S1 of S to its complement S\S1. As
for mechanisms, whether and how much the constellation of
concepts generated by a set of mechanisms is irreducible can be
assessed with respect to the minimum information partition (MIP)
of the set of elements S. This corresponds to the unidirectional
partition that makes the least difference to the constellation of
concepts (in other words, the minimum ‘‘difference’’ partition;
Figure 12). To find the unidirectional MIP, for each subset S1 one
must evaluate both the connections from S1 to S\S1 and the
connections from S\S1 to S1 and take the minimum MIP. This
corresponds, at the level of mechanisms, to finding the minimum

Figure 9. A concept: A mechanism that specifies a maximally irreducible cause-effect repertoire. The core cause and effect of
mechanism A are Ac=BCp and Ac=Bf , respectively. Together, they specify ‘‘what’’ the concept of A is about. The QMax value of the concept specifies
‘‘how much’’ the concept exists intrinsically.
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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 information Q for a mechanism, integrated
conceptual information W for a set of elements is defined as the
distance D between the constellation of the whole set and that of
the partitioned set:

WMIP(CDs0)~D(CECMIP
? ),
ð11Þ

where CMIP
?
denotes the constellation of the unidirectionally
partitioned set of elements.
The extended EMD between the whole and the partitioned
constellation corresponds to the minimal cost of transforming C
into CMIP
?
in concept space. Through the partition, concepts of C
may change location, lose QMax(P,FDs0), or disappear. Their
QMax(P,FDs0) has to be allocated to fill the concepts in CMIP
?
with
an associated cost of transportation that is proportional to the
distance in concept space and the amount of QMax that is moved.
Any residual QMax is transported to the ‘‘null’’ concept (puc) under
the same cost of transportation.
Figure 12 shows the conceptual structure for the candidate
system ABC and its MIP (see Text S2 for a calculation of
WMIP(C(ABC)D100)). In this case, 4 of the 6 concepts of ABC are

lost through the partition; their QMax(P,FDs0) is thus transported to
the location of the ‘‘null’’ concept (puc). Since W is always evaluated
over the MIP, in what follows the superscript MIP is dropped, as it
was for Q.
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
concepts. Therefore, a minimum partition between the two subsets
makes no difference and integrated conceptual information W~0.
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 theory, 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

Figure 10. Information: A conceptual structure C (constellation of concepts) is the set of all concepts 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 concepts
generated by the candidate set. Core causes are plotted on the left, core effects on the right. QMax 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 concepts, with the exception of mechanism AC, which
can be fully reduced QMax(AC~10)~0. (D) The concepts generated by the candidate set plotted in concept 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’’ concept puc is
indicated by the small black crosses in concept space.
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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.
Exclusion: A maximally irreducible conceptual structure
(MICS) specified by a set of elements (a complex).
The
exclusion postulate at the level of systems of mechanisms says that
only a conceptual structure that is maximally irreducible can give
rise to consciousness – other constellations generated by overlap-
ping elements are excluded. A complex is thus defined as a set of
elements within a system that generates a local maximum of
integrated conceptual information WMax (meaning that it has
maximal W as compared to all overlapping sets of elements). Only
a complex exists as an entity from the intrinsic perspective.
Because of exclusion, complexes cannot overlap and at each point
in time, an element/mechanism can belong to one complex only
(complexes
should
be
evaluated
as
maxima
of
integrated
information 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 complex has been identified, concept space can
be called ‘‘qualia space,’’ and the constellation of concepts can be
called a ‘‘quale ‘sensu lato’’’. A quale in the broad sense of the word
is therefore a maximally irreducible conceptual structure (MICS) or,
alternatively, an integrated information structure.
To determine whether an integrated set of elements is a
complex, W 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 W(CDs0) for all possible candidate sets that are subsets
of ABC (AB,AC,BC,ABC) and for one superset (ABCD). The
latter, and all other sets that include elements D, E, or F, have
W = 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

