Integrated information theory

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 consciousness as certain) and reasons about the properties that a postulated physical substrate would have 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 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.

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").

Axioms: essential properties of experience

The axioms are intended to capture the essential aspects of every conscious experience. Every axiom should apply to every possible experience.

The wording of the axioms has changed slightly as the theory has developed, and the most recent and complete statement of the axioms is as follows:

Postulates: properties required of the physical substrate

The axioms describe regularities in conscious experience, and IIT seeks to explain these regularities. What could account for the fact that every experience exists, is structured, is differentiated, is unified, and is definite? IIT argues that the existence of an underlying causal system with these same properties offers the most parsimonious explanation. Thus a physical system, if conscious, is so by virtue of its causal properties.

The properties required of a conscious physical substrate are called the "postulates," since the existence of the physical substrate is itself only postulated (remember, IIT maintains that the only thing one can be sure of is the existence of one's own consciousness). In what follows, a "physical system" is taken to be a set of elements, each with two or more internal states, inputs that influence that state, and outputs that are influenced by that state (neurons or logic gates are the natural examples). Given this definition of "physical system", the postulates are:

Mathematics: formalization of the postulates

For a complete and thorough account of the mathematical formalization of IIT, see. What follows is intended as a brief summary, adapted from, of the most important quantities involved. Pseudocode for the algorithms used to calculate these quantities can be found at.

A system refers to a set of elements, each with two or more internal states, inputs that influence that state, and outputs that are influenced by that state. A mechanism refers to a subset of system elements. The mechanism-level quantities below are used to assess the integration of any given mechanism, and the system-level quantities are used to assess the integration of sets of mechanisms ("sets of sets").

In order to apply the IIT formalism to a system, its full transition probability matrix (TPM) must be known. The TPM specifies the probability with which any state of a system transitions to any other system state. Each of the following quantities is calculated in a bottom-up manner from the system's TPM.

Cause-effect space

For a system of N simple binary elements, cause-effect space is formed by 2 × 2 N axes, one for each possible past and future state of the system. Any cause-effect repertoire R , which specifies the probability of each possible past and future state of the system, can be easily plotted as a point in this high-dimensional space: The position of this point along each axis is given by the probability of that state as specified by R . If a point is also taken to have a scalar magnitude (which can be informally thought of as the point's "size", for example), then it can easily represent a concept: The concept's cause-effect repertoire specifies the location of the point in cause-effect space, and the concept's φ Max value specifies that point's magnitude.

In this way, a conceptual structure C can be plotted as a constellation of points in cause-effect space. Each point is called a star, and each star's magnitude ( φ Max ) is its size.

Central Identity

IIT addresses the mind-body problem by proposing an identity between phenomenological properties of experience and causal properties of physical systems: The conceptual structure specified by a complex of elements in a state is identical to its experience.

Specifically, the form of the conceptual structure in cause-effect space completely specifies the quality of the experience, while the irreducibility Φ Max of the conceptual structure specifies the level to which it exists (i.e., the complex's level of consciousness). The maximally irreducible cause-effect repertoire of each concept within a conceptual structure specifies what the concept contributes to the quality of the experience, while its irreducibility φ Max specifies how much the concept is present in the experience.

According to IIT, an experience is thus an intrinsic property of a complex of mechanisms in a state.

Extensions

The calculation of even a modestly-sized system's Φ Max is often computationally intractable, so efforts have been made to develop heuristic or proxy measures of integrated information. For example, Masafumi Oizumi has developed Φ ∗ , a practical approximation for integrated information that solves the theoretical shortcomings of previously proposed proxy measures, such as the one proposed by Adam Barrett.

A significant computational challenge in calculating integrated information is finding the Minimum Information Partition of a neural system, which requires iterating through all possible network partitions. To solve this problem, Daniel Toker has suggested using the most modular decomposition of a network as an extremely quick proxy for the Minimum Information Partition.

Related Experimental Work

While the algorithm for assessing a system's Φ Max and conceptual structure is relatively straightforward, its high time complexity makes it computationally intractable for many systems of interest. Heuristics and approximations can sometimes be used to provide ballpark estimates of a complex system's integrated information, but precise calculations are often impossible. These computational challenges, combined with the already difficult task of reliably and accurately assessing consciousness under experimental conditions, make testing many of the theory's predictions difficult.

Despite these challenges, researchers have attempted to use measures of information integration and differentiation to assess levels of consciousness in a variety of subjects. For instance, a recent study using a less computationally-intensive proxy for Φ Max was able to reliably discriminate between varying levels of consciousness in wakeful, sleeping (dreaming vs. non-dreaming), anesthetized, and comatose (vegetative vs. minimally-conscious vs. locked-in) individuals.

IIT also makes several predictions which fit well with existing experimental evidence, and can be used to explain some counterintuitive findings in consciousness research. For example, IIT can be used to explain why some brain regions, such as the cerebellum do not appear to contribute to consciousness, despite their size and/or functional importance. IIT can also help to explain why severing the corpus callosum appears to lead to the development of two separate consciousnesses in split-brain patients.

Reception

Integrated Information Theory has received both broad criticism and support.

Support

Neuroscientist Christof Koch, who has helped to develop the theory, has called IIT "the only really promising fundamental theory of consciousness.” Technologist Virgil Griffith says "IIT is currently the leading theory of consciousness."

Criticism

Meanwhile, some critics have challenged that IIT proposes conditions which are necessary for consciousness, but are not entirely sufficient. Objections have also been made to the claim that all of IIT's axioms are self-evident. Since IIT is not a functionalist theory of consciousness, historical criticisms of non-functionalism have been levied against it. Disagreements over the definition of consciousness also lead to inevitable criticism of the theory.