Entropy
February 11, 2023
William Marshall, Matteo Grasso, William G. P. Mayner et al.
19 citations
Integrated information theory (IIT) proposes that consciousness is identical to the cause-effect structure generated by a maximally irreducible substrate (a Φ-structure). This work introduces a definition for system-integrated information (φs) grounded in IIT's postulates of existence, intrinsicality, information, and integration. It examines how determinism, degeneracy, and connectivity fault lines affect system-integrated information. The proposed measure identifies complexes as systems whose φs exceeds that of any overlapping candidate systems.
Entropy (Basel, Switzerland)
April 4, 2026
William G. P. Mayner, William Marshall, Giulio Tononi
Integrated information theory (IIT) begins with the fact of consciousness and identifies its essential features: every experience is intrinsic, specific, unitary, definite, and structured. The theory then translates these features into operational terms based on the cause-effect power of a substrate of units. To have cause-effect power intrinsically and specifically, substrate units in their current state must both (i) ensure the intrinsic availability of a repertoire of cause-effect states and (ii) increase the probability of a specific cause-effect state. A previous study showed that requirement (ii) can be measured by the intrinsic difference of a state's probability from maximal differentiation.
arXiv Preprint Archive
October 4, 2025
William G. P. Mayner, William Marshall, Giulio Tononi
Integrated information theory (IIT) defines consciousness by its essential properties: intrinsic, specific, unitary, definite, and structured existence. The theory operationalizes existence as cause-effect power of a substrate of units. For substrate units to have cause-effect power intrinsically and specifically, they must both ensure the intrinsic availability of a repertoire of cause-effect states and increase the probability of a specific cause-effect state. Previous work addressed the second requirement via intrinsic difference from maximal differentiation; this paper shows the first requirement can be assessed by intrinsic difference from maximal specification. Using simple micro-unit systems, the authors illustrate that for macro systems like neural systems, a tradeoff between differentiation and specification is a necessary condition for intrinsic existence, i.e., consciousness.
arXiv Preprint Archive
December 30, 2024
William G. P. Mayner, Bjørn Erik Juel, Giulio Tononi
Integrated information theory (IIT) holds that consciousness arises from a maximally irreducible complex of units whose cause-effect structure fully accounts for the quality of experience. The feeling of an experience is its intrinsic meaning for the subject, whether occurring in a dream or triggered by the environment. This work extends IIT to characterize the relationship between intrinsic meaning, extrinsic stimuli, and causal processes, using a simple sensory-hierarchy model. Perception is framed as a structured interpretation in which a stimulus merely triggers the complex's state, and the structure comes from the complex's intrinsic connectivity. Perceptual differentiation—the richness of structures triggered by representative stimulus sequences—quantifies how meaningful different environments are to a complex, reflecting the match between intrinsic meanings and environmental causal processes.
The Behavioral and brain sciences
March 23, 2022
Giulio Tononi, Melanie Boly, Matteo Grasso et al.
Integrated information theory (IIT) begins with phenomenology and predicts that only select physical substrates can support consciousness. The theory's account of experience—a cause-effect structure quantified by integrated information—has nothing to do with information transfer. This commentary outlines IIT's axioms and postulates, correcting major misconceptions from a target article that misrepresents the theory's foundations and ignores essential publications.