Figure 11. Assessing the conceptual information CI of a conceptual structure (constellation of concepts). CI is quantified by measuring
the distance in concept space between C, the constellation of concepts generated by a set of elements, and puc, the unconstrained past and future
repertoire, which can be termed the ‘‘null’’ concept (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 repertoires
of all concepts and puc, weighted by their QMax values. (A) Therefore, a system with many different elementary and higher order concepts 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 concept and thus has low CI.
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as candidate sets since they cannot be partitioned and thus cannot
be complexes by definition. In this example, the set of elements
ABC generates the highest value of WMax and is therefore the
complex. 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).
Identity
between
an
experience
and
a
maximally
irreducible conceptual structure (MICS or quale ‘‘sensu
lato’’) generated by a complex.
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 structure
(MICS, integrated information structure, or quale ‘‘sensu lato’’) specified by
the mechanisms of a complex in a state. Subsets of elements within the
complex constitute the concepts that make up the MICS. The
maximally irreducible cause-effect repertoire (MICE) of each

concept specifies what the concept is about (what it contributes to
the quality of the experience, i.e. its quale ‘‘sensu stricto’’ (in the
narrow sense of the term)). The value of irreducibility QMax of a
concept specifies how much the concept is present in the
experience. An experience (i.e. consciousness) is thus an intrinsic
property of a complex 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 complex, and that it specifies a MICS
or quale (top right). As before, the constellation of concepts in
qualia space is plotted over 3 representative axes separately for
past and future states of the system. For clarity, the concepts are
also represented as probability distributions over all 16 past and
future states (cause-effect repertoires, bottom right).
The central identity of IIT can also be formulated to express the
classic distinction between level and content of consciousness [26]:
the quantity or level of consciousness corresponds to the WMax

Figure 12. Assessing the integrated conceptual information W of a constellation C. W (‘‘big phi’’) is quantified by measuring the distance C
between the constellation of concepts of the whole set of elements C and that of the partitioned set CMIP
?
, 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 concepts intact (A and B, with zero distance to A and B from constellation C, indicated by the red
stars), while the other concepts 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 repertoires of the destroyed concepts and the ‘‘null’’ concept puc, weighted by their QMax
values (see Text S2).
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value of the quale; the quality or content of the experience
corresponds to the particular constellation of concepts that
constitutes the quale – a particular shape in qualia space. 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 (axioms) of consciousness has been
translated into a set of postulates that the physical mechanisms
generating consciousness 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 conscious-
ness), 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 complex
of physical mechanisms in a certain state is necessarily associated
with its quale.

Results/Discussion

The Models section presented a way of constructing the
experience or quale 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 concepts
introduced above using example systems of mechanisms and the
conceptual structures they generate.

A system may condense into a major complex and
several minor complexes
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 complex because
they lack either inputs or outputs, or both. H and K also cannot
be part of the complex, 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 ABCDEFG cannot form a
complex as a whole, since the subset of elements FG is not
connected to the rest of the system. The subset of elements
ABCDE does generate a small amount of integrated concep-
tual information W and could thus potentially form a complex.
Among the power set of elements ABCDE, however, it is the
smaller subset ABC that generates the local maximum of
WMax. This excludes ABCDE from being a complex, since an
element can participate in only one complex at each point in
time. The remaining elements DE, however, can still form a
minor complex, with lower WMax than ABC. Thus, ABCDE
condenses down to the major complex ABC, the minor
complex DE, and their residual interactions. Finally, FG forms
a minor complex that does not interact with the rest of the
system.
This simple example of ‘‘condensation’’ into major and minor
complexes may be relevant also for much more complicated
systems of interconnected elements. For example, IIT predicts that

Figure 13. A set of elements generates integrated conceptual
information W 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 structure
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.
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Figure 14. A complex: A local maximum of integrated conceptual information W. Integrated conceptual information W 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 complex, the one that generates the maximum amount of integrated conceptual information WMax. In the example system the set
of elements ABC form the complex. Therefore, no subset or superset of ABC can form another complex. Note that all candidate sets that include D, E,
or F are not strongly integrated and thus have W = 0 (only one example is shown).
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in the human brain there should be a dominant ‘‘main’’ complex
of high WMax, constituted of neural elements within the cortical
system, which satisfies the postulates described above and
generates the changing qualia of waking consciousness [12]. The
set of neuronal elements constituting this main complex 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 complex 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 complex in both directions, many
of
these
smaller
systems
may
constitute
minor
complexes
specifying little more than a few concepts, which would qualify
them as ‘‘minimally conscious’’ (see below). In the healthy, adult
human brain the qualia and WMax generated by the dominant
main complex are likely to dwarf those specified by the minimally
conscious minor complexes. In addition to the fully conscious
main complex and minimally conscious minor complexes, there
will be a multitude of unconscious processes mediated by purely
feed-forward systems (see below) or by the residual interactions
between main complex and minor complexes, as in Figure 16.
Under special circumstances, such as after split brain surgery,
the main complex may split into two main complexes, both having
high WMax. There is solid evidence that in such cases consciousness
itself splits in two individual consciousnesses that are unaware of
each other [28]. A similar situation may occur in dissociative and
conversion disorders, where splits of the main complex 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,

