This page lists the changes and ingredients introduced in IIT 4.0 relative to IIT 3.x.
For a complete mathematical account of IIT 3.x, cf. Kleiner & Tull, The Mathematical Structrue of IIT, 2021. For brevity, we will also use the terminology introduced in this paper.
What is IIT 3.x?
IIT 3.0 refers to IIT as introduced in Oizumi & Albantakis &Tononi, From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3.0, 2014.
IIT 3.x refers to the same version of the theory, but with all changes that have been proposed by the group in published papers before the 4.0 version taken into account. A mathematical introduction to and definition of IIT 3.x is available in the paper mentioned in the introduction.
There are a number of purely terminological changes:
- Distinctions are what has previously been called concepts.
- -Structure refers to what has previously been called Maximally Irreducible Conceptual Structures, but with new things, such as the relations, added in.
- Causal Relations
- Causal relations are a new ingredient introduced in IIT 4.0. They give rise to a relational structure on the space of conscious experiences.
- Most informative
- Whereas in IIT 3.x, the the term "core" was used in characterizing cause-effect structures and the like of particular interest, in IIT 4.0 these are referred to as "most informative". For example the "most informative effect state".
The following is trying to be (become) a complete list of changes and additions in IIT 4.0 relative to IIT 3.x. Please extend in case there are further updates not already listed.
New distance function
IIT 3.x makes use of a distance function on a space probability distributions. The theory uses this space of probability distributions in order to construct a space which it claims is identical to conscious experiences. Both the individual spaces as well as the prodcts are instantiations of what is called an experience space in Kleiner & Tull, which includes the said distance function.
Whereas in IIT 3.x the distance function is an adaptation of the first Wasserstein metric over probability distributions (also, known as Earth Mover's Distace; cf. Kleiner & Tull for details), IIT introduces a new distance measure, called Intrinsic Difference. It is similar to the KL-divergence, but extends to product spaces by use of the 'maximum' of the distances of the component spaces. For details and a conceptual justification of this new measures, cf. Barbosa et al., A measure for intrinsic information, 2020, Theorem 1 in the Supplementary Material (!).
More constrained partitions
In IIT 3.x, every choice of subsystems gave a partition of the system. In IIT 4.0, partitions are more constrained, they have to destroy the mechanism.
Introduction of relations
The most significant change in IIT 4.0 is the introduction of relations.
Relations are introduced on what is called the 'mechanism level' in Kleiner & Tull, once the mechanisms (now called distinctions) are determined, roughly as follows:
- For any two of the core causes and core effects of a mechanism (old terminology), one determines the maximal overlap between them. Here, overlap defers to subsystems: A cause overlaps with another cause or effect if they both comprise the same subsystem.
- For every such maximal overlap, one defines a relational small phi values in a specific way.
- A relation is then a tripe of the core effect/cause, the maximal overlap and the -value. As with mechanisms aka distinctions, they only count if .
The result of this is, for every candidate system, something similar to the concept defined in Eq. (8) in Kleiner & Tull, but now for relations. This relational structure is being added (in the sense of a directional product) to the concept. Extending the distance from concept spaces to relation sapces conceived in this way, the system level algorithm is then applied as before.
Some change in picking a state differently when partitioning
TBA (Johannes didn't understand the comment ;-) )
How to identify conscious systems