Integrated information theory (IIT) proposes a mathematical model for the consciousness of a system. It comprises a framework ultimately intended to explain why some physical systems (such as human brains) are conscious, and to be capable of providing a concrete inference about whether any physical system is conscious, to what degree, and what particular experience it has; why they feel the particular way they do in particular states (e.g. why our visual field appears extended when we gaze out at the night sky), and what it would take for other physical systems to be conscious (Are other animals conscious? Might the whole universe be?). The theory inspired the development of new clinical techniques to empirically assess consciousness in unresponsive patients.
According to IIT, integrated information (Φ) corresponds to the quantity of consciousness. That is, a system's consciousness (what it is like subjectively) is conjectured to be mathematically described by the system's causal structure (what it is like objectively). Therefore, it should be possible to account for the conscious experience of a physical system by unfolding its complete causal powers.
IIT was proposed by neuroscientist Giulio Tononi in 2004. Despite significant interest, IIT remains controversial. In 2023, a number of scholars characterized it as unfalsifiable pseudoscience for lacking sufficient empirical support, a claim reiterated in a 2025 Nature Neuroscience commentary. A survey of researchers in the field found only a small minority fully endorsing the "pseudoscience" label. Other researchers have defended the theory in response.
Overview
Relationship to the "hard problem of consciousness" David Chalmers has argued that any attempt to explain consciousness in purely physical terms (i.e., to start with the laws of physics as they are currently formulated and derive the necessary and inevitable existence of consciousness) eventually runs into the so-called "hard problem". Rather than try to start from physical principles and arrive at consciousness, IIT "starts with consciousness" (accepts the existence of our own consciousness as certain) and reasons about the properties that a postulated physical substrate would need to have in order to account for it. The ability to perform this jump from phenomenology to mechanism rests on IIT's assumption that if the formal properties of a conscious experience can be fully accounted for by an underlying physical system, then the properties of the physical system must be constrained by the properties of the experience. The limitations on the physical system for consciousness to exist are unknown and consciousness may exist on a spectrum, as implied by studies involving split-brain patients and conscious patients with large amounts of brain matter missing.
IIT aims to explain which physical systems are conscious, to what degree, and in what way. The theory begins from the phenomenological certainty that experience exists, and infers necessary physical postulates that any conscious substrate must satisfy. Specifically, IIT moves from phenomenology to mechanism by attempting to identify the essential properties of conscious experience (dubbed "axioms") and, from there, the essential properties of conscious physical systems (dubbed "postulates").
IIT is grounded in:
Realism – something exists, and persists, independently of one's own experience (a better hypothesis than solipsism) Operational physicalism – what exists is assessed operationally, by observing and manipulating a substrate's units to establish that they can reliably "take and make a difference"; this cause–effect power is the signature of physical existence Operational reductionism ("atomism") – what exists physically should ideally be accounted for in terms of the smallest units that can be observed and manipulated, so that cause–effect power holds "all the way down" to the atomic units
Axioms and postulates Starting from the zeroth axiom (experience exists), IIT identifies five essential properties of experience:
Intrinsicality – experience is intrinsic: it exists for itself Information – experience is specific: it is this one Integration – experience is unitary: it is a whole, irreducible to separate experiences Exclusion – experience is definite: it is this whole Composition – experience is structured: it is composed of distinctions and the relations that bind them together, yielding a phenomenal structure that feels the way it feels
Each axiom is formulated as a corresponding physical postulate that the substrate of consciousness must satisfy, expressed in terms of cause–effect power:
Intrinsicality – its cause–effect power must be intrinsic: it must take and make a difference within itself Information – its cause–effect power must be specific: it must be in this state and select this cause–effect state, the one with maximal intrinsic information (ii) Integration – its cause–effect power must be unitary: it must specify its cause–effect state as a whole set of units, irreducible to separate subsets of units; irreducibility is measured by integrated information (φs) over the substrate's minimum partition Exclusion – its cause–effect power must be definite: it must specify its cause–effect state as this whole set of units, namely the set that is maximally irreducible (maximum φs, φ*), called a maximal substrate or complex Composition – its cause–effect power must be structured: subsets of its units must specify cause–effect states over subsets of units (distinctions) that can overlap with one another (relations), yielding a cause–effect structure or Φ-structure
Mathematical formalism A system is described by its transition probability matrix (TPM), denoted , over all its possible states. The formalism proceeds in two stages: first identifying the maximally irreducible set of units (the complex), then unfolding its cause–effect structure. From this, IIT defines:
Intrinsic information (ii) measures how much a state constrains a cause/effect state , capturing both selectivity and informativeness. It is evaluated relative to the unconstrained probability using the intrinsic difference measure, and the relevant state is the one that maximizes this quantity:
Intrinsic information is computed using the intrinsic difference (ID), which IIT 4.0 identifies as the unique measure of the difference between two probability distributions that satisfies the properties of causality, intrinsicality, and specificity required by the postulates. It is evaluated separately on the cause side () and the effect side ().