Figure 15. A quale: The maximally irreducible conceptual structure (MICS) generated by a complex. An experience is identical with the
constellation of concepts specified by the mechanisms of the complex. The WMax value of the complex corresponds to the quantity of the experience,
the ‘‘shape’’ of the constellation of concepts in qualia space completely specifies the quality of a particular experience and distinguishes it from other
experiences.
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Figure 16. A system can condense into a major complex and
minor complexes that may or may not interact with it. The set of
elements ABC specifies the local maximum of integrated information
WMax and thus forms the major complex of the system. The sets of
elements DE and FG also specify local maxima of integrated information
albeit with lower WMax than the main complex. DE and FG thus form
minor complexes. The set of elements ABCDE is strongly integrated, but
is excluded from forming a complex, since it overlaps with ABC, which is
a local maximum of integrated information. The elements I, J, and L
cannot be part of any complex 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.
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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 complexes separated from the main
one. According to IIT such minor complexes, if endowed with
non-trivial values of WMax, should be considered paraconscious (i.e.
conscious ‘‘on the side’’ of the conscious subject) rather than
unconscious. In principle, the presence of paraconscious minor
complexes 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
complex, or to multiple major complexes that generate
separate consciousnesses. Similar issues apply to systems
composed of non-neural elements, such as ant colonies,
computer architectures, and so on. While determining rigor-
ously how such systems condense in terms of major and minor
complexes, and what kind of MICS they may generate, is not
practically feasible, the predictions of IIT are in principle
testable and should lead to definite answers.

Consciousness and connectivity: Modular,
homogeneous, and specialized networks
Whether a set of elements as a whole constitutes a complex or
decomposes into several complexes depends first of all on the
connectivity among its elementary mechanisms. In Figure 17 we
show the complexes and the associated MICS of three simple
networks,
representative
of
a
modular,
homogeneous,
and
specialized system architecture.
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 complex, 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 complex, because each generates more W
than the whole system, although each module has just two
concepts. The purviews of module AB’s concepts are shown in
Figure 17A (middle), and their representation in qualia space 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 repertoire, their 5 first order (elementary)
concepts are identical. Moreover, there are no higher order
concepts, since combining elements yields nothing above the
elementary mechanisms. In qualia space, the 5 identical concepts
are concentrated on a single point (Figure 17B, bottom).
Accordingly, the homogeneous network has a low value of CI
and WMax.
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
concept specifies a different cause-effect repertoire. For the same
reason, there are many higher order concepts (all but the highest
order concept of the power set). The specialized network thus gives

rise to a rich constellation in qualia space (Figure 17C, bottom)
with a high value of CI and WMax.
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 WMax if its architecture
is primarily modular, is potentially consistent with neuropsy-
chological 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 consciousness 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 consciousness, 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 organi-
zation that yields a comparatively high value of WMax 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
connectivity is unchanged, functional and effective connectiv-
ity
become
virtually
homogeneous
[39,40].
Under
such
conditions, consciousness invariably fades [14]. The examples
of Figure 17B and C also suggest that both the richness of
concepts and the level of consciousness should increase with
the refinement of cortical connections during neural develop-
ment and the associate increase in functional specialization
(e.g. [41]).

Consciousness and activity: Inactive systems can be
conscious
The conceptual structure generated by a complex depends not
only on the connectivity among its elements and the input/output
function they perform, but also on their current state. An
important corollary of IIT is that both active and inactive
elements can contribute to its conceptual structure. Moreover,
high-order concepts 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 complex and
specify a MICS 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 A~0 specifies an irreducible cause (D had to
be off at t{1) and an irreducible effect (B will be on at tz1)
within the complex. Thus, IIT predicts that, even if all the
neurons in a main complex were inactive (or active at a low
baseline rate), they would still generate consciousness 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 consciousness
if they are active in such a way that they can ‘‘signal’’ or

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‘‘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 MICS that is specified by a
complex.
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 complex 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 complex and gives rise to a MICS at time t0. Thus,
according to IIT, the activation or deactivation of a neuron (over
the time scale at which integrated information reaches a maximum
[20]) can modify an experience as long as it affects the shape of the
MICS specified by the complex 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
MICS. Taking into account the axioms and postulates of IIT, we

Figure 17. Qualia generated by modular, homogeneous and specialized networks. (A) The modular network decomposes into three small
complexes and their residual interactions. (B) The homogenous system forms a complex, but it has low WMax and only 5 identical concepts. (C) The
specialized network also forms a complex, with all but one concepts of its power set and a high WMax value. In the middle row, the respective
concepts of each system are listed. The bottom row shows the constellation of the respective complexes in qualia space (projected into 3 dimensions
for the past and the future subspaces).
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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.
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
repertoires
are
maximally
irreducible,
and
the
conceptual
structure specified by the two elements is also maximally
irreducible. Consequently, the system DP~11 forms a complex
that gives rise to a MICS, albeit one having just two concepts and
a WMax 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 photodiode. 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 space 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 MICS
(Figure 19D) and thus the same minimal experience. More-
over, the symmetry of the MICS implies that the quality of the
experience would be the same regardless of the system’s state:
the photodiode in state DP~00, 01, or 10, receiving one
external input, generates exactly the same MICS as DP~11.
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 concepts and break the symme-
tries in the shape of the MICS can generate additional
meaning. Ultimately, only a set of concepts comparable to
that of our main complex 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].

Complex systems can be unconscious: A ‘‘zombie’’ feed-
forward network
Another corollary of IIT is that certain structures do not give
rise to consciousness 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 complex, and generates no quale.
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
connectivity (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 complex. 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
quale. Therefore, systems with a purely feed-forward architecture
cannot generate consciousness.
The idea that ‘‘feed-back’’, ‘‘reentry’’, or ‘‘recursion’’ of some
kind may be an essential ingredient of consciousness 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 consciousness [46]. Moreover, several
recent studies indicate that an impairment of reentrant interac-
tions over feed-back connections is associated with loss of
consciousness during anesthesia [47–49] and in brain-damaged

Figure 18. Quale 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 complex and specifies a MICS. Moreover, an
element can contribute to experience as long as it affects the shape of the MICS, 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 MICS that is specified by
a complex.
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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 consciousness [51]. IIT offers some

specific insights with respect to these issues. First, the need for
reciprocal interactions within a complex is not merely an empirical
observation, but it has theoretical validity because it is derived
directly from the phenomenological axiom of (strong) integration.
Second, (strong) integration is by no means the only requirement
for consciousness, but must be complemented by information and
exclusion. Third, for IIT it is the potential for interactions among
the parts of a complex that matters and not the actual occurrence
of ‘‘feed-back’’ or ‘‘reentrant’’ signaling, as is usually assumed. As
was discussed above, a complex 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 complexes and unconscious ‘‘zombie’’
systems can be functionally equivalent
The last section showed that according to IIT feed-forward
systems cannot give rise to a quale. However, without restrictions
on the number of nodes, feed-forward networks 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 network that produces the
same input-output behavior over at least 4 time steps (94 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

Figure 19. Quantity and quality of experience of a ‘‘minimally conscious’’ photodiode. (A) The minimally conscious photodiode 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 MICS specified by the minimally conscious photodiode. D and P both specify a first order concept about the other element. (D)
A minimally conscious thermistor or a minimally conscious blue detector with the same internal mechanisms as the minimally conscious photodiode
generate the same MICS and therefore have the same minimal experience.
doi:10.1371/journal.pcbi.1003588.g019

Figure 20. Feed-forward ‘‘zombie’’ systems do not generate
consciousness. (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 complex
and generate no quale. (B) Even complicated systems cannot form a
complex 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
complex and it remains unconscious, just like the unconscious
photodiode DO.
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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 complex with WMax.0 in every state, and
would therefore be conscious, the feed-forward system does not
constitute a complex and is thus unconscious.
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 consciousness. Behavior and reportability can be
reliable guides under ordinary conditions (typically adult awake
humans) and can be employed to evaluate neural correlates of
consciousness [9] and to validate theoretical constructs [14].
However, behavior and reportability become problematic for
evaluating
consciousness
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 consciousness 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 complex
functions, there is an evident evolutionary advantage towards the