System integrated information () as the irreducibility of the system's cause–effect power over itself. It is measured over the directional minimum partition (MIP)—the partition, cutting the inputs and/or outputs of each part, that makes the least difference—and, by the principle of minimal existence, is taken as the minimum of the irreducibility on the cause side () and the effect side ():
Complexes (maximal substrates) are the sets of units whose system integrated information is maximal relative to all overlapping candidate systems—whether subsets, supersets, or partially overlapping sets—in accordance with the exclusion postulate. A complex's distinctions are its subsets of units (mechanisms) that specify a maximally irreducible cause and effect state over subsets of units (purviews), each with an associated irreducibility . Relations are the congruent overlaps among the cause and/or effect states of these distinctions, each with an associated irreducibility . Together, distinctions and relations compose the cause–effect structure, or -structure, of the complex:
The structure integrated information ("big phi") corresponds to the quantity of consciousness, while the particular structure of distinctions and relations defines its quality.
Explanatory identity IIT proposes an explanatory identity: an experience is identical to the cause–effect structure (Φ-structure) unfolded from a complex (maximal substrate) in its current state, such that every property of the experience is accounted for by a corresponding property of the Φ-structure, with no additional ingredients. The identity is meant to be explanatory rather than ontologically reductive: IIT does not claim that experience "arises from" or is "nothing but" a Φ-structure, but that the properties of an experience can be accounted for, in objective and physical terms, by those of a substrate that can be observed and manipulated.
Contents of experience Beyond accounting for the quantity of consciousness (Φ), IIT aims to account for its quality—specific contents of experience, such as colours and shapes, sounds, the spatial extendedness of the visual field and the feeling of time flowing. On the theory's central claim that the explanatory identity extends to phenomenal quality, every property of an experience must be accounted for by a corresponding property of the cause–effect structure (Φ-structure) unfolded by the substrate, together with its sub-structures. In summary, IIT holds that "all quality is structure".
Research within the programme has so far concentrated on two especially pervasive modes of experience that are relatively accessible to introspection: the extendedness of space and the flow of time. The account of spatial experience holds that for the "canvas" of space to feel extended, it must be composed of many phenomenal distinctions ("spots"), each of which overlaps itself (reflexivity), related to one another through inclusion, connection, and fusion. IIT shows that a substrate of units with grid-like connectivity specifies a cause–effect structure whose distinctions and relations reproduce these properties — it is that structure, rather than the connectivity as such, that accounts for the way space feels — and predicts that spatial experience is supported by brain regions with grid-like connectivity. The account of temporal experience applies the same principles to directed grids: the conscious present feels flowing because it is composed of phenomenal distinctions ("moments") that are directed — pointing away from themselves, where spots point to themselves — and related through directed inclusion, connection, and fusion, so that time is understood not as a process in clock time but as a structure specified by the substrate's current state, extending between the now and the then. IIT proposes that accounts of further contents can be pursued in the same manner: objects, understood as the binding of a general concept with a particular configuration of features within a hierarchy, and narrow qualia such as hues.
Extensions The calculation of even a modestly-sized system's is often computationally intractable, so efforts have been made to develop heuristic or proxy measures of integrated information. For example, Masafumi Oizumi and colleagues have developed both and geometric integrated information or , which are practical approximations for integrated information. These are related to proxy measures developed earlier by Anil Seth and Adam Barrett. However, none of these proxy measures have a mathematically proven relationship to the actual value, which complicates the interpretation of analyses that use them. They can give qualitatively different results even for very small systems.
In 2021, Angus Leung and colleagues published a direct application of IIT's mathematical formalism to neural data. To circumvent the computational challenges associated with larger datasets, the authors focused on neuronal population activity in the fly. The study showed that can readily be computed for smaller sets of neural data. Moreover, matching IIT's predictions, was significantly decreased when the animals underwent general anesthesia.