Figure 21. Functionally equivalent conscious and unconscious systems. (A) A strongly integrated system gives rise to a complex in every
network state. In the depicted state (yellow: 1, white: 0), elements ABDHIJ form a complex with WMax = 0.76 and 17 concepts. (B) Given many more
elements and connections, it is possible to construct a feed-forward network 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 (t%Dt) to compensate for the additional layers (A1,A2,B1,B2). Despite the functional equivalence, the feed-
forward system is unconscious, a ‘‘zombie’’ without phenomenological experience, since its elements do not form a complex.
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selection of integrated architectures that can perform the same
functions consciously. Among the benefits of integrated architec-
tures 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 network 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 concepts within a complex are self-generated, self-
referential, and holistic
The final example (Figure 22A) considers a simple percep-
tual system – a recurrent segment/dot system. The segment/
dot system consists of 10 heavily interconnected elements
that, in their current state, form a complex (Figure 22A,
blue circle). Elements A,B, and C are the ports-in of the
complex: they each receive 2 inputs from an external source in
addition
to
feed-back
inputs
from
within
the
complex.
Elements F and J are the ports-out of the complex: they
output to the external elements O1 and O2, respectively, in
addition to their outputs within the complex. 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 complex are excitatory (+1, black) or
inhibitory (21, red).
The elementary mechanisms comprising the segment/dot
system have specialized functions and generate elementary
concepts. In the segment/dot system, the concepts of mech-
anisms in the ‘‘off’’ state (0) tend to have lower QMax 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 concepts, the segment-dot system gives
rise to many higher order concepts. Dependent on the state of
the system, certain higher order concepts may or may not exist.
For instance, in the current state of the segment/dot system,
the second order concept DI exists, while EG does not because
it is reducible (QMax~0). 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 neurosci-
entist recording the activity of ‘‘neurons’’ A{J), 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 complex.
From the intrinsic perspective of the system, instead, the
function of each mechanism is given by its concept. Each
concept is self-generated, because it must be specified exclusively
by a subset of elements belonging to the complex. It is also self-
referential, because its cause-effect repertoire refers exclusively

to elements within the complex, and therefore only indirectly
to external inputs. For example, the concept of D, in its current
state 1, is about the purview D=ABEFJp,Af . From the intrinsic
perspective, the function of D~1 is thus to constrain the
possible past states of A,B,E,F and J, and to constrain the
possible future state of A (Figure 22C). Therefore, D = 1
specifies a concept that is exclusively self-referential to the
complex 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 concept’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 D~1
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 concept of D~1 additionally
takes into account the internal context E,F,J (blue shaded
states in Figure 22C). However, the correspondence between
intrinsic and extrinsic perspective breaks down for the ports-in
A,B,C: even though their state is partly determined by the
external inputs, their concept 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 concepts specified by
ports-in may have some implications with respect to the role of
primary areas in consciousness. 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 consciousness, 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 complex. Under this assumption, V1 units would
have to specify concepts about other units in the complex –
either other V1 units or units in higher areas – rather than
about their feed-forward inputs, which would remain outside
the complex. V1 concepts could relate for example to Gestalt
properties such as spatial continuity, rather than to oriented
bars. In that case, what V1 contributes to consciousness during
binocular rivalry – namely spatial continuity – would not
change substantially between the two rivalrous percepts.
Instead, concepts 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 consciousness not only by generating their own
concepts (such as spatial continuity), but also by providing the
cause repertoire for concepts 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 consciousness [63,64].
The self-referential nature of concepts within a complex has
implications with respect to how concepts 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

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the intrinsic perspective of the complex, 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 repertoires of multiple
concepts within a MICS (such as that of element F interlocked
with those of elements D, E, and so on). In this view, the
meaning of a concept depends on the context provided by the
entire MICS to which it belongs, and corresponds to how it
constrains the overall ‘‘shape’’ of the MICS. Meaning is thus
both
self-referential
(internalistic)
and
holistic.
A
proper
treatment of how the conceptual structure of a complex 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 concepts and
meaning,
IIT
naturally
recognizes
that
in
the
end
most
concepts 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
concepts 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 concepts within the MICS will be ‘‘on’’ or ‘‘off’’,

and their meaning will be defined entirely within the quale. 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 consciousness – the
phenomenological axioms – and translates them into postulates
that lay out how a system of mechanisms must be constructed
to satisfy those axioms and thus generate consciousness. 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,

Figure 22. A complex 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 21). A,B and C are the ports-in of the complex. They receive external
inputs of strength 0, 1, or 2. Elements F and J are the ports-out of the complex. They output to the external elements O1 and O2. The current state of
the system corresponds to a sustained input with value 2-2-0. From an extrinsic perspective, the different layers of the complex 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 concepts and many higher order
concepts exist. (C) Both, elementary mechanisms that are ‘‘on’’ (1) and those that are ‘‘off’’ (0) constitute concepts. Note that the cause repertoire of
D~1 is the mirror image of the cause repertoire of E~0 (highlighted in blue). (C,D,E) From the intrinsic perspective, the function of a mechanism is
given by its cause-effect repertoire. The purview of a concept can only contain elements within the complex. The concepts that constitute the MICS
generated by the complex are self-generated (specified exclusively by elements belonging to the complex); self-referential (specified exclusively over
elements belonging to the complex); and holistic (their meaning is constructed in the context of the other concepts in the MICS).
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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 perturba-
tions of brain states using naturalistic stimuli such as movies
can
provide
useful
approximations.
Also,
circumscribed
regions of the cerebral cortex could be perturbed systemati-
cally using optogenetic methods coupled with calcium imaging.
Moreover, discrete, analytically tractable brain models based
on neuroanatomical connectivity such as [68] could provide a
suitable approximation of large-scale neural mechanisms yet
permit the rigorous measurement of integrated information. iii)
Variables recorded in most neurophysiological experiments
may not correspond to the spatial and temporal grain at which
integrated information 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 WMax exhaustively, all possible
partitions
of
every
mechanism
and
of
every
system
of
mechanisms should be evaluated, which leads to a combina-
torial explosion, not to mention that the analysis should be
performed at every spatio-temporal grain. For these reasons,
the primary aim of IIT 3.0 is simply to begin characterizing, in
a self-consistent and explicit manner, the fundamental prop-
erties of consciousness 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 theory
[14,69]. Deriving bounded approximations to the explicit
formalism of IIT 3.0 is also crucial for establishing in more
complex 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 MICS 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 grain 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 information reaches a maximum [20]. In terms of
integrated information, 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
complex (it is self-generated and self-referential), we did not
discuss in any detail how meaning originates through the
nesting of concepts within MICS (its holistic nature). iv) In IIT,
the relationship between the MICS generated by a complex 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 MICS 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 consciousness, will be investigated in
future work, both by evolving simulated agents in virtual
environments (‘‘animats’’ [71–73]), and through neurophysio-
logical experiments. v) IIT 3.0 explicitly treats integrated
information 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 consciousness is a local maximum of causal
power. Hence, if having causal power is a requirement
for existence, then consciousness is maximally real. More-
over, 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

Figure S1
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
S1S2 and four weak inputs W1W2W3W4. The core cause is
Ac=S1Sp
2 with QMax
cause~0:44 (in the case of identical QMax
cause 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
Ac=S1{2W1{4), but the subset that is most affected by a partition.
(PDF)

Text S1
Main differences between IIT 3.0 and earlier versions.
(PDF)

Text S2
Supplementary methods.
(PDF)

Text S3
Some differences between integrated information and
Shannon information.
(PDF)

Acknowledgments

We thank Chiara Cirelli, Lice Ghilardi, Melanie Boly, Christof Koch, and
Marcello Massimini for many invaluable discussions concerning the
concepts 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 concept of synergy and its
relation to integrated information; 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
structures we are indebted to B. Shababo, A. Nere, A. Hashmi, U. Olcese,
and P. Rana.

Author Contributions

Conceived and designed the experiments: GT MO LA. Performed the
experiments: MO LA. Analyzed the data: MO LA. Wrote the paper: MO
LA GT.

References

1. Le QV, Ranzato MA, Monga R, Devin M, Chen K, et al. (2011) Building high-
level features using large scale unsupervised learning. In: ICML2012.
2. The DeepQA Research Team (2013) Available: http://researcher.ibm.com/
researcher/view_project.php?id = 2099. Accessed October 21, 2013.
3. Thompson C (2010) Smarter Than You Think – I.B.M.s Supercomputer to
Challenge Jeopardy! Champions. N Y Times Mag.

4. Tononi G (2004) An information integration theory of consciousness. BMC
Neurosci 5: 42.
5. Tononi G (2008) Consciousness as integrated information: a provisional
manifesto. Biol Bull 215: 216–242.
6. Tononi G (2012) Integrated information theory of consciousness: an updated
account. Arch Ital Biol 150: 56–90.

Integrated Information Theory 3.0

PLOS Computational Biology | www.ploscompbiol.org
24
May 2014 | Volume 10 | Issue 5 | e1003588


7. Baars BJ (1988) A Cognitive Theory of Consciousness (Cambridge University
Press).
8. Crick F, Koch C (2003) A framework for consciousness. Nat Neurosci 6: 119–
126.
9. Koch C (2004) The Quest for Consciousness: A Neurobiological Approach
(Roberts and Co.).
10. Dehaene S, Changeux JP (2011) Experimental and theoretical approaches to
conscious processing. Neuron 70: 20027.
11. Chalmers DJ (1996) The Conscious Mind: In Search of a Fundamental Theory
(Oxford University Press).
12. Tononi G, Koch C (2008) The neural correlates of consciousness: an update.
Ann N Y Acad Sci 1124: 239–61.
13. Tononi G, Laureys S (2009) The neurology of consciousness: an overview. The
neurology of con-sciousness, 375–412.
14. Casali AG, Gosseries O, Rosanova M, Boly M, Sarasso S, et al. (2013) A
theoretically based index of consciousness independent of sensory processing and
behavior. Science translational medicine 5(198): 198ra105–198ra105.
15. King JR, Sitt JD, Faugeras F, Rohaut B, El Karoui I, et al. (2013) Information
sharing in the brain indexes consciousness in noncommunicative patients. Curr
Biol 23:19149.
16. Tononi G (2001) Information measures for conscious experience. Arch Ital Biol
139:367–71.
17. Balduzzi D, Tononi G (2008) Integrated information in discrete dynamical
systems: Motivation and theoretical framework. PLoS Comput Biol 4: e1000091.
18. Balduzzi D, Tononi G (2009) Qualia: the geometry of integrated information.
PLoS Comput Biol 5: e1000462.
19. Ascoli G (2013) The Mind-Brain Relationship as a Mathematical Problem.
ISRN Neurosci 2013:113.
20. Hoel E, Albantakis L, Tononi G (2013) Quantifying causal emergence shows
that ‘‘macro’’ can beat ‘‘micro’’. Proc Natl Acad Sci [epub ahead of print]
doi:10.1073/pnas.1314922110.
21. Ay N, Polani D (2008) Information Flows in Causal Networks. Adv Complex
Syst 11:1741.
22. Korb KB, Nyberg EP, Hope L (2011) in Causality in the Sciences (Oxford
University Press, Oxford).
23. Griffith V, Koch C (2012) Quantifying synergistic mutual information. arXiv
preprint arXiv:1205.4265.
24. Rubner Y, Tomasi C, Guibas L (2000) The earth movers distance as a metric for
image retrieval. Int J Comput Vis: 40(2), 99–121.
25. Wilson RJ (1985) Introduction to Graph Theory, 3/e (Longman Scientific &
Technical).
26. Plum F, Posner JB (1982) The Diagnosis of Stupor and Coma (Oxford
University Press).
27. Tononi G, Edelman GM (1998) Consciousness and complexity. Science 282:
1846–1851.
28. Gazzaniga MS (2005) Forty-five years of split-brain research and still going
strong. Nat Rev Neurosci 6:6539.
29. Lynn S, Rhue J (1994) Dissociation: Clinical and theoretical perspectives
(Guilford Press).
30. Mudrik L, Breska A, Lamy D, Deouell LY (2011) Integration without awareness:
expanding the limits of unconscious processing. Psychol Sci 22: 76470.
31. Mudrik L, Faivre N, Koch S (2014) Information integration in the absence of
awareness. Trends in Cognitive Sciences, in press.
32. Glickstein M (2007) What does the cerebellum really do? Curr Biol
17:R824R827.
33. Schmahmann JD, Weilburg JB, Sherman JC (2007) The neuropsychiatry of the
cerebellum –insights from the clinic. Cerebellum 6:25467.
34. Boyd CAR (2010) Cerebellar agenesis revisited. Brain 133:9414.
35. Cohen D (1998) Patches of synchronized activity in the cerebellar cortex evoked
by mossy-fiber stimulation: Questioning the role of parallel fibers. Proc Natl
Acad Sci 95:1503215036.
36. Bower JM (2002) The Organization of Cerebellar Cortical Circuitry Revisited.
Implications for Function. Ann N Y Acad Sci 978:135155.
37. Sporns O (2010) Networks of the Brain (MIT Press).
38. van den Heuvel MP, Sporns O (2013) An anatomical substrate for integration
among functional networks in human cortex. J Neurosci 33:14489500.
39. Massimini M, Ferrarelli F, Huber R, Esser SK, Singh H, et al. (2005)
Breakdown of cortical effective connectivity during sleep. Science 309:222832.
40. Ferrarelli F, Massimini M, Sarasso S, Casali A, Riedner BA, et al. (2010)
Breakdown in cortical effective connectivity during midazolam-induced loss of
consciousness. Proc Natl Acad Sci U S A 107:26816.
41. Sanes DH, Reh TA, Harris WA (2011) Development of the Nervous System
(Academic Press).

42. Sullivan PR (1995) Contentless Consciousness and Information-Processing
Theories of Mind. Philos Psychiatry, Psychol 2:5159.
43. Edelman GM (1989) The Remembered Present: A Biological Theory of
Consciousness (Basic Books).
44. Harth E (1993) The creative loop: How the brain makes a mind (Addison-
Wesley, Reading, MA).
45. Hofstadter DR (2007) I Am a Strange Loop (Basic Books).
46. Lamme VAF (2003) Why visual attention and awareness are different. Trends
Cogn Sci 7:1218.
47. Imas OA, Ropella KM,Ward BD,Wood JD, Hudetz AG (2005) Volatile
anesthetics disrupt frontal-posterior recurrent information transfer at gamma
frequencies in rat. Neurosci Lett 387:145150.
48. Boly M, Moran R, MurphyM, Boveroux P, Bruno MA, et al. (2012)
Connectivity changes underlying spectral EEG changes during propofol-induced
loss of consciousness. J Neurosci 32:708290.
49. Mashour GA (2013) Cognitive unbinding: A neuroscientific paradigm of general
anesthesia and related states of unconsciousness. Neurosci Biobehav Rev.
50. Boly M, Garrido MI, Gosseries O, Bruno MA, Boveroux P, et al. (2011)
Preserved feedforward but impaired top-down processes in the vegetative state.
Science 332:85862.
51. Koch C, Crick F (2001) The zombie within. Nature 411: 893.
52. Cybenko G (1989) Approximation by superpositions of a sigmoidal function.
Math Control Signals Syst 2: 303–314.
53. Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks
are universal approx-imators. Neural Networks 2: 359–366.
54. Rumelhart D, Hinton G, Williams R (1986) Learning internal representations by
error propagation, Parallel distributed processing, 1986. Cambridge, MA.
55. Goldman M (2009) Memory without feedback in a neural network. Neuron 61:
499–501.
56. Dalal N, Triggs B (2005) In: IEEE Computer Society Conference on Computer
Vision and Pattern Recognition; 25–25 June 2005; San Diego, CA, United
States. CVPR 2005. Available: http://ieeexplore.ieee.org/stamp/stamp.
jsp?tp = & arnumber = 1467360. Accessed 17 March 2014.
57. Serre T, Wolf L, Bileschi S, Riesenhuber M, Poggio T (2007) Robust object
recognition with cortex-like mechanisms. IEEE Trans Pattern Anal Mach Intell
29:41126.
58. Sung K-K, Poggio T (1998) Example-based learning for view-based human face
detection. IEEE Trans Pattern Anal Mach Intell 20:3951.
59. Zhao W, Chellappa R, Phillips PJ, Rosenfeld A (2003) Face recognition. ACM
Comput Surv 35:399458.
60. Poggio T, Ullman S (2013) Vision: are models of object recognition catching up
with the brain? Ann N Y Acad Sci 1305:72–82
61. Crick F, Koch C (1995) Are we aware of neural activity in primary visual cortex?
Nature 375: 121123.
62. Blake R, Logothetis NK (2002) Visual competition. Nat Rev Neurosci 3: 1321.
63. Tong F (2003) Primary visual cortex and visual awareness. Nat Rev Neurosci
4:21929.
64. Pollen DA (2008) Fundamental requirements for primary visual perception.
Cereb Cortex 18:19918.
65. Tononi G, Sporns O, Edelman GM (1996) A complexity measure for selective
matching of signals by the brain. Proc Natl Acad Sci U S A 93:34223427.
66. Friston K, Kiebel S (2009) Predictive coding under the free-energy principle.
Philos Trans R Soc Lond B Biol Sci 364:121121.
67. Friston K (2010) The free-energy principle: a unified brain theory? Nat Rev
Neurosci 11:12738.
68. Deco G, Senden M, Jirsa V (2012) How anatomy shapes dynamics: a semi-
analytical study of the brain at rest by a simple spin model. Front Comput
Neurosci 6:68.
69. Barrett AB, Seth AK (2011) Practical measures of integrated information for
time-series data. PLoS Comput Biol 7:e1001052.
70. Hashmi A, Nere A, Tononi G (2013) Sleep-Dependent Synaptic Down-
Selection (II): Single-Neuron Level Benefits for Matching, Selectivity, and
Specificity. Front Neurol 4:148.
71. Albantakis L, Hintze A, Koch C, Adami C, Tononi G (2013) Information
Matching – Environment dependent increase in integrated information (W).
European Conference on Complex Systems (ECCS13).
72. Edlund JA, Chaumont N, Hintze A, Koch C, Tononi G, et al. (2011) Integrated
information increases with fitness in the evolution of animats. PLoS Comput Biol
7:e1002236.
73. Joshi NJ, Tononi G, Koch C (2013) The minimal complexity of adapting agents
increases with fitness. PLoS Comput Biol 9:e1003111.

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May 2014 | Volume 10 | Issue 5 | e1